{"text_format":"1","workbook":"xlsx","n_sheets":21,"sheets":["Read Me First","Simulated Data Specifications","Simulated Data","Results Summary","Pearson's Correlation","Spearman's Correlation","Quadrant Correlation","Kendall's Tau Correlation","Goodman-Kruskal Gamma","Correlation Median Estimator","Tukey Biweight MidCorrelation","Fisher-Yates Normal Scores","Bivariate Alpha-Trimmed","Univariate Alpha-Winsorized","Median Correlation Coefficient","MAD Correlation (Gideon)","MAD Correlation (Shevylakov)","Absolute Value Correlation","Footrule Correlation","Greatest Deviation Correlation","Percentage Bend Correlation"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Read Me First","index":0,"n_rows":43,"n_cols":6,"rows_kept":43,"cut":false,"hidden":false,"merged":[[0,0,0,5],[2,2,10,4]]}
["Listing and Description of All Available Macros in this Workbook"]
[]
[null,null,"This workbook contain a number of macros for calculating robust correlation coefficients between two variables, X and Y.  This spreadsheet contains a list of the macros available.  Each macro is demonstrated in the associated worksheet listed.  Other worksheets are provided as well.  These include:\nSimulated Data Specifications - the parameters used to create various (X,Y) combinations of random variables.\nSimulated Data - 1,000 observations of various (X,Y) variables, to be used for testing purposes.\nResults Summary - The results of each of the macros listed below, applied to the various simulated (X,Y) variables.\n\nNotes are embedded in each worksheet discussing important aspects of each correlation measure.  In some cases the correlation formulas are too complex to be illustrated in a single worksheet, so only the macro results are provided."]
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[null,null,"Worksheet","Related Macro","Statistical Procedure","Comments"]
[null,null,"Pearson's Correlation","=CORREL(X, Y)","Pearson's Product Moment Correlation Coefficient","This is just the standard function already in Excel, shown for comparison purposes, Pearson (1896)"]
[null,null,"Spearman's Correlation","=Spearman(X, Y)","Spearman's Rank Correlation Coefficient","A member of the rank-based family of correlation coefficients, Spearman (1904)"]
[null,null,"Quadrant Correlation","=QuadCorr(X, Y)","Quadrant Correlation Coefficient, aka Quadrant Count Ratio","A member of the rank-based family of correlation coefficients, Blomqvist (1950)"]
[null,null,"Kendall's Tau Correlation","=KendTau(X, Y, ties)","Kendall's Tau Rank Correlation Coefficient","If 'ties' set to TRUE then the macro calculates Kendall's tau-b, adjusting for ties, Kendall (1949)"]
[null,null,"Goodman-Kruskal Gamma","=GKGamma(X, Y)","Goodman and Kruskal's Gamma Rank Correlation Coefficient","A member of the rank-based family of correlation coefficients, Goodman and Kruskal (1954)"]
[null,null,"Correlation Median Estimator","=CorrMed(X, Y)","Correlation Median Estimator","As discussed by Pasman and Shevylakov (1987)"]
[null,null,"Tukey BiWeight MidCorrelation","=BiWeight(X, Y)","Tukey's BiWeight MidCorrelation Coefficient","A type of M-estimator or Maximum Likelihood-type Estimator, Wilcox (1997)"]
[null,null,"Fisher Yates Normal Scores","=ScoreCorr(X, Y)","Fisher and Yates Normal Scores Correlation Coefficient","As described in Fieller and Pearson (1961)"]
[null,null,"Bivariate Alpha-Trimmed","=BVTCorr(X, Y, alpha)","Bivariate Alpha-Trimmed Correlation Coefficient","As described in Wilcox (1994)"]
[null,null,"Univariate Alpha-Winsorized","=UVWCorr(X, Y, alpha)","Univariate Alpha-Winsorized Pearson Correlation Coefficient","As described in Wilcox (1993)"]
[null,null,"Median Correlation Coefficient","=MedCorr(X, Y)","Median Correlation Coefficient","As discussed by Shevylakov (2011)"]
[null,null,"MAD Correlation (Gideon)","=MADCorr_G(X, Y)","MAD Correlation Coefficient (Gideon)","As desribed by Gideon (2007)"]
[null,null,"MAD Correlation (Shevylakov))","=MADCorr_S(X, Y)","MAD Correlation Coefficient (Shevylakov)","As discussed by Pasman and Shevylakov (1987)"]
[null,null,"Absolute Value Correlation","=AVCorr(X, Y)","Absolute Value Correlation Coefficient","As desribed by Gideon (2007)"]
[null,null,"Footrule Correlation","=FootCorr(X, Y)","Spearman's Footrule Rank Correlation Coefficient","A member of the rank-based family of correlation coefficients, Spearman (1906)"]
[null,null,"Percentage Bend Correlation","=PBCorr(X,Y, bend)","Percentage Bend Correlation","Requires a \"Bend\" value between (0,1), Wilcox recommend bend = 0.2, Wilcox (1994)"]
[]
[null,null,null,null,"Citation","Published Article"]
[null,null,null,null,"Wilcox (1994)","Wilcox, R.R., (1994).  The Percentage Bend Correlation Coefficient. Psychometrika, 59, 601-616"]
[null,null,null,null,"Wilcox (1993)","Wilcox, R.R., (1993). Some Results on a Winsorized Correlation Coefficient, British Journal of\nMathematical and Statistical Psychology, 4, 167-183."]
[null,null,null,null,"Shevylakov and Smirnov (2011)","Shevylakov, G. and P. Smirnov, (2011). Robust Estimation of the Correlation Coefficient: An\nAttempt of Survey. Austrian Journal of Statistics, 40, 147-156."]
[null,null,null,null,"Blomqvist (1950)","Blomqvist, N. (1950). On a Measure of Dependence Between Two Random Variables. The \nAnnals of Mathematical Statistics, 21, 593-600."]
[null,null,null,null,"Spearman (1904)","Spearman, C. (1904). The Proof and Measurement of Association Between Two Things. \nAmerican Journal of Psychology, 15, 88-93."]
[null,null,null,null,"Pasman and Shevylakov (1987)","Pasman, V.R., and Shevylakov, G.L. (1987). Robust Methods of Estimation of a Correlation\nCoefficient. Automation and Remote Control,??, 332-340."]
[null,null,null,null,"Kendall (1949)","Kendall, M.G. (1949). Rank and Product-Moment Correlation, Biometrika, 51, 42-46."]
[null,null,null,null,"Gideon (2007)","Gideon, R.A. (2007). The Correlation Coefficients. Journal of Modern Applied Statistical\nMethods, 6, 517-529."]
[null,null,null,null,"Spearman (1906)","Spearman, C. (1906). 'Footrule' for Measuring Correlations, British Journal of Psychology, 2,\n89-108."]
[null,null,null,null,"Fieller and Pearson (1961)","Fieller, E.C., and Pearson, E.S., (1961). Tests for Rank Correlation Coefficients.I., Biometrika,\n48, 29-40"]
[null,null,null,null,"Wilcox (1997)","Wilcox, R.R., (1997). Introduction to Robust Estimation and Hypothesis Testing."]
[null,null,null,null,"Goodman and Kruskal (1954)","Goodman, L.A. and Kruskal, W.H. (1954). Measures of Association for Cross Classification. \nJournal of the American Statistical Association, 49 (268), 732-764."]

{"sheet":"Simulated Data Specifications","index":1,"n_rows":29,"n_cols":9,"rows_kept":29,"cut":false,"hidden":false,"merged":[[0,0,0,8],[13,4,13,6],[11,4,11,6],[20,4,20,6],[22,4,22,6],[17,1,17,6],[5,1,5,6],[6,1,6,6],[8,1,8,6],[12,4,12,5],[4,1,4,6],[19,4,19,5],[21,4,21,5],[23,4,23,5],[14,4,14,5],[10,4,10,5],[24,4,24,6],[26,4,26,6],[15,4,15,6],[25,4,25,5]]}
["Parameters and Processes for Creating the Simulated Data Set"]
[]
[]
[null,null,null,null,null,null,null,null,"Notes:"]
[null,"Table 1: Formulas to calculate correlated bivariate normal RVs:",null,null,null,null,null,null,"1.  Simulated data set contains 1,000 observations"]
[null,"X = μ1 + σ1∙N1(0,1)",null,null,null,null,null,null,"of various data necessary to perform the required"]
[null,"Y = μ2 + σ2[N1(0,1)∙ρ + N2(0,1)∙ρ∙sqrt(1-ρ2)]",null,null,null,null,null,null,"simulations."]
[null,null,null,null,null,null,null,null,"2.  1,000 replications of two independent uniform"]
[null,"Table 2: Population Parameters",null,null,null,null,null,null,"random variables were simulated in the range of"]
[null,null,"Mean (μ)","Std. Dev. (σ)",null,null,null,null,"(0,1) using Excel's Rand() function."]
[null,"U1(0,1)",0.5,{"$f":"SQRT(1/12)","v":0.28867513459481287},"Correlation = ",null,0,null,"3.  1,000 replications of two independent standard"]
[null,"U2(0,1)",0.5,{"$f":"SQRT(1/12)","v":0.28867513459481287},null,null,null,null,"normal random variables with mean zero and SD"]
[null,"N1(0,1)",0,1,"Correlation = ",null,0,null,"of one were simulated using the Box-Muller method."]
[null,"N2(0,1)",0,1,null,null,null,null,"4.  The two independent standard normal random"]
[null,"X(μ,σ;ρ)",70,3,"Correlation (ρ) = ",null,0.5,null,"variables (X, Y) were converted into two correlated"]
[null,"Y(μ,σ;ρ)",162,14,null,null,null,null,"random normal variables with mean mu and SD sigma"]
[null,null,null,null,null,null,null,null,"using the formulas in Table 1 and the mu/sigma"]
[null,"Table 3: Sample Parameters, N=1000",null,null,null,null,null,null,"parameters for X and Y listed in Table 2."]
[null,null,"Mean","Std. Dev.",null,null,null,null,"5.  The univariate ranks of the correlated random"]
[null,"U1(0,1)",{"$f":"AVERAGE('Simulated Data'!B4:B1003)","v":0.49845421575901017},{"$f":"_xlfn.STDEV.S('Simulated Data'!B$4:B$1003)","v":0.28763082490901337},"Correlation = ",null,{"$f":"CORREL('Simulated Data'!B$4:B$1003,'Simulated Data'!C$4:C$1003)","v":1.5643196360423481E-2},null,"variables (X, Y), each variable value ranked from 1 to"]
[null,"U2(0,1)",{"$f":"AVERAGE('Simulated Data'!C4:C1003)","v":0.49948508847062117},{"$f":"_xlfn.STDEV.S('Simulated Data'!C$4:C$1003)","v":0.28644416977758191},null,null,null,null,"1,000, are provided."]
[null,"N1(0,1)",{"$f":"AVERAGE('Simulated Data'!D4:D1003)","v":-2.9909874804862342E-3},{"$f":"_xlfn.STDEV.S('Simulated Data'!D$4:D$1003)","v":0.98599801794616704},"Correlation = ",null,{"$f":"CORREL('Simulated Data'!D$4:D$1003,'Simulated Data'!E$4:E$1003)","v":-2.3628572258251025E-2},null,"6.  Using the correlated random normal variables (X,Y),"]
[null,"N2(0,1)",{"$f":"AVERAGE('Simulated Data'!E4:E1003)","v":4.2673642244203409E-3},{"$f":"_xlfn.STDEV.S('Simulated Data'!E$4:E$1003)","v":1.0068969217406771},null,null,null,null,"2% of the X values and 1% of the Y values were changed"]
[null,"X",{"$f":"AVERAGE('Simulated Data'!F4:F1003)","v":69.991027037558439},{"$f":"_xlfn.STDEV.S('Simulated Data'!F$4:F$1003)","v":2.9579940538385019},"Correlation = ",null,{"$f":"CORREL('Simulated Data'!F$4:F$1003,'Simulated Data'!G$4:G$1003)","v":0.47643471739126048},null,"to be duplicates of their nearest neighbor.  The values"]
[null,"Y",{"$f":"AVERAGE('Simulated Data'!G4:G1003)","v":162.03080212919414},{"$f":"_xlfn.STDEV.S('Simulated Data'!G$4:G$1003)","v":13.881291249500094},null,null,null,null,"chosen to be duplicated were those that were already"]
[null,"X2%",{"$f":"AVERAGE('Simulated Data'!J4:J1003)","v":69.991027037558425},{"$f":"_xlfn.STDEV.S('Simulated Data'!J$4:J$1003)","v":2.9579940538126905},"Correlation = ",null,{"$f":"CORREL('Simulated Data'!J$4:J$1003,'Simulated Data'!K$4:K$1003)","v":0.47643475570080618},null,"the closest in value to each other."]
[null,"Y1%",{"$f":"AVERAGE('Simulated Data'!K4:K1003)","v":162.03080212919417},{"$f":"_xlfn.STDEV.S('Simulated Data'!K$4:K$1003)","v":13.881291249494151},null,null,null,null,"7.  The univariate ranks of the correlated normal random"]
[null,null,null,null,null,null,null,null,"variables with duplicates, each variable value ranked from"]
[null,null,null,null,null,null,null,null,"1 to 1,000, are provided."]

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["Sample Data Set to Be Used to Test Robust Correlation Statistics"]
[null,"Uniform Distributed\nRandom Variables",null,"Standard Normal \nRandom Variables",null,"Bivariate (Correlated) \nNormal RVs",null,"Bivariate (Correlated) \nNormal RVs as Ranks",null,"Bivariate Normal RVs\nwith Induced Duplicates",null,"Bivariate Normal RVs\nwith Duplicates as Ranks"]
["Observation\nNumber","U1(0,1)","U2(0,1)","N1(0,1)","N2(0,1)","X","Y","Xrnk","Yrnk","X2%","Y1%","Xrnk(2%)","Yrnk(1%)"]
[1,0.32270988016411695,0.2644734665256534,-0.13658413703160191,1.4977809919799208,69.5902475889052,179.20354047781973,{"$f":"_xlfn.RANK.AVG(F4,F$4:F$1003,1)","v":452},{"$f":"_xlfn.RANK.AVG(G4,G$4:G$1003,1)","v":892},69.5902475889052,179.20354047781973,{"$f":"_xlfn.RANK.AVG(J4,J$4:J$1003,1)","v":452},892]
[2,1.1816917480420575E-2,0.86475350901650239,1.966807043912528,-2.2378820860277409,75.900421131737588,148.6347709869498,{"$f":"_xlfn.RANK.AVG(F5,F$4:F$1003,1)","v":977},{"$f":"_xlfn.RANK.AVG(G5,G$4:G$1003,1)","v":171},75.900421131737588,148.6347709869498,{"$f":"_xlfn.RANK.AVG(J5,J$4:J$1003,1)","v":977},{"$f":"_xlfn.RANK.AVG(K5,K$4:K$1003,1)","v":171}]
[3,0.61743393104109234,0.67745679636513689,-0.43226914381289244,-0.88176516615635425,68.70319256856132,148.28328151641921,350,162,68.70319256856132,148.28328151641921,350,162]
[4,0.98619831561761984,0.85506570258281733,0.1022383630296151,-0.13169260957397416,70.30671508908884,161.11898050586314,544,482,70.30671508908884,161.11898050586314,544,482]
[5,0.42815322190202165,0.36723006050269569,-0.87497443182832291,0.9648668552608346,67.375076704515038,167.57356788815855,190,656,67.375076704515038,167.57356788815855,190,656]
[6,0.94093721588871093,0.20315246801463116,0.10123372292266651,0.33393031884705643,70.303701168768001,166.7573260094741,543,634,70.303701168768001,166.7573260094741,543,634]
[7,0.61492113968623308,0.87157223867587097,0.68214533246490283,-0.71217992143585696,72.04643599739471,158.14029467085311,757,392,72.04643599739471,158.14029467085311,757,392]
[8,0.7192929890260239,0.7276437271972922,-0.11365379353240689,-0.8037759845929987,69.659038619402779,151.45915754274174,458,226,69.659038619402779,151.45915754274174,458,226]
[9,0.18491513610402655,0.10797177603047126,1.4304828717196487,1.1530114134475136,74.291448615158941,185.99290055062283,923,956,74.291448615158941,185.99290055062283,923,956]
[10,0.32863391122997154,0.53771023072134416,-1.4501705086415055,-0.35018174572489957,65.649488474075483,147.60307841115861,69,153,65.649488474075483,147.60307841115861,69,153]
[11,0.85367909921578922,0.72563745069862173,-8.5767618027032436E-2,-0.55591703643835166,69.742697145918896,154.65949081048038,464,300,69.742697145918896,154.65949081048038,464,300]
[12,0.85375962871649747,0.74278139979051638,-2.5496029735055031E-2,-0.56174828215023676,69.923511910794829,155.01069183161337,488,311,69.923511910794829,155.01069183161337,488,311]
[13,0.8872148614997708,8.3026632566090885E-2,0.42414751717928589,0.24379308401770167,71.272442551537864,167.92486667662297,656,661,71.272442551537864,167.92486667662297,656,661]
[14,0.46933529933300777,0.33064839718032502,-0.5969384822589211,1.0754255587631154,68.209184553223238,170.8602725769386,281,735,68.209184553223238,170.8602725769386,281,735]
[15,0.54703949438906785,0.14724755263387868,0.6608901623648038,0.87732134819930663,71.98267048709441,177.2631871840758,748,860,71.98267048709441,177.2631871840758,748,860]
[16,6.1203737489867294E-2,0.37551898499659409,-1.6768320515741522,1.6659316652489076,64.969503845277544,170.46052364202347,47,727,64.969503845277544,170.46052364202347,47,727]
[17,0.71037509223427275,0.46957522982334354,-0.81193228736861212,0.1571313456328626,67.564203137894168,158.22159030710421,204,396,67.564203137894168,158.22159030710421,204,396]
[18,0.73523902120969864,1.0141790196536826E-2,0.78270358382828975,4.9943641065212561E-2,72.348110751484867,168.08445955367756,788,668,72.348110751484867,168.08445955367756,788,668]
[19,0.20829690102910237,0.13950382428419783,1.1333325762307647,1.3613004400892912,73.399997728692298,186.43821871981902,874,957,73.399997728692298,186.43821871981902,874,957]
[20,0.31019684266809955,0.77194381086502439,0.21029294423252298,-1.5155438927787133,70.630878832697576,145.0970574458735,580,111,70.630878832697576,145.0970574458735,580,111]
[21,0.13685135528445369,0.7531836096713288,3.9892184503983498E-2,-1.994023192905144,70.119676553511951,138.10299892045091,512,36,70.119676553511951,138.10299892045091,512,36]
[22,0.33675801771763059,0.58478506913315587,-1.2709449076064128,-0.74931992603992625,66.187165277180767,144.01836436558077,105,99,66.187165277180767,144.01836436558077,105,99]
[23,7.0479667911750088E-2,0.15783417822719092,1.2604802300057549,1.927706307535433,73.781440690017263,194.19555847709682,901,991,73.781440690017263,194.19555847709682,901,991]
[24,0.58790892258870064,0.44434843924700551,-0.96833929173176692,0.35310832525330693,67.094982124804702,159.50283587727762,173,439,67.094982124804702,159.50283587727762,173,439]
[25,0.97828158175855029,0.73434998952876385,-2.0573262146847893E-2,-0.20854785983524929,69.938280213559452,159.32747874166122,490,432,69.938280213559452,159.32747874166122,490,432]
[26,0.69967798319382246,0.3042645003518063,-0.28260487785152522,0.79649521693268899,69.152185366445423,169.67875714103042,396,709,69.152185366445423,169.67875714103042,396,709]
[27,0.83365736693968107,0.25184327106595294,-6.9860204956135735E-3,0.6031722636261776,69.979041938513163,169.26417290074878,494,695,69.979041938513163,169.26417290074878,494,695]
[28,0.28226054490319274,0.50568057588752457,-1.5895370264213549,-5.6758035818501577E-2,65.231388920735938,150.1850862026223,55,196,65.231388920735938,150.1850862026223,55,196]
[29,0.95083634972696851,0.41181799993340229,-0.27002718177688112,0.16706869306635505,69.189918454669353,162.13540998077724,399,522,69.189918454669353,162.13528693309559,399,521.5]
[30,0.39892607970900351,0.2216023187155709,0.24061556640385373,1.3341898048966145,70.721846699211568,179.8605006679764,592,902,70.721846699211568,179.8605006679764,592,902]
[31,0.58219033962876032,0.97648814302902576,1.0288222695588836,-0.15310264212041658,73.086466808676647,167.34548500243301,857,650,73.086466808676647,167.34548500243301,857,650]
[32,0.54387297197005313,0.11954754982330218,0.80668258794279146,0.75322130606647697,72.420047763828379,176.77910111575324,799,854,72.420047763828379,176.77910111575324,799,854]
[33,8.6519387811243798E-2,0.59160594058933558,-1.8559457127386854,-1.2042587008582686,64.432162861783951,134.40751922342531,30,19,64.432162861783951,134.40751922342531,30,19]
[34,0.91226524027720612,0.78428423176716289,9.1601920186099209E-2,-0.41863836819749833,70.274805760558294,157.56549297529213,532,376,70.274805760558294,157.56549297529213,532,376]
[35,0.26640558058416741,0.68773316611851809,-0.6202287671744684,-1.5035913876989089,68.139313698476599,139.42832188855618,270,50,68.139313698476599,139.42832188855618,270,50]
[36,0.31306159193527938,3.3626965691329391E-2,1.490153017542994,0.31961639697710764,74.470459052628982,176.30621399227613,937,845,74.470459052628982,176.30621399227613,937,845]
[37,0.3319615330010659,0.59991380213037571,-1.201930204773235,-0.8722592191085845,66.394209385680298,143.0109075725224,113,89,66.394209385680298,143.0109075725224,113,89]
[38,0.8582642766768771,6.5826757700956584E-2,0.50626910425184113,0.22221165219713937,71.518807312755527,168.23805683123777,686,672,71.518807312755527,168.23805683123777,686,672]
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[972,0.8073544948613135,0.50491314444790869,-0.65389382753966441,-2.0192245880662197E-2,68.038318517381001,157.17792523673273,258,365,68.038318517381001,157.17792523673273,258,365]
[973,0.61335322054389718,0.68152578977151479,-0.41239365998564298,-0.89864345251593369,68.762819020043068,148.21777155657355,356,161,68.762819020043068,148.21777155657355,356,161]
[974,0.26798069330266272,0.41618406795000884,-1.4029726902987349,0.81568885749369202,65.791081929103797,162.06889297833703,77,518,65.791081929103797,162.06889297833703,77,518]
[975,4.721870187595556E-2,0.34849700845976861,-1.4334849087006201,2.0127224085530435,65.699545273898138,176.36856795111959,72,846,65.699545273898138,176.36856795111959,72,846]
[976,0.2319921923330216,0.69345928501841447,-0.59458650542151703,-1.6026758907554681,68.216240483735447,138.40648196607015,282,39,68.216294287138524,138.40648196607015,282.5,39]
[977,0.31026227561242525,0.99468600582488431,1.5290736194161885,-5.1072929069912176E-2,74.587220858248571,172.08428897963017,943,766,74.587220858248571,172.08428897963017,943,766]
[978,0.4994073376743654,0.6766934894271236,-0.5237877174020652,-1.0556101759773491,68.428636847793811,145.5348927737291,310,118,68.428636847793811,145.5348927737291,310,118]
[979,0.74366341223936416,0.46209427749187637,-0.74790661556490101,0.18157420860530657,67.756280153305298,158.96612397358521,221,424,67.756346562823268,158.96612397358521,221.5,424]
[980,0.91285009083223667,0.78496350863472131,9.306136623764874E-2,-0.41678147025894174,70.279184098712946,157.59822278867134,535,377,70.279184098712946,157.59822278867134,535,377]
[981,0.48565634062982754,0.41947447107667946,-1.0512951207722347,0.58248314614827501,66.8461146376833,161.70316698036402,154,504,66.8461146376833,161.70316698036402,154,504]
[982,0.9825656668444267,0.65000018976522822,-0.11024082272899746,-0.15173385575618109,69.669277531813009,159.38863900911079,459,437,69.669277531813009,159.38863900911079,459,437]
[983,0.86225522258134202,0.36960124299903774,-0.37169491773744179,0.39780752714146828,68.884915246787671,164.22129551633441,365,580,68.884915246787671,164.22129551633441,365,580]
[984,0.55666917209961575,0.5084753775617733,-1.0808557311868068,-5.7612596749984396E-2,66.757432806439581,153.7354942686037,145,279,66.757432806439581,153.7354942686037,145,279]
[985,0.15042552829956291,0.16571635911216587,0.98326057910321529,1.6798133602435752,72.94978173730965,189.24947866394663,846,972,72.94978173730965,189.24947866394663,846,972]
[986,0.88831561607765697,4.0316847904623643E-2,0.47114710053747566,0.12197032798701954,71.413441301612423,166.77684133938783,674,635,71.413441301612423,166.77684133938783,674,635]
[987,0.46135490491507436,0.48986218588473351,-1.2413324755787949,7.9177217601325567E-2,66.276002573263611,154.27064541676046,108,291,66.276002573263611,154.27064541676046,108,291]
[988,0.19374180949281183,9.6086762736851905E-2,1.4914791656190198,1.0285658311356813,74.474437496857064,184.91105210852731,938,944,74.474437496857064,184.91105210852731,938,944]
[989,0.39955756507785112,0.10382231152528032,1.0764152093140009,0.82226830161971665,73.229245627942007,179.50437979620904,868,895,73.229245627942007,179.50437979620904,868,895]
[990,0.25247714701301316,0.3278462558195816,-0.77956677209663583,1.4646312608730494,67.661299683710098,174.30074290262405,211,803,67.661241423786549,174.30074290262405,210.5,803]
[991,0.29276020679387094,0.6799000672777844,-0.66826499700447395,-1.4178239374329578,67.995205008986574,140.13194335022001,246,58,67.995205008986574,140.13194335022001,246,58]
[992,0.52310588570587935,0.17166099343726759,0.53798510263238608,1.0032521036641839,71.613955307897157,177.92968103285378,695,878,71.613955307897157,177.92968103285378,695,878]
[993,0.38310731623552552,0.59857449406227137,-1.1279276027045082,-0.8041514677349958,66.616217191886477,144.35468838738177,126,104,66.616299467728325,144.35468838738177,126.5,104]
[994,0.83472860348255551,0.87575819640971608,0.42704775680842655,-0.42299820197122651,71.281143270425275,159.86075365638786,658,450,71.281143270425275,159.86075365638786,658,450]
[995,0.15132340060678673,0.33456139821191222,-0.98464035263029537,1.6754567702605241,67.046078942109119,175.42135129542331,169,832,67.046078942109119,175.42135129542331,169,832]
[996,0.63684033897484937,0.94766723957996368,0.89909029910978455,-0.30677228395504513,72.697270897329361,164.5742158186199,819,589,72.697270897329361,164.5742158186199,819,589]
[997,0.23209762112154042,0.14808328596708986,1.0211923639505105,1.3705329569386411,73.063577091851528,185.76517555171091,855,953,73.063577091851528,185.76517555171091,855,953]
[998,0.88950286606515339,0.18267490208043169,0.19865799494775807,0.44127100583430184,70.595973984843269,168.74073257871854,572,678,70.595973984843269,168.74073257871854,572,678]
[999,0.41336222226129493,0.12253149402444075,0.95437455780687019,0.92521956381321446,72.863123673420617,179.89831295341651,838,903,72.863123673420617,179.89831295341651,838,903]
[1000,0.70617570114597061,0.88846106946263215,0.6375414627403857,-0.53788780543200743,71.912624388221161,159.94124718472298,737,455,71.912624388221161,159.94124718472298,737,455]

{"sheet":"Results Summary","index":3,"n_rows":26,"n_cols":8,"rows_kept":26,"cut":false,"hidden":false,"merged":[[3,2,3,7],[21,2,21,7],[0,0,0,7]]}
["Summary of Macro Results Compared with Output from the R Statistical Package"]
[]
[null,null,"U1(0,1) & U2(0,1)","N1(0,1) & N2(0,1)","X & Y","Xrnk & Yrnk","X2% & Y1%","Xrnk2% & Yrnk1%"]
[null,"MACRO PROCEDURE","Estimates From the Macros Included in this Workbook"]
[null,"Pearson's Correlation",1.5643196360423481E-2,-2.3628572258251025E-2,0.47643471739126048,0.4505496185496185,0.47643475570080618,0.45057077223241615]
[null,"Spearman's Correlation",1.6415092415092411E-2,-2.0841152841152837E-2,0.4505496185496185,0.4505496185496185,0.45057077223241615,0.45057077223241615]
[null,"Quadrant Correlation",0.02,4.0000000000000001E-3,0.3,0.3,0.3,0.3]
[null,"Kendall's Tau-a Correlation",1.1147147147147147E-2,-1.3449449449449449E-2,0.31218818818818816,0.31218818818818816,0.31221021021021023,0.31221021021021023]
[null,"Kendall's Tau-b Correlation",1.1147147147147147E-2,-1.3449449449449449E-2,0.31218818818818816,0.31218818818818816,0.31222052382752374,0.31222052382752374]
[null,"Goodman-Kruskal Gamma",1.1147147147147147E-2,-1.3449449449449449E-2,0.31218818818818816,0.31218818818818816,0.31223083807338625,0.31223083807338625]
[null,"Correlation Median Estimator",6.8845516718048843E-3,1.0343649560643205E-3,0.3187895869539728,0.321384,0.31879445960970171,0.321384]
[null,"Tukey BiWeight MidCorrelation",1.6816169914409644E-2,-2.2246640793311411E-2,0.46516966507777291,0.44570797338192464,0.46516934448550157,0.44573030610508607]
[null,"Fisher Yates Normal Scores",-2.7597950241146575E-3,-2.4171785781532781E-2,0.47519659087412541,0.47519659087412541,0.47520301955569211,0.47520301955569211]
[null,"Bivariate Alpha-Trimmed",2.1623181954868648E-2,-2.651371221549401E-2,0.46778412027752542,0.4562855114108606,0.46778412547229831,0.45630922086995351]
[null,"Univariate Alpha-Winsorized",1.8500969835349931E-2,-2.2571911874744971E-2,0.46265286898467034,0.44503848127878531,0.46265293303142091,0.44506055844077563]
[null,"Median Correlation Coefficient",4.5616848833694545E-2,-3.3998232284133748E-2,0.46942908792741195,0.5991544461343119,0.46941081119530359,0.5991544461343119]
[null,"MAD Correlation (Gideon)",2.6829437615448759E-2,-2.2737159365861515E-2,0.33472125067401182,0.37800000000000006,0.33471365899970984,0.37800000000000006]
[null,"MAD Correlation (Shevylakov))",2.7595657030367902E-2,-1.7387554705960019E-2,0.46439911913394605,0.6058814558058927,0.46441531550567605,0.6058814558058927]
[null,"Absolute Value Correlation",1.183643995440542E-2,-1.5027443580606259E-2,0.34282995929938309,0.35205199999999925,0.34283004089848046,0.35207799999999939]
[null,"Footrule Correlation",8.6730086730086864E-3,2.4900024900020856E-4,0.28939528939528936,0.28939528939528936,0.28940728940728944,0.28940728940728944]
[null,"Percentage Bend Correlation",2.0457527057698821E-2,-2.2672054873132855E-2,0.44705743496276296,0.43517722005211373,0.44705752297092943,0.43520193850799666]
[null,"MACRO PROCEDURE","Estimates From the R Statistical Package"]
[null,"Pearson's Correlation",1.5643196360423502E-2,-2.3628572258251001E-2,0.47643471739125898,0.450549618549618,0.47643475570080501,0.45057077223241598]
[null,"Spearman's Correlation",1.6415092415092401E-2,-2.0841152841152798E-2,0.450549618549618,0.450549618549618,0.45057077223241598,0.45057077223241598]
[null,"Kendall's Tau-b Correlation",1.11471471471471E-2,-1.34494494494494E-2,0.312188188188188,0.312188188188188,0.31222052382752302,0.31222052382752302]
[null,"Percentage Bend Correlation",2.04575270576988E-2,-2.2672054873132799E-2,0.44705743496276301,0.43517722005211301,0.44705752297092899,0.43520193850799699]

{"sheet":"Pearson's Correlation","index":4,"n_rows":1003,"n_cols":17,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[17,15,26,16],[16,15,16,16],[2,15,3,16],[2,10,2,12],[0,0,0,16],[9,10,10,12],[13,10,13,11],[14,10,14,11],[15,10,15,11],[3,10,3,11],[4,10,4,11],[11,10,11,11],[12,10,12,11]]}
["Calculating the Pearson Product Moment Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","X-Xmean","Y-Ymean","(X-Xmean)2","(Y-Ymean)2","(X-Xmean)∙(Y-Ymean)",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Pearson Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,-0.400779448653239,17.172738348625586,0.16062416646279423,294.9029423903558,-6.8824806072284961,null,null,"Calculated Pearson =",null,{"$f":"M16/(SQRT(M14)*SQRT(M15))","v":0.47643471739126042}]
[2,75.900421131737588,148.6347709869498,5.9093940941791487,-13.39603114224434,34.920938560319399,179.45365036398019,-79.162427317418661,null,null,"Excel Pearson = ",null,{"$f":"CORREL(B4:B1003,C4:C1003)","v":0.47643471739126048},null,null,"U1(0,1), U2(0,1)",{"$f":"CORREL('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":1.5643196360423481E-2}]
[3,68.70319256856132,148.28328151641921,-1.2878344689971186,-13.747520612774935,1.6585176195370905,188.99432299867172,17.704530908379951,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"CORREL('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-2.3628572258251025E-2}]
[4,70.30671508908884,161.11898050586314,0.31568805153040103,-0.91182162333100791,9.9658945879061128E-2,0.8314186727739945,-0.28785119161265316,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"CORREL('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.47643471739126048}]
[5,67.375076704515038,167.57356788815855,-2.6159503330434006,5.542765758964407,6.8431961449498786,30.722252258748281,-14.499599933144498,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"CORREL('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.4505496185496185}]
[6,70.303701168768001,166.7573260094741,0.31267413120956178,4.7265238802799558,9.7765112327654252E-2,22.34002799085669,1.477861747907782,null,null,null,null,null,null,null,"(X, Y) with duplicates",{"$f":"CORREL('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.47643475570080618}]
[7,72.04643599739471,158.14029467085311,2.0554089598362708,-3.890507458341034,4.2247059921752204,15.136048283407211,-7.9965838881839986,null,null,"Intermediate Calculations for\nthe Pearson Correlation",null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"CORREL('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.45057077223241615}]
[8,69.659038619402779,151.45915754274174,-0.33198841815566027,-10.571644586452408,0.11021630978949754,111.75966926226849,3.5096635635601841]
[9,74.291448615158941,185.99290055062283,4.3004215776005026,23.962098421428692,18.493625745091997,574.18216075823545,103.0471250960989,null,null,"Mean X = ",null,69.991027037558439]
[10,65.649488474075483,147.60307841115861,-4.3415385634829562,-14.427723718035537,18.848957098209652,208.1592116839652,62.638518905128983,null,null,"Mean Y = ",null,162.03080212919414]
[11,69.742697145918896,154.65949081048038,-0.24832989163954267,-7.3713113187137651,6.1667735081707004E-2,54.33623055739767,1.8305169410175237,null,null,"Sum of (X - Xmean)2 = ",null,8740.9790937213911]
[12,69.923511910794829,155.01069183161337,-6.7515126763609601E-2,-7.0201102975807714,4.5582923419062735E-3,49.28194859019959,0.47396363663568691,null,null,"Sum of (Y - Ymean)2 = ",null,192497.55650669444]
[13,71.272442551537864,167.92486667662297,1.2814155139794252,5.894064547428826,1.6420257194671546,34.73999688925737,7.5527457514714174,null,null,"Sum of Cross-Product = ",null,19543.216894571658]
[14,68.209184553223238,170.8602725769386,-1.7818424843352005,8.8294704477444554,3.1749626389818393,77.959548387592676,-15.732725557973216,null,null,null,null,null,null,null,"Notes:"]
[15,71.98267048709441,177.2631871840758,1.9916434495359709,15.232385054881661,3.9666436300795418,232.02555446018218,30.337479915364682,null,null,null,null,null,null,null,"1.  The CORREL function is provided by Excel. It can also be called by using the PEARSON function. This spreadsheet simply shows the manual calculations used by the formula.\n2.  The Pearson Correlation is the most commonly used measure of association in statistical research.\n3.  The Pearson Correlation can serve as a useful benchmark for the other correlation formulas provided in this workbook."]
[16,64.969503845277544,170.46052364202347,-5.0215231922808954,8.4297215128293317,25.215695170614914,71.060204783857642,-42.330042081141684]
[17,67.564203137894168,158.22159030710421,-2.4268238996642708,-3.8092118220899351,5.8894742399816984,14.510094705549724,9.2442862887315389]
[18,72.348110751484867,168.08445955367756,2.3570837139264285,6.0536574244834185,5.5558436344572053,36.646768213003213,14.268977324939673]
[19,73.399997728692298,186.43821871981902,3.4089706911338595,24.407416590624877,11.621081173009664,595.72198462831045,83.204167803734521]
[20,70.630878832697576,145.0970574458735,0.63985179513913693,-16.93374468332064,0.40941031974277603,286.75170899989001,-10.835086934050528]
[21,70.119676553511951,138.10299892045091,0.12864951595351215,-23.927803208743228,1.6550697955072979E-2,572.53976639634277,-3.078300300635711]
[22,66.187165277180767,144.01836436558077,-3.8038617603776714,-18.012437763613377,14.469364292063517,324.44791418804527,68.516823220191625]
[23,73.781440690017263,194.19555847709682,3.7904136524588239,32.164756347902681,14.367235656746242,1034.5715509199458,121.91773158910195]
[24,67.094982124804702,159.50283587727762,-2.8960449127537373,-2.5279662519165242,8.3870761366868027,6.3906133708288797,7.3211038034759826]
[25,69.938280213559452,159.32747874166122,-5.2746823998987225E-2,-2.7033233875329188,2.7822274419801347E-3,7.3079573375824554,0.14259172293454481]
[26,69.152185366445423,169.67875714103042,-0.83884167111301622,7.6479550118362738,0.70365534919567763,58.491215863071581,-6.4154233627259076]
[27,69.979041938513163,169.26417290074878,-1.1985099045276115E-2,7.2333707715546325,1.4364259912507844E-4,52.321652718780861,-8.6692665128287577E-2]
[28,65.231388920735938,150.1850862026223,-4.7596381168225008,-11.845715926571842,22.654155003109643,140.32098581303779,56.381321045162707]
[29,69.189918454669353,162.13540998077724,-0.8011085828890856,0.10460785158309704,0.64177496157855896,1.0942802612831259E-2,-8.3802247740806662E-2]
[30,70.721846699211568,179.8605006679764,0.73081966165312906,17.829698538782253,0.53409737785879408,317.89814998385401,13.030294253490135]
[31,73.086466808676647,167.34548500243301,3.0954397711182082,5.3146828732388656,9.5817473766203456,28.245854043098525,16.451280736704376]
[32,72.420047763828379,176.77910111575324,2.4290207262699397,14.748298986559092,5.9001416886489455,217.51232299693996,35.823923915577986]
[33,64.432162861783951,134.40751922342531,-5.5588641757744881,-27.623282905768832,30.900970924708979,763.04575849214052,153.55407776216217]
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[997,73.063577091851528,185.76517555171091,3.0725500542930888,23.734373422516768,9.4405638361364623,563.32048175947034,72.925050347966334]
[998,70.595973984843269,168.74073257871854,0.60494694728483012,6.7099304495243928,0.365960809029235,45.023166637454622,4.0591519419333091]
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[1000,71.912624388221161,159.94124718472298,1.9215973506627222,-2.0895549444711605,3.692536378073993,4.366239865963875,-4.0152832453599734]

{"sheet":"Spearman's Correlation","index":5,"n_rows":1005,"n_cols":15,"rows_kept":1005,"cut":false,"hidden":false,"merged":[[2,12,3,13],[14,12,29,13],[13,12,13,13],[0,0,0,13],[2,7,2,9],[3,7,3,8],[4,7,4,8]]}
["Calculating the Spearman Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","Xrnk","Yrnk",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Spearman Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,452,892,null,null,"Calculated Spearman =",null,{"$f":"CORREL(D4:D1003,E4:E1003)","v":0.4505496185496185}]
[2,75.900421131737588,148.6347709869498,977,171,null,null,"VBA Spearman = ",null,{"$f":"spearman(B4:B1003,C4:C1003)","v":0.4505496185496185},null,null,"U1(0,1), U2(0,1)",{"$f":"spearman('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":1.6415092415092411E-2}]
[3,68.70319256856132,148.28328151641921,350,162,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"spearman('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-2.0841152841152837E-2}]
[4,70.30671508908884,161.11898050586314,544,482,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"spearman('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.4505496185496185}]
[5,67.375076704515038,167.57356788815855,190,656,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"spearman('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.4505496185496185}]
[6,70.303701168768001,166.7573260094741,543,634,null,null,null,null,null,null,null,"(X, Y) with duplicates",{"$f":"spearman('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.45057077223241615}]
[7,72.04643599739471,158.14029467085311,757,392,null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"spearman('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.45057077223241615}]
[8,69.659038619402779,151.45915754274174,458,226]
[9,74.291448615158941,185.99290055062283,923,956]
[10,65.649488474075483,147.60307841115861,69,153]
[11,69.742697145918896,154.65949081048038,464,300,null,null,null,null,null,null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,488,311,null,null,null,null,null,null,null,"1.  The Spearman correlation is simply the Pearson correlation applied to the ranks of the X and Y variable.\n2.  In the event either the X or Y variable leads to tied ranks, the average rank of the tied values becomes the ranks for each tie.\n3.  Note that the Spearman's correlation macro returns the same value whether it is applied to the original X and Y values or to the ranked versions of the X and Y variables.\n4.  Spearman's Rank Correlation is a non-parametric estimator.\n5.  For normally distributed data, the Spearman's correlation must be adjusted by sin(0.5prS) to be a consistent estimator of ρ in the multivariate normal CDF."]
[13,71.272442551537864,167.92486667662297,656,661]
[14,68.209184553223238,170.8602725769386,281,735]
[15,71.98267048709441,177.2631871840758,748,860]
[16,64.969503845277544,170.46052364202347,47,727]
[17,67.564203137894168,158.22159030710421,204,396]
[18,72.348110751484867,168.08445955367756,788,668]
[19,73.399997728692298,186.43821871981902,874,957]
[20,70.630878832697576,145.0970574458735,580,111]
[21,70.119676553511951,138.10299892045091,512,36]
[22,66.187165277180767,144.01836436558077,105,99]
[23,73.781440690017263,194.19555847709682,901,991]
[24,67.094982124804702,159.50283587727762,173,439]
[25,69.938280213559452,159.32747874166122,490,432]
[26,69.152185366445423,169.67875714103042,396,709]
[27,69.979041938513163,169.26417290074878,494,695]
[28,65.231388920735938,150.1850862026223,55,196]
[29,69.189918454669353,162.13540998077724,399,522]
[30,70.721846699211568,179.8605006679764,592,902]
[31,73.086466808676647,167.34548500243301,857,650]
[32,72.420047763828379,176.77910111575324,799,854]
[33,64.432162861783951,134.40751922342531,30,19]
[34,70.274805760558294,157.56549297529213,532,376]
[35,68.139313698476599,139.42832188855618,270,50]
[36,74.470459052628982,176.30621399227613,937,845]
[37,66.394209385680298,143.0109075725224,113,89]
[38,71.518807312755527,168.23805683123777,686,672]
[39,71.110333645128406,154.63128579463387,637,297]
[40,69.828091828731687,178.51054410827797,479,882]
[41,71.003847780521227,174.76476874014267,620,815]
[42,68.1622931523939,165.52786009697638,273,610]
[43,69.415685455940761,142.51469910413542,421,81]
[44,70.859628547228837,175.83772864987318,606,836]
[45,68.009080122378336,170.53613457786034,250,730]
[46,71.794560651216031,161.16549604869812,719,484]
[47,67.756412972341224,154.8749645974199,222,307]
[48,68.650601790017191,159.3540303641403,345,434]
[49,71.657131082103163,187.63602188388052,703,965]
[50,68.959977085019389,167.85438772308584,369,659]
[51,68.442374616495457,163.80167125809115,312,562]
[52,72.648912335845125,164.46518267301462,813,587]
[53,64.166896838800838,157.77140207039417,23,382]
[54,69.536771215104523,160.63787952561177,442,469]
[55,68.527943015374262,142.84776624718435,330,87]
[56,68.51182490133948,133.19711497110532,328,13]
[57,70.280391459192344,179.51517039635146,536,896]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(O904:O1003)","v":0}]

{"sheet":"Quadrant Correlation","index":6,"n_rows":1003,"n_cols":14,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[14,12,29,13],[0,0,0,13],[3,7,3,8],[4,7,4,8],[2,7,2,9],[10,7,10,8],[11,7,11,8],[12,7,12,8],[2,12,3,13],[13,12,13,13],[7,7,8,9],[9,7,9,8]]}
["Calculating the Quadrant (Sign) Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","(X-Xmed)∙(Y-Ymed)","Sign of\nColumn D",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Quadrant Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,{"$f":"(B4-$J$10)*(C4-$J$11)","v":-7.7270201183883396},{"$f":"SIGN(D4)","v":-1},null,null,"Calculated Quadrant =",null,{"$f":"J13/J12","v":0.3}]
[2,75.900421131737588,148.6347709869498,-76.155459218056691,{"$f":"SIGN(D5)","v":-1},null,null,"VBA Quadrant = ",null,{"$f":"QuadCorr(B4:B1003,C4:C1003)","v":0.3},null,null,"U1(0,1), U2(0,1)",{"$f":"QuadCorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":0.02}]
[3,68.70319256856132,148.28328151641921,17.668056942224442,1,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"QuadCorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":4.0000000000000001E-3}]
[4,70.30671508908884,161.11898050586314,-0.13510299392419969,-1,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"QuadCorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.3}]
[5,67.375076704515038,167.57356788815855,-15.83935175689891,-1,null,null,"Intermediate Calculations for\nthe Quadrant Correlation",null,null,null,null,"Ranks of (X, Y)",{"$f":"QuadCorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.3}]
[6,70.303701168768001,166.7573260094741,1.4132749902076269,1,null,null,null,null,null,null,null,"(X, Y) with duplicates",{"$f":"QuadCorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.3}]
[7,72.04643599739471,158.14029467085311,-6.9907765558019195,-1,null,null,"Median (X) =",null,70.029345874092442,null,null,"Ranks of (X, Y) with duplicates",{"$f":"QuadCorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.3}]
[8,69.659038619402779,151.45915754274174,3.7574744455880227,1,null,null,"Median (Y) =",null,161.60606770451261]
[9,74.291448615158941,185.99290055062283,103.93918711933692,1,null,null,"Number of Obs = ",null,1000]
[10,65.649488474075483,147.60307841115861,61.331096278854794,1,null,null,"Sum of Signs (Col. D) =",null,300]
[11,69.742697145918896,154.65949081048038,1.9912274318340806,1,null,null,null,null,null,null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,0.69801476806637952,1,null,null,null,null,null,null,null,"1.  The Quadrant Correlation is a count of the observations in the first and third quadrants minus the sum of the observations in the second and fourth quadrants, after medians have been subtracted.\n2.  In the event any of the values of X or Y equal their respective median the observation is not counted in the numerator.\n3.  Note that the Quadrant Correlation macro returns the same value whether it is applied to the original X and Y values or to the ranked versions of the X and Y variables.\n4.  The Quadrant Correlation is a non-parametric estimator.\n"]
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{"sheet":"Kendall's Tau Correlation","index":7,"n_rows":1003,"n_cols":13,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[5,5,5,6],[6,5,6,6],[13,5,13,6],[14,5,14,6],[15,5,15,6],[13,10,13,11],[14,10,29,11],[10,5,11,7],[12,5,12,6],[16,5,16,6],[3,5,3,6],[4,5,4,6],[2,5,2,7],[2,10,3,12],[0,0,0,12]]}
["Calculating the Kendall Tau Correlation Coefficient"]
[]
["Observation\nNumber","X","Y",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Kendall Tau Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,null,null,"Calculated Kendall Tau(a) =",null,{"$f":"(H13-H14)/H17","v":0.31218818818818816}]
[2,75.900421131737588,148.6347709869498,null,null,"VBA Kendall Tau(a) = ",null,{"$f":"kendtau($B$4:$B$1003,$C$4:$C$1003,FALSE)","v":0.31218818818818816},null,null,null,"Kendall Tau(a)","Kendall Tau(b)"]
[3,68.70319256856132,148.28328151641921,null,null,"Calculated Kendall Tau(b) =",null,{"$f":"(H13-H14)/SQRT((H17-H15)*(H17-H16))","v":0.31218818818818816},null,null,"U1(0,1), U2(0,1)",1.1147147147147147E-2,1.1147147147147147E-2]
[4,70.30671508908884,161.11898050586314,null,null,"VBA Kendall Tau(b) = ",null,{"$f":"kendtau($B$4:$B$1003,$C$4:$C$1003,TRUE)","v":0.31218818818818816},null,null,"N1(0,1), N2(0,1)",-1.3449449449449449E-2,-1.3449449449449449E-2]
[5,67.375076704515038,167.57356788815855,null,null,null,null,null,null,null,"X, Y (Correlated)",0.31218818818818816,0.31218818818818816]
[6,70.303701168768001,166.7573260094741,null,null,null,null,null,null,null,"Ranks of (X, Y)",0.31218818818818816,0.31218818818818816]
[7,72.04643599739471,158.14029467085311,null,null,null,null,null,null,null,"(X, Y) with duplicates",0.31221021021021023,0.31222052382752374]
[8,69.659038619402779,151.45915754274174,null,null,"Intermediate Calculations for\nthe Kendall Tau Correlation",null,null,null,null,"Ranks of (X, Y) with duplicates",0.31221021021021023,0.31222052382752374]
[9,74.291448615158941,185.99290055062283]
[10,65.649488474075483,147.60307841115861,null,null,"# of Concordant Pairs = ",null,327719]
[11,69.742697145918896,154.65949081048038,null,null,"# of Discordant Pairs = ",null,171781,null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,null,null,"# of Ties in X = ",null,0,null,null,"1. Kendall's Tau is too complicated to show as a manual example, so only the intermediate and final results of the macro are shown in this worksheet.\n2. In addition to the X and Y variable, the macro requires you to enter \"True\" or \"False\" for the \"ties\" variable.  If \"True\" then the macro calculates Kendall's Tau-a, if \"False\" the macro calculates Kendall's Tau-b."]
[13,71.272442551537864,167.92486667662297,null,null,"# of Ties in Y = ",null,0]
[14,68.209184553223238,170.8602725769386,null,null,"# of Unique Pairs = ",null,{"$f":"COMBIN(1000,2)","v":499500}]
[15,71.98267048709441,177.2631871840758]
[16,64.969503845277544,170.46052364202347]
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{"sheet":"Goodman-Kruskal Gamma","index":8,"n_rows":1005,"n_cols":16,"rows_kept":1005,"cut":false,"hidden":false,"merged":[[13,10,13,11],[14,10,29,11],[10,5,11,7],[12,5,12,6],[13,5,13,6],[14,5,14,6],[0,0,0,11],[2,5,2,7],[3,5,3,6],[4,5,4,6],[2,10,3,11]]}
["Calculating the Goodman-Kruskal Gamma Correlation Coefficient"]
[]
["Observation\nNumber","X","Y",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Goodman-Kruskal Gamma Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,null,null,"Calculated Goodman-Kruskal Gamma = ",null,{"$f":"(H13-H14)/(H13+H14)","v":0.31218818818818816}]
[2,75.900421131737588,148.6347709869498,null,null,"VBA Goodman-Kruskal Gamma = ",null,{"$f":"gkgamma(B4:B1003,C4:C1003)","v":0.31218818818818816},null,null,"U1(0,1), U2(0,1)",1.1147147147147147E-2]
[3,68.70319256856132,148.28328151641921,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",-1.3449449449449449E-2]
[4,70.30671508908884,161.11898050586314,null,null,null,null,null,null,null,"X, Y (Correlated)",0.31218818818818816]
[5,67.375076704515038,167.57356788815855,null,null,null,null,null,null,null,"Ranks of (X, Y)",0.31218818818818816]
[6,70.303701168768001,166.7573260094741,null,null,null,null,null,null,null,"(X, Y) with duplicates",0.31223083807338625]
[7,72.04643599739471,158.14029467085311,null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",0.31223083807338625]
[8,69.659038619402779,151.45915754274174,null,null,"Intermediate Calculations for\nthe Goodman-Kruskal Gamma Correlation"]
[9,74.291448615158941,185.99290055062283]
[10,65.649488474075483,147.60307841115861,null,null,"# of Concordant Pairs = ",null,327719]
[11,69.742697145918896,154.65949081048038,null,null,"# of Discordant Pairs = ",null,171781,null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,null,null,"# of Unique Pairs = ",null,{"$f":"COMBIN(1000,2)","v":499500},null,null,"1. Goodman-Kruskal's Gamma Correlation is too complicated to show as a manual example, so only the intermediate and final results of the macro are shown in this worksheet.\n2.  Ties are not counted or incorporated into the Goodman-Kruskal Gamma correlation."]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(P904:P1003)","v":0}]

{"sheet":"Correlation Median Estimator","index":9,"n_rows":1005,"n_cols":15,"rows_kept":1005,"cut":false,"hidden":false,"merged":[[2,13,3,14],[13,13,13,14],[14,13,29,14],[0,0,0,14],[14,8,14,9],[10,8,10,9],[11,8,11,9],[3,8,3,9],[4,8,4,9],[12,8,12,9],[13,8,13,9],[2,8,2,10],[8,8,9,10]]}
["Calculating the Correlation Median Estimator"]
[]
["Observation\nNumber","X","Y","|X-Xmed|","|Y-Ymed|","(X-Xmed)∙(Y-Ymed)",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Correlation Median Estimator Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,{"$f":"ABS($B4-$K$11)","v":0.43909828518724225},{"$f":"ABS($C4-$K$12)","v":17.597472773307118},{"$f":"($B4-$K$11)*($C4-$K$12)","v":-7.7270201183883396},null,null,"Calculated CorrMed =",null,{"$f":"K15/(K13*K14)","v":0.3187895869539728}]
[2,75.900421131737588,148.6347709869498,{"$f":"ABS($B5-$K$11)","v":5.8710752576451455},{"$f":"ABS($C5-$K$12)","v":12.971296717562808},{"$f":"($B5-$K$11)*($C5-$K$12)","v":-76.155459218056691},null,null,"VBA CorrMed = ",null,{"$f":"corrmed(B4:B1003,C4:C1003)","v":0.3187895869539728},null,null,"U1(0,1), U2(0,1)",{"$f":"corrmed('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":6.8845516718048843E-3}]
[3,68.70319256856132,148.28328151641921,1.3261533055311219,13.322786188093403,17.668056942224442,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"corrmed('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":1.0343649560643205E-3}]
[4,70.30671508908884,161.11898050586314,0.27736921499639777,0.48708719864947625,-0.13510299392419969,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"corrmed('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.3187895869539728}]
[5,67.375076704515038,167.57356788815855,2.6542691695774039,5.9675001836459387,-15.83935175689891,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"corrmed('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.321384}]
[6,70.303701168768001,166.7573260094741,0.27435529467555853,5.1512583049614875,1.4132749902076269,null,null,"Intermediate Calculations for\nthe Correlation Median Estimator",null,null,null,null,"(X, Y) with duplicates",{"$f":"corrmed('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.31879445960970171}]
[7,72.04643599739471,158.14029467085311,2.0170901233022676,3.4657730336595023,-6.9907765558019195,null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"corrmed('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.321384}]
[8,69.659038619402779,151.45915754274174,0.37030725468966352,10.146910161770876,3.7574744455880227,null,null,"Median of X = ",null,{"$f":"MEDIAN(B4:B1003)","v":70.029345874092442}]
[9,74.291448615158941,185.99290055062283,4.2621027410664993,24.386832846110224,103.93918711933692,null,null,"Median of Y = ",null,{"$f":"MEDIAN(C4:C1003)","v":161.60606770451261}]
[10,65.649488474075483,147.60307841115861,4.3798574000169594,14.002989293354005,61.331096278854794,null,null,"MAD of X = ",null,{"$f":"MEDIAN(D4:D1003)","v":1.9976850840580553}]
[11,69.742697145918896,154.65949081048038,0.28664872817354592,6.9465768940322334,1.9912274318340806,null,null,"MAD of Y = ",null,{"$f":"MEDIAN(E4:E1003)","v":9.4242113473348752},null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,0.10583396329761285,6.5953758728992398,0.69801476806637952,null,null,"Co-Median of (X,Y) = ",null,{"$f":"MEDIAN(F4:F1003)","v":6.0017260899816272}]
[13,71.272442551537864,167.92486667662297,1.243096677445422,6.3187989721103577,7.854878007675933]
[14,68.209184553223238,170.8602725769386,1.8201613208692038,9.2542048724259871,-16.844145764189108]
[15,71.98267048709441,177.2631871840758,1.9533246130019677,15.657119479563192,30.583436848143343]
[16,64.969503845277544,170.46052364202347,5.0598420288148986,8.8544559375108634,-44.802148294907091]
[17,67.564203137894168,158.22159030710421,2.4651427361982741,3.3844773974084035,8.3432198720485644]
[18,72.348110751484867,168.08445955367756,2.3187648773924252,6.4783918491649501,15.021867481829052]
[19,73.399997728692298,186.43821871981902,3.3706518545998563,24.832151015306408,83.700535873446242]
[20,70.630878832697576,145.0970574458735,0.60153295860513367,16.509010258639108,-9.9307137845216857]
[21,70.119676553511951,138.10299892045091,9.0330679419508897E-2,23.503068784061696,-2.1230481717077438]
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[943,68.087171293328623,148.18322985745044,1.9421745807638189,13.422837847062169,26.069494468278691]
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[945,65.081620831171904,167.23078872947454,4.9477250429205384,5.6247210249619286,-27.829573074645811]
[946,75.29765052028462,153.46086468230587,5.2683046461921776,8.1452030222067435,-42.911410926070353]
[947,76.328237654952801,184.31351257821842,6.2988917808603588,22.707444873705811,143.03173787932522]
[948,69.506911916991555,154.11279634264073,0.52243395710088691,7.4932713618718765,3.9147394092134764]
[949,68.005617591003997,148.32134224269456,2.0237282830884453,13.284725461818056,26.884674650146408]
[950,71.624995487172498,174.24375688216597,1.5956496130800559,12.637689177653357,20.165323846548588]
[951,74.973795398985601,193.23656188137949,4.9444495248931588,31.630494176866875,156.39538190494525]
[952,71.873045801006441,168.03200020950018,1.8436999269139989,6.4259325049875713,11.847491289799875]
[953,68.336302393893561,187.04256961076453,1.693043480198881,25.43650190625192,-43.06510371144622]
[954,66.726307931796228,133.8178904718269,3.3030379422962142,27.788177232685712,91.785403746812719]
[955,68.193220209947654,155.13575229669999,1.8361256641447881,6.4703154078126204,11.880312175396202]
[956,66.345021385320479,140.46873245451278,3.6843244887719635,21.137335249999836,77.876801888957246]
[957,65.998474633827485,171.19216310318342,4.0308712402649576,9.5860953986708068,-38.640316248938397]
[958,71.732056793810898,166.46134629439925,1.7027109197184558,4.8552785898866375,8.2671358732752029]
[959,67.276418676790001,161.98905061000559,2.7529271973024407,0.38298290549298031,-1.0543240566335359]
[960,71.610127043785425,130.00738042447429,1.5807811696929832,31.59868728003832,-49.950609839301762]
[961,68.05782941410915,151.65312405222787,1.9715164599832917,9.9529436522847448,19.622392235765595]
[962,74.532793813216188,166.7535982937145,{"$f":"ABS($B965-$K$11)","v":4.5034479391237454},{"$f":"ABS($C965-$K$12)","v":5.1475305892018923},{"$f":"($B965-$K$11)*($C965-$K$12)","v":23.181636023517701}]
[963,75.867124862587389,165.09075729274707,5.8377789884949465,3.4846895882344597,20.342847659622237]
[964,71.815451773933574,159.08227108793085,1.7861058998411323,2.5237966165817625,-4.507768026875774]
[965,61.877655199001573,152.08396733094887,8.1516906750908689,9.5221003735637453,77.621216822458862]
[966,66.379785682903631,150.33862786018673,3.6495601911888116,11.267439844325878,41.121199912466388]
[967,65.901947342454605,154.63298294101941,4.1273985316378372,6.9730847634932047,28.780699813828029]
[968,65.574685680426299,163.58129464849748,4.4546601936661432,1.9752269439848646,-8.7989648408262013]
[969,71.752799741851916,175.89650736672533,1.7234538677594742,14.290439662212719,24.628913507823906]
[970,73.13332135243401,152.16529383619647,3.1039754783415674,9.4407738683161426,-29.303930583821167]
[971,72.964746306546573,148.03734757981741,2.9354004324541307,13.568720124695204,-39.829626921879367]
[972,68.038318517381001,157.17792523673273,1.9910273567114416,4.4281424677798782,8.8165527927654512]
[973,68.762819020043068,148.21777155657355,1.2665268540493742,13.388296147939059,16.956636601330612]
[974,65.791081929103797,162.06889297833703,4.2382639449886454,0.4628252738244214,-1.9615756708795422]
[975,65.699545273898138,176.36856795111959,4.3298006001943037,14.762500246606976,-63.91868242812744]
[976,68.216240483735447,138.40648196607015,1.8131053903569949,23.199585738442465,42.063293956419301]
[977,74.587220858248571,172.08428897963017,4.557874984156129,10.478221275117562,47.758422628310875]
[978,68.428636847793811,145.5348927737291,1.600709026298631,16.071174930783513,25.725274774929446]
[979,67.756280153305298,158.96612397358521,2.2730657207871445,2.6399437309273992,6.000765599577992]
[980,70.279184098712946,157.59822278867134,0.24983822462050398,4.0078449158412752,-1.0013128583280975]
[981,66.8461146376833,161.70316698036402,3.1832312364091422,9.7099275851405764E-2,-0.30908944792290272]
[982,69.669277531813009,159.38863900911079,0.3600683422794333,2.2174286954018214,0.7984258744761803]
[983,68.884915246787671,164.22129551633441,1.1444306273047715,2.6152278118217964,-2.9929468052281036]
[984,66.757432806439581,153.7354942686037,3.2719130676528607,7.8705734359089092,25.751832074871835]
[985,72.94978173730965,189.24947866394663,2.9204358632172074,27.643410959434021,80.730808747582714]
[986,71.413441301612423,166.77684133938783,1.3840954275199806,5.1707736348752178,7.1568441447716591]
[987,66.276002573263611,154.27064541676046,3.7533433008288313,7.3354222877521522,27.532358102485041]
[988,74.474437496857064,184.91105210852731,4.4450916227646218,23.304984404014704,103.59279094294592]
[989,73.229245627942007,179.50437979620904,3.1998997538495644,17.898312091696425,57.272804456542076]
[990,67.661299683710098,174.30074290262405,2.3680461903823442,12.69467519811144,-30.061577241029028]
[991,67.995205008986574,140.13194335022001,2.0341408651058686,21.474124354292599,43.681393891431746]
[992,71.613955307897157,177.92968103285378,1.5846094338047152,16.323613328341168,25.8665516738698]
[993,66.616217191886477,144.35468838738177,3.413128682205965,17.251379317130841,58.881177554914025]
[994,71.281143270425275,159.86075365638786,1.251797396332833,1.7453140481247544,-2.1847795812256843]
[995,67.046078942109119,175.42135129542331,2.9832669319833229,13.815283590910695,-41.214678692735696]
[996,72.697270897329361,164.5742158186199,2.6679250232369185,2.9681481141072936,7.9187966263003169]
[997,73.063577091851528,185.76517555171091,3.0342312177590856,24.1591078471983,73.304319223177572]
[998,70.595973984843269,168.74073257871854,0.56662811075082686,7.1346648742059244,4.0427016785115883]
[999,72.863123673420617,179.89831295341651,2.8337777993281748,18.292245248903896,51.836158486210145]
[1000,71.912624388221161,159.94124718472298,1.8832785141287189,1.6648205197896289,-3.1353207148004136]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(N904:N1003)","v":0}]

{"sheet":"Tukey Biweight MidCorrelation","index":10,"n_rows":1003,"n_cols":20,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[0,0,0,19],[18,14,18,15],[10,14,11,16],[2,18,3,19],[13,18,13,19],[14,18,29,19],[13,14,13,15],[14,14,14,15],[15,14,15,15],[16,14,16,15],[17,14,17,15],[3,14,3,15],[4,14,4,15],[2,14,2,16],[12,14,12,15]]}
["Calculating the Tukey Biweight Midcorrelation Coefficient"]
[]
["Obs.\nNumber","X","Y","|X-medx|","|Y-medy|","U(i)","V(i)","a(i)","b(i)","MidVar(X)","MidVar(Y)","MidCovar(X,Y)",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,"Tukey Biweight MidCorrelation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,0.43909828518724225,17.597472773307118,{"$f":"($B4-$Q$13)/(9*$Q$15)","v":-2.4422617330169826E-2},{"$f":"($C4-$Q$14)/(9*$Q$16)","v":0.20747356786970006},{"$f":"OR(F4>=-1,F4<=1)*1","v":1},{"$f":"OR(G4>=-1,G4<=1)*1","v":1},{"$f":"H4*(D4^2)*(1-F4^2)^4","v":0.19234770481439153},{"$f":"I4*(E4^2)*(1-G4^2)^4","v":259.69653602789833},{"$f":"$H4*($B4-$Q$13)*(1-$F4^2)^2*$I4*($C4-$Q$14)*(1-$G4^2)^2","v":-7.0676751943771556},null,null,"Calculated Tukey BiWeight = ",null,{"$f":"Q19/(SQRT(Q17)*SQRT(Q18))","v":0.46516966507777291}]
[2,75.900421131737588,148.6347709869498,5.8710752576451455,12.971296717562808,0.32654881417483073,-0.15293111940320528,{"$f":"OR(F5>=-1,F5<=1)*1","v":1},{"$f":"OR(G5>=-1,G5<=1)*1","v":1},{"$f":"H5*(D5^2)*(1-F5^2)^4","v":21.955974893419754},{"$f":"I5*(E5^2)*(1-G5^2)^4","v":153.05768574388128},-57.970084573317543,null,null,"VBA Tukey Biweight = ",null,{"$f":"BiWeight(B4:B1003,C4:C1003)","v":0.46516966507777291},null,"U1(0,1), U2(0,1)",{"$f":"BiWeight('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":1.6816169914409644E-2}]
[3,68.70319256856132,148.28328151641921,1.3261533055311219,13.322786188093403,-7.3760558386866126E-2,-0.15707516755483708,1,1,1.7207205095849429,160.6171079787577,16.624594788723957,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"BiWeight('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-2.2246640793311411E-2}]
[4,70.30671508908884,161.11898050586314,0.27736921499639777,0.48708719864947625,1.542725723499009E-2,-5.7427404644577419E-3,1,1,7.6860466624103216E-2,0.23722264298120971,-0.13502978572647895,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"BiWeight('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.46516966507777291}]
[5,67.375076704515038,167.57356788815855,2.6542691695774039,5.9675001836459387,-0.14763027414742455,7.0356611447192241E-2,1,1,6.4507464959498595,34.911170182799054,-15.006768763667953,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"BiWeight('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.44570797338192464}]
[6,70.303701168768001,166.7573260094741,0.27435529467555853,5.1512583049614875,1.5259623187801562E-2,6.0733149203670095E-2,1,1,7.5200743115210356E-2,26.146117071799139,1.402215187971013,null,null,null,null,null,null,"(X, Y) with duplicates",{"$f":"BiWeight('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.46516934448550157}]
[7,72.04643599739471,158.14029467085311,2.0170901233022676,3.4657730336595023,0.11219041809937737,-4.0861338783296085E-2,1,1,3.8676441944425131,11.931562898783495,-6.793161265280375,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"BiWeight('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.44573030610508607}]
[8,69.659038619402779,151.45915754274174,0.37030725468966352,10.146910161770876,-2.0596464802896827E-2,-0.11963170400861391,1,1,0.13689492513997326,97.190979308095351,3.6475953499068949,null,null,"Intermediate Calculations for\nthe Tukey Biweight Midcorrelation Coefficient"]
[9,74.291448615158941,185.99290055062283,4.2621027410664993,24.386832846110224,0.23705787013617635,0.28751987770080339,1,1,14.413660386171218,421.13136044014453,77.910489713199098]
[10,65.649488474075483,147.60307841115861,4.3798574000169594,14.002989293354005,-0.24360737641166866,-0.16509473757733098,1,1,15.01904225007029,175.56392026980282,51.349799767089074,null,null,"Median(X) = ",null,70.029345874092442]
[11,69.742697145918896,154.65949081048038,0.28664872817354592,6.9465768940322334,-1.5943383138873127E-2,-8.1899890470194733E-2,1,1,8.2083980110437868E-2,46.973201290463635,1.9636056937302897,null,null,"Median(Y) = ",null,161.60606770451261,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,0.10583396329761285,6.5953758728992398,-5.8864779785023288E-3,-7.7759243126533553E-2,1,1,1.1199275405325905E-2,42.456420096465237,0.6895514059042499,null,null,"MAD(x) = ",null,1.9976850840580553]
[13,71.272442551537864,167.92486667662297,1.243096677445422,6.3187989721103577,6.9140954273390037E-2,7.4498411464156755E-2,1,1,1.515951714005555,39.048185949596963,7.6938393809007444,null,null,"MAD(y) = ",null,9.4242113473348752]
[14,68.209184553223238,170.8602725769386,1.8201613208692038,9.2542048724259871,-0.10123725124503533,0.10910674091746603,1,1,3.1792420396405534,81.634604026518247,-16.110126163705758,null,null,"Sum of MidVar(X)",null,6470.4792871785303]
[15,71.98267048709441,177.2631871840758,1.9533246130019677,15.657119479563192,0.10864378467022803,0.18459687267790972,1,1,3.6384979930785177,213.40055745196378,27.864986991039615,null,null,"Sum of MidVar(Y)",null,142597.93140782593]
[16,64.969503845277544,170.46052364202347,5.0598420288148986,8.8544559375108634,-0.28142807610410314,0.10439371542526255,1,1,18.40483102419801,75.039165954947293,-37.162927355061221,null,null,"Sum of MidCoVar(X,Y)",null,14129.806807241735]
[17,67.564203137894168,158.22159030710421,2.4651427361982741,3.3844773974084035,-0.13711107453937163,-3.9902866170635633E-2,1,1,5.6326825949704995,11.381906923208117,8.0069138264332889]
[18,72.348110751484867,168.08445955367756,2.3187648773924252,6.4783918491649501,0.12896954779735659,7.6380005715538796E-2,1,1,5.0277733578341408,40.998712361037271,14.35730593510943]
[19,73.399997728692298,186.43821871981902,3.3706518545998563,24.832151015306408,0.18747543129897715,0.2927701628179073,1,1,9.8462834615207786,430.87992505611089,65.134981998779253]
[20,70.630878832697576,145.0970574458735,0.60153295860513367,16.509010258639108,3.3457223029767606E-2,-0.19464063416838215,1,1,0.36022445593849117,233.5339686970149,-9.1719489105118122]
[21,70.119676553511951,138.10299892045091,9.0330679419508897E-2,23.503068784061696,5.024186363415591E-3,-0.277100331356265,1,1,8.1588077992545659E-3,401.29275243505475,-1.8094392607521965]
[22,66.187165277180767,144.01836436558077,3.8421805969116747,17.587703338931846,-0.21370182849100242,-0.20735838659156897,1,1,12.244826526271387,259.46008221429747,56.365270310770136]
[23,73.781440690017263,194.19555847709682,3.7520948159248206,32.589490772584213,0.20869126336207408,0.38422891813765964,1,1,11.781293722800918,560.61405099770104,81.269667157760693]
[24,67.094982124804702,159.50283587727762,2.9343637492877406,2.1032318272349926,-0.16320911598599672,-2.479702721378587E-2,1,1,7.7290630002114371,4.4127140343051572,5.8400466413430063]
[25,69.938280213559452,159.32747874166122,9.1065660532990478E-2,2.2785889628513871,-5.0650659639173519E-3,-2.6864481503752469E-2,1,1,8.2921035416069488E-3,5.1769956994290016,0.20719117832118039]
[26,69.152185366445423,169.67875714103042,0.87716050764701947,8.0726894365178055,-4.8787608920553081E-2,9.5176716638478265E-2,1,1,0.76211117049823518,62.838870333146488,-6.9202749239015855]
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[965,61.877655199001573,152.08396733094887,8.1516906750908689,9.5221003735637453,-0.45339649155487599,-0.11226521919177829,1,1,26.468021135467179,86.185038547510359,47.761359086991632]
[966,66.379785682903631,150.33862786018673,3.6495601911888116,11.267439844325878,-0.20298829437427154,-0.13284270846012972,1,1,11.256035831226844,118.22803508636564,36.4798437385315]
[967,65.901947342454605,154.63298294101941,4.1273985316378372,6.9730847634932047,-0.22956563099377933,-8.2212417292911816E-2,1,1,13.718362194264053,47.322605708043234,25.479180620249245]
[968,65.574685680426299,163.58129464849748,4.4546601936661432,1.9752269439848646,-0.24776790280439334,2.3287854267490273E-2,1,1,15.401812907655913,3.8930648053607402,-7.7434007883840037]
[969,71.752799741851916,175.89650736672533,1.7234538677594742,14.290439662212719,9.5858389154359847E-2,0.16848376703518825,1,1,2.8626147232371331,181.99725710299001,22.825162163099588]
[970,73.13332135243401,152.16529383619647,3.1039754783415674,9.4407738683161426,0.17264290904128876,-0.11130638263476493,1,1,8.5363391999744263,84.79274001337167,-26.903895451205287]
[971,72.964746306546573,148.03734757981741,2.9354004324541307,13.568720124695204,0.16326677623455491,-0.15997471977715472,1,1,7.7339268551335225,165.97447039075217,-35.827844113504817]
[972,68.038318517381001,157.17792523673273,1.9910273567114416,4.4281424677798782,-0.11074080876022487,-5.2207639623071449E-2,1,1,3.773278126756717,19.395536096095505,8.5548087125380849]
[973,68.762819020043068,148.21777155657355,1.2665268540493742,13.388296147939059,-7.0444139133090888E-2,-0.1578475276133107,1,1,1.5724860940156116,162.0388018059142,15.962573806587455]
[974,65.791081929103797,162.06889297833703,4.2382639449886454,0.4628252738244214,-0.23573195788859583,5.4566932478099057E-3,1,1,14.29077930221875,0.21418172271907632,-1.7495210001447057]
[975,65.699545273898138,176.36856795111959,4.3298006001943037,14.762500246606976,-0.24082322054478722,0.17404934426077107,1,1,14.762064742593546,192.69996963680546,-53.335255016492923]
[976,68.216240483735447,138.40648196607015,1.8131053903569949,23.199585738442465,-0.10084480086064254,-0.27352227721896333,1,1,3.1556521168783958,394.34455680751364,35.276255972950182]
[977,74.587220858248571,172.08428897963017,4.557874984156129,10.478221275117562,0.25350870256605867,0.1235378500584709,1,1,15.926972419173044,103.24252671005398,40.550473183389187]
[978,68.428636847793811,145.5348927737291,1.600709026298631,16.071174930783513,-8.90313292605317E-2,-0.18947857148018804,1,1,2.4819901182505029,223.14119358381052,23.533683040477118]
[979,67.756280153305298,158.96612397358521,2.2730657207871445,2.6399437309273992,-0.12642776375553019,-3.1124841156826035E-2,1,1,4.8443181959142336,6.9423359120737542,5.7992141002904631]
[980,70.279184098712946,157.59822278867134,0.24983822462050398,4.0078449158412752,1.3895985386856309E-2,-4.7252346678969069E-2,1,1,6.2370940298715399E-2,15.919841370131211,-0.9964614772591428]
[981,66.8461146376833,161.70316698036402,3.1832312364091422,9.7099275851405764E-2,-0.17705110901791016,1.1447969522654011E-3,1,1,8.9209091440232822,9.4282199457113892E-3,-0.29001429882948776]
[982,69.669277531813009,159.38863900911079,0.3600683422794333,2.2174286954018214,-2.0026977177670626E-2,-2.6143404161392599E-2,1,1,0.12944133748817305,4.9035611847171765,0.79669537353048669]
[983,68.884915246787671,164.22129551633441,1.1444306273047715,2.6152278118217964,-6.3653155146511403E-2,3.0833441364021889E-2,1,1,1.2886235982680885,6.813444610986731,-2.9631006582986741]
[984,66.757432806439581,153.7354942686037,3.2719130676528607,7.8705734359089092,-0.18198358655578184,-9.279377629755102E-2,1,1,9.3561541211537662,59.839738420922458,23.661568317330044]
[985,72.94978173730965,189.24947866394663,2.9204358632172074,27.643410959434021,0.16243444789187336,0.32591481593548766,1,1,7.6638052548074791,487.64624165147831,61.13285392696563]
[986,71.413441301612423,166.77684133938783,1.3840954275199806,5.1707736348752178,7.6983295346607347E-2,6.0963234237897138E-2,1,1,1.8707087612354341,26.341637858532902,7.0197957753234173]
[987,66.276002573263611,154.27064541676046,3.7533433008288313,7.3354222877521522,-0.20876070400914959,-8.6484363605856721E-2,1,1,11.787706162497962,52.216541635065568,24.809539488188687]
[988,74.474437496857064,184.91105210852731,4.4450916227646218,23.304984404014704,0.24723569952916349,0.27476492367602434,1,1,15.352942574252911,396.76491014711206,78.04811900979567]
[989,73.229245627942007,179.50437979620904,3.1998997538495644,17.898312091696425,0.17797821084600113,0.2110204525585285,1,1,9.0023334046538412,266.98880133138977,49.025730029180167]
[990,67.661299683710098,174.30074290262405,2.3680461903823442,12.69467519811144,-0.1317105711383334,0.1496697616884107,1,1,5.2285333643958287,147.19264691095006,-27.741695430662439]
[991,67.995205008986574,140.13194335022001,2.0341408651058686,21.474124354292599,-0.11313877922105041,-0.25317914987320145,1,1,3.9299041812541189,353.79305789380408,37.287703301699096]
[992,71.613955307897157,177.92968103285378,1.5846094338047152,16.323613328341168,8.8135871000012841E-2,0.19245481106204668,1,1,2.433870743850862,229.12245516210822,23.61470813663248]
[993,66.616217191886477,144.35468838738177,3.413128682205965,17.251379317130841,-0.18983798961682896,-0.20339313853224622,1,1,10.058753095682182,251.335562906337,50.280437263802121]
[994,71.281143270425275,159.86075365638786,1.251797396332833,1.7453140481247544,6.9624887677488867E-2,-2.0577189536375742E-2,1,1,1.5368321000109977,3.0409652390870043,-2.161817058505767]
[995,67.046078942109119,175.42135129542331,2.9832669319833229,13.815283590910695,-0.16592910774522732,0.16288169413086098,1,1,7.9594794972943523,171.39932241375337,-36.935746812571885]
[996,72.697270897329361,164.5742158186199,2.6679250232369185,2.9681481141072936,0.14838981181699415,3.4994358970321132E-2,1,1,6.511303791708845,8.766827821825883,7.5553609601072989]
[997,73.063577091851528,185.76517555171091,3.0342312177590856,24.1591078471983,0.16876373792028279,0.28483500819561813,1,1,8.2016679459169346,416.07940429176034,58.416993359260999]
[998,70.595973984843269,168.74073257871854,0.56662811075082686,7.1346648742059244,3.1515817720589458E-2,8.4117440957287057E-2,1,1,0.31979371841758847,49.477943204454014,3.9777802147688606]
[999,72.863123673420617,179.89831295341651,2.8337777993281748,18.292245248903896,0.15761453215926519,0.21566491024179216,1,1,7.2615767519134362,276.56431045710008,44.813981827374455]
[1000,71.912624388221161,159.94124718472298,1.8832785141287189,1.6648205197896289,0.104747825323625,-1.9628173747049373E-2,1,1,3.3936204108621872,2.767358584489592,-3.0645333374754742]

{"sheet":"Fisher-Yates Normal Scores","index":11,"n_rows":1005,"n_cols":18,"rows_kept":1005,"cut":false,"hidden":false,"merged":[[2,15,3,16],[13,15,13,16],[14,15,29,16],[0,0,0,16],[16,11,16,12],[14,11,14,12],[4,11,4,12],[11,11,12,13],[15,11,15,12],[13,11,13,12],[2,11,2,13],[3,11,3,12]]}
["Calculating the Fisher-Yates Normal Scores Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","Xrnk","Yrnk","Rankit of\nX","Rankit of\nY","Rankit X∙\nRankit Y","(Rankit X)2",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,"Normal Scores Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,452,892,{"$f":"_xlfn.NORM.INV((D4-0.375)/(COUNTA($A$4:$A$1003)+(1-2*0.375)),0,1)","v":-0.1218418820670685},{"$f":"_xlfn.NORM.INV((E4-0.375)/(COUNTA($A$4:$A$1003)+(1-2*0.375)),0,1)","v":1.234019330849764},{"$f":"F4*G4","v":-0.15035523777787974},{"$f":"F4^2","v":1.4845444225645429E-2},null,null,"Calculated Normal Scores Correlation = ",null,{"$f":"N16/N17","v":0.47519659087412541}]
[2,75.900421131737588,148.6347709869498,977,171,{"$f":"_xlfn.NORM.INV((D5-0.375)/(COUNTA($A$4:$A$1003)+(1-2*0.375)),0,1)","v":1.9841583460310666},{"$f":"_xlfn.NORM.INV((E5-0.375)/(COUNTA($A$4:$A$1003)+(1-2*0.375)),0,1)","v":-0.95186646496827798},{"$f":"F5*G5","v":-1.8886537907738965},{"$f":"F5^2","v":3.9368843421247375},null,null,"VBA Normal Scores Correlation = ",null,{"$f":"scorecorr(B4:B1003,C4:C1003)","v":0.47519659087412541},null,"U1(0,1), U2(0,1)",{"$f":"scorecorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":-2.7597950241146575E-3}]
[3,68.70319256856132,148.28328151641921,350,162,-0.38656910844055942,-0.98796618830859051,0.38191720858386968,0.14943567560052898,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"scorecorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-2.4171785781532781E-2}]
[4,70.30671508908884,161.11898050586314,544,482,0.10922788377725032,-4.6377652972691356E-2,-5.0657328887627794E-3,1.1930730594456504E-2,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"scorecorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.47519659087412541}]
[5,67.375076704515038,167.57356788815855,190,656,-0.87945391304078002,0.40010697024967479,-0.35187564062096743,0.77343918516273991,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"scorecorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.47519659087412541}]
[6,70.303701168768001,166.7573260094741,543,634,0.10670723247121949,0.3410489477289575,3.6392389349378655E-2,1.138643346166688E-2,null,null,null,null,null,null,"(X, Y) with duplicates",{"$f":"scorecorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.47520301955569211}]
[7,72.04643599739471,158.14029467085311,757,392,0.694883653034436,-0.27534104089332995,-0.19132998832626114,0.48286329125448246,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"scorecorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.47520301955569211}]
[8,69.659038619402779,151.45915754274174,458,226,-0.10670723247121933,-0.75352046922165761,8.0406083881057688E-2,1.1386433461666845E-2]
[9,74.291448615158941,185.99290055062283,923,956,1.4213632061906976,1.6994857723419698,2.4155865462514563,2.0202733639126995,null,null,"Intermediate Calculations for\nthe Fisher-Yates Normal Scores Correlation"]
[10,65.649488474075483,147.60307841115861,69,153,-1.4862398285836358,-1.0254016571915652,1.5239927832137679,2.2089088280683149]
[11,69.742697145918896,154.65949081048038,464,300,-9.1596986968368252E-2,-0.52569487541949456,4.8152066653137413E-2,8.3900080216834233E-3,null,null,"Number of Observations = ",null,1000,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,488,311,-3.13301469204827E-2,-0.49429943185638198,1.5486473822771574E-2,9.8157810605903166E-4,null,null,"Rankit Correction Factor = ",null,0.375]
[13,71.272442551537864,167.92486667662297,656,661,0.40010697024967479,0.41371856409890384,0.16553168121765829,0.16008558764237416,null,null,"Sum of Rankit(X)∙Rankit(Y) = ",null,473.19092270309454]
[14,68.209184553223238,170.8602725769386,281,735,-0.58119398286432422,0.62630147250427581,-0.36400264727855108,0.33778644571769639,null,null,"Sum of Rankit(X)2 = ",null,995.77928754214872]
[15,71.98267048709441,177.2631871840758,748,860,0.66644967681666334,1.077673015112578,0.71821483263581676,0.44415517172903501]
[16,64.969503845277544,170.46052364202347,47,727,-1.6786170918529368,0.60209151582046339,-1.0106811093158727,2.8177553410608112]
[17,67.564203137894168,158.22159030710421,204,396,-0.82892258781816897,-0.26494447389567422,0.21961845892972559,0.68711265659517007]
[18,72.348110751484867,168.08445955367756,788,668,0.79752926402066915,0.43290508033124947,0.34525447010739002,0.63605292696935023]
[19,73.399997728692298,186.43821871981902,874,957,1.1426433401339098,1.7102038017302046,1.9541529843187118,1.3056338027523777]
[20,70.630878832697576,145.0970574458735,580,111,0.20056370562329306,-1.2233574916469312,-0.24536111182672532,4.0225800013346961E-2]
[21,70.119676553511951,138.10299892045091,512,36,2.882301076853656E-2,-1.8039943546812081,-5.1996548711355624E-2,8.3076594976317448E-4]
[22,66.187165277180767,144.01836436558077,105,99,-1.2557746071379536,-1.2895679781600262,1.6194067211515921,1.5769698639324818]
[23,73.781440690017263,194.19555847709682,901,991,1.2838335553747735,2.34074728942565,3.0051299148171964,1.6482285979062317]
[24,67.094982124804702,159.50283587727762,173,439,-0.94401162246485071,-0.15473435814289691,0.14607103248153339,0.89115794334871978]
[25,69.938280213559452,159.32747874166122,490,432,-2.6316055777496197E-2,-0.17251300078065671,4.5398617508870072E-3,6.9253479168429101E-4]
[26,69.152185366445423,169.67875714103042,396,709,-0.26494447389567422,0.54885607562977257,-0.14541638420217448,7.0195574247855594E-2]
[27,69.979041938513163,169.26417290074878,494,695,-1.6289731931508115E-2,0.5085078637370497,-8.2834567853403967E-3,2.653553664003951E-4]
[28,65.231388920735938,150.1850862026223,55,196,-1.6016967042448702,-0.85752969305609972,1.3735024831600702,2.565432332388879]
[29,69.189918454669353,162.13540998077724,399,522,-0.25716586044520912,5.3905132696642932E-2,-1.3862559832345356E-2,6.6134279778524777E-2]
[30,70.721846699211568,179.8605006679764,592,902,0.23134635323142733,1.2895679781600262,0.29833684899134699,5.3521135153480344E-2]
[31,73.086466808676647,167.34548500243301,857,650,1.0643322673712774,0.38387009613338091,0.40856532979367155,1.1328031753676844]
[32,72.420047763828379,176.77910111575324,799,854,0.83601011497485789,1.0511783038919646,0.87879569469579744,0.69891291234027508]
[33,64.432162861783951,134.40751922342531,30,19,-1.886443679352507,-2.0831155772224932,3.9296802140121216,3.5586697553690243]
[34,70.274805760558294,157.56549297529213,532,376,7.9021218310549757E-2,-0.31723903281196308,-2.5068614868461792E-2,6.244352943283564E-3]
[35,68.139313698476599,139.42832188855618,270,50,-0.61415149696538662,-1.6486215368853683,1.0125033848075253,0.37718206122482528]
[36,74.470459052628982,176.30621399227613,937,845,1.5251640076267075,1.0127654504812829,1.5446334132419011,2.3261252501599592]
[37,66.394209385680298,143.0109075725224,113,89,-1.2128329325753131,-1.34940879137575,1.6366074216871598,1.470963722339234]
[38,71.518807312755527,168.23805683123777,686,672,0.48300423836930739,0.44394032550736601,0.21442505880310772,0.23329309428271472]
[39,71.110333645128406,154.63128579463387,637,297,0.34902807449087536,-0.53434664693516232,-0.1865019812904353,0.12182059678280804]
[40,69.828091828731687,178.51054410827797,479,882,-5.3905132696642932E-2,1.1820378007196304,-6.3717904500239647E-2,2.9057633310426829E-3]
[41,71.003847780521227,174.76476874014267,620,815,0.3040894619572756,0.89430783193191954,0.27194958743635506,9.2470400873465364E-2]
[42,68.1622931523939,165.52786009697638,273,610,-0.60509824306526561,0.27794479548585627,-0.1681839074176262,0.36614388376067125]
[43,69.415685455940761,142.51469910413542,421,81,-0.2005637056232932,-1.4010146322797337,0.28099268628247887,4.0225800013347017E-2]
[44,70.859628547228837,175.83772864987318,606,836,0.26754088827423261,0.97579168105554681,0.26106417312020769,7.1578126898565422E-2]
[45,68.009080122378336,170.53613457786034,250,730,-0.67586679930884697,0.61112818596058383,-0.41304125101260164,0.45679593040798522]
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[943,68.087171293328623,148.18322985745044,267,160,-0.62325537020699684,-0.99616453598152011,0.62086489666024358,0.38844725649186068]
[944,73.131629712157917,153.51031846187652,860,272,1.077673015112578,-0.60811045063013103,-0.65534422285204175,1.1613791275018346]
[945,65.081620831171904,167.23078872947454,52,648,-1.6294197342879551,0.37848042661364689,-0.61670347616600041,2.6550086704870299]
[946,75.29765052028462,153.46086468230587,969,271,1.8575412267791462,-0.61112818596058383,-1.1351958002685372,3.4504594091841754]
[947,76.328237654952801,184.31351257821842,988,939,2.2376530515665563,1.5414011052967502,3.449120886955336,5.0070911791851209]
[948,69.506911916991555,154.11279634264073,435,284,-0.16488723252810686,-0.57231554102805615,9.4367525692942378E-2,2.718779945077798E-2]
[949,68.005617591003997,148.32134224269456,248,163,-0.68217829351852555,-0.98389181647860702,0.6711896403722184,0.46536722414784759]
[950,71.624995487172498,174.24375688216597,698,802,0.5170822764540477,0.84672088954069158,0.43782436508489708,0.26737408062290019]
[951,74.973795398985601,193.23656188137949,962,987,1.7669852871805001,2.2080155500405265,3.9015309907873696,3.1222370051123542]
[952,71.873045801006441,168.03200020950018,730,666,0.61112818596058383,0.4274072477736488,0.26120061599831579,0.37347765967547392]
[953,68.336302393893561,187.04256961076453,296,964,-0.53723944987765238,1.7913840163294297,-0.96240216345244223,0.28862622650484254]
[954,66.726307931796228,133.8178904718269,141,18,-1.0776730151125775,-2.105576109415356,2.269122554382657,1.1613791275018337]
[955,68.193220209947654,155.13575229669999,278,314,-0.59011847697056496,-0.48582220875167687,0.28669266190701542,0.34823981686205924]
[956,66.345021385320479,140.46873245451278,110,63,-1.2286709526312134,-1.5332320286322403,1.8838376572242626,1.5096323098396935]
[957,65.998474633827485,171.19216310318342,92,744,-1.3309538430280892,0.65398461200357172,-0.87042333262738758,1.7714381322712394]
[958,71.732056793810898,166.46134629439925,710,626,0.55177178027405094,0.3198754692883331,0.17649825715522105,0.30445209750679553]
[959,67.276418676790001,161.98905061000559,186,513,-0.89430783193192032,3.13301469204827E-2,-2.8018795766565414E-2,0.79978649825477188]
[960,71.610127043785425,130.00738042447429,694,7,0.50565804504011258,-2.4770674022166692,-1.2525490600374711,0.25569005851378851]
[961,68.05782941410915,151.65312405222787,262,229,-0.63854461674951268,-0.74357155687532228,0.47480361481079114,0.40773922757978204]
[962,74.532793813216188,166.7535982937145,941,633,{"$f":"_xlfn.NORM.INV((D965-0.375)/(COUNTA($A$4:$A$1003)+(1-2*0.375)),0,1)","v":1.5580550668219622},{"$f":"_xlfn.NORM.INV((E965-0.375)/(COUNTA($A$4:$A$1003)+(1-2*0.375)),0,1)","v":0.33839408174113844},{"$f":"F965*G965","v":0.52723661363934593},{"$f":"F965^2","v":2.4275355912495891}]
[963,75.867124862587389,165.09075729274707,975,599,1.9494878641430031,0.24940277645958905,0.48620768599153913,3.8005029324408484]
[964,71.815451773933574,159.08227108793085,722,426,0.58713845539127341,-0.18779514639904876,-0.11026175218671555,0.34473156579925035]
[965,61.877655199001573,152.08396733094887,4,236,-2.6852209171075958,-0.72063808228481974,1.9350724522155027,7.2104113736721578]
[966,66.379785682903631,150.33862786018673,111,201,-1.2233574916469312,-0.83956966689747226,1.0270938417585411,1.4966035523686714]
[967,65.901947342454605,154.63298294101941,85,298,-1.3747540824203539,-0.53145830867933563,0.73062447949313325,1.8899487871314293]
[968,65.574685680426299,163.58129464849748,67,559,-1.5015371098099821,0.1471302132067954,-0.22092147510425802,2.2546136921365143]
[969,71.752799741851916,175.89650736672533,712,839,0.55761732481429294,0.98796618830859051,0.55090706293161018,0.31093708093304867]
[970,73.13332135243401,152.16529383619647,861,239,1.0821627773931561,-0.71092499311387536,-0.76933656506632175,1.1710762767752696]
[971,72.964746306546573,148.03734757981741,847,156,1.0211714700863885,-1.0127654504812829,-1.0342071839206752,1.0427911713183959]
[972,68.038318517381001,157.17792523673273,258,365,-0.65088423371523274,-0.34636592087527907,0.22544411699397696,0.42365028569906571]
[973,68.762819020043068,148.21777155657355,356,161,-0.37041643238295263,-0.99205702725372924,0.36747422475576397,0.13720833337931451]
[974,65.791081929103797,162.06889297833703,77,518,-1.4282785576164869,4.386909798405618E-2,-6.26572919926041E-2,2.0399796381470323]
[975,65.699545273898138,176.36856795111959,72,846,-1.4639258977221374,1.0169594778287576,-1.4887533165275002,2.1430790340215662]
[976,68.216240483735447,138.40648196607015,282,39,-0.57822944355886741,-1.7669852871805007,1.0217229193830866,0.33434928939839742]
[977,74.587220858248571,172.08428897963017,943,766,1.575152732104,0.72389090053052141,1.1402387297158756,2.4811061294546954]
[978,68.428636847793811,145.5348927737291,310,118,-0.49713305488151405,-1.18709233306086,0.59014283796096911,0.24714127425582647]
[979,67.756280153305298,158.96612397358521,221,424,-0.77027005580476149,-0.19289878008865693,0.14858415410356018,0.59331595886947042]
[980,70.279184098712946,157.59822278867134,535,377,8.6565052452928823E-2,-0.3146047995610225,-2.7233780975943072E-2,7.4935083061783182E-3]
[981,66.8461146376833,161.70316698036402,154,504,-1.0211714700863885,8.7711186724061165E-3,-8.9568161490031269E-3,1.0427911713183959]
[982,69.669277531813009,159.38863900911079,459,437,-0.10418725896788868,-0.15980873616975086,1.665003418064883E-2,1.0854984931241899E-2]
[983,68.884915246787671,164.22129551633441,365,580,-0.34636592087527907,0.20056370562329306,-6.9468432592370288E-2,0.11996935114378007]
[984,66.757432806439581,153.7354942686037,145,279,-1.0599272321129911,-0.58713845539127307,0.62232403788996893,1.1234457373747064]
[985,72.94978173730965,189.24947866394663,846,972,1.0169594778287576,1.9015065829432327,1.9337551416778951,1.0342065795457394]
[986,71.413441301612423,166.77684133938783,674,635,0.4494782032659515,0.34370621971954696,0.15448845409087431,0.20203065521118801]
[987,66.276002573263611,154.27064541676046,108,291,-1.2394032432874145,-0.55177178027405094,0.68386773402612933,1.5361203994713619]
[988,74.474437496857064,184.91105210852731,938,944,1.5332320286322403,1.583877077955373,2.4284510653376215,2.350800453623735]
[989,73.229245627942007,179.50437979620904,868,895,1.1142225957064575,1.2502802219373588,1.3930904742474897,1.2414919927828358]
[990,67.661299683710098,174.30074290262405,211,803,-0.80443687189849689,0.8503127816914382,-0.68402295423917003,0.6471186808698387]
[991,67.995205008986574,140.13194335022001,246,58,-0.68851708009703227,-1.5751527321039993,1.0845195598151085,0.47405576958534318]
[992,71.613955307897157,177.92968103285378,695,878,0.5085078637370497,1.1621151290264078,0.59094468167772451,0.25858024748241792]
[993,66.616217191886477,144.35468838738177,126,104,-1.1474705370891791,-1.2613071658284354,1.447312811007585,1.3166886334877292]
[994,71.281143270425275,159.86075365638786,658,450,0.40554257440712999,-0.12689280208996931,-5.1460433633300599E-2,0.16446477965676257]
[995,67.046078942109119,175.42135129542331,169,832,-0.95978047986829729,0.95978047986829729,-0.92117856953621902,0.92117856953621902]
[996,72.697270897329361,164.5742158186199,819,589,0.90936174074675336,0.22363125835606074,0.20336171038405432,0.82693877553396544]
[997,73.063577091851528,185.76517555171091,855,953,1.0555426685914409,1.668451190943508,1.761121422503078,1.1141703252171404]
[998,70.595973984843269,168.74073257871854,572,678,0.1801488144309788,0.46059565734751534,8.2975761603212239E-2,3.2453595340887237E-2]
[999,72.863123673420617,179.89831295341651,838,903,0.98389181647860702,1.2953451230658557,1.2744794660999694,0.96804310653357295]
[1000,71.912624388221161,159.94124718472298,737,455,0.63241119516909272,-0.11427128538415131,-7.2266440163299611E-2,0.39994391977520027]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(R904:R1003)","v":0}]

{"sheet":"Bivariate Alpha-Trimmed","index":12,"n_rows":1003,"n_cols":17,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[14,11,14,12],[15,11,15,12],[8,11,8,12],[9,11,9,12],[10,11,10,12],[11,11,11,12],[2,15,3,16],[13,15,13,16],[14,15,29,16],[0,0,0,16],[21,11,21,12],[6,11,7,13],[2,11,2,13],[3,11,3,12],[4,11,4,12],[16,11,16,12],[17,11,17,12],[18,11,18,12],[19,11,19,12],[20,11,20,12],[12,11,12,12],[13,11,13,12]]}
["Calculating the Bivariate Alpha-Trimmed Correlation Coefficient"]
[]
["Obs.\nNumber","X","Y","(X-medx)^2","(Y-medy)^2","(X-Xmed)∙(Y-Ymed)","Trimmed\n(X-medx)^2","Trimmed\n(Y-medy)^2","Trimmed\n(X-Xmed)∙(Y-Ymed)",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,"Alpha-Trimmed Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,0.19280730405437674,309.67104800728532,-7.7270201183883396,{"$f":"AND(D4<$N$14,D4>$N$17)*D4","v":0.19280730405437674},{"$f":"AND(E4<$N$15,E4>$N$18)*E4","v":309.67104800728532},{"$f":"AND(F4<$N$16,F4>$N$19)*F4","v":-7.7270201183883396},null,null,"Calculated Alpha-Trimmed Correlation = ",null,{"$f":"N22/(SQRT(N20*N21))","v":0.46778412027752542}]
[2,75.900421131737588,148.6347709869498,34.469524680933013,168.25453853505567,-76.155459218056691,0,168.25453853505567,0,null,null,"VBA Alpha-Trimmed Correlation = ",null,{"$f":"bvtcorr(B4:B1003,C4:C1003,N9)","v":0.46778412027752542},null,"U1(0,1), U2(0,1)",{"$f":"bvtcorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003,N9)","v":2.1623181954868648E-2}]
[3,68.70319256856132,148.28328151641921,1.7586825897711211,177.49663181365236,17.668056942224442,1.7586825897711211,177.49663181365236,17.668056942224442,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"bvtcorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003,N9)","v":-2.651371221549401E-2}]
[4,70.30671508908884,161.11898050586314,7.6933681427717934E-2,0.23725393908819434,-0.13510299392419969,7.6933681427717934E-2,0,-0.13510299392419969,null,null,"Intermediate Calculations for\nthe Alpha-Trimmed Correlation",null,null,null,"X, Y (Correlated)",{"$f":"bvtcorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003,N9)","v":0.46778412027752542}]
[5,67.375076704515038,167.57356788815855,7.0451448245691211,35.611058441814315,-15.83935175689891,7.0451448245691211,35.611058441814315,-15.83935175689891,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"bvtcorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003,N9)","v":0.4562855114108606}]
[6,70.303701168768001,166.7573260094741,7.5270827716512556E-2,26.535462124434698,1.4132749902076269,7.5270827716512556E-2,26.535462124434698,1.4132749902076269,null,null,"alpha (% of Obs to be trimmed) = ",null,0.1,null,"(X, Y) with duplicates",{"$f":"bvtcorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003,N9)","v":0.46778412547229831}]
[7,72.04643599739471,158.14029467085311,4.068652565523557,12.011582720841389,-6.9907765558019195,4.068652565523557,12.011582720841389,-6.9907765558019195,null,null,"# of Observations =",null,1000,null,"Ranks of (X, Y) with duplicates",{"$f":"bvtcorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003,N9)","v":0.45630922086995351}]
[8,69.659038619402779,151.45915754274174,0.13712746287579533,102.95978583104906,3.7574744455880227,0.13712746287579533,102.95978583104906,3.7574744455880227,null,null,"# of Observations to be Trimmed =",null,50]
[9,74.291448615158941,185.99290055062283,18.165519775406565,594.71761626412047,103.93918711933692,18.165519775406565,594.71761626412047,103.93918711933692,null,null,"Median(X) =",null,70.029345874092442]
[10,65.649488474075483,147.60307841115861,19.183150844483318,196.0837091497869,61.331096278854794,19.183150844483318,196.0837091497869,61.331096278854794,null,null,"Median(Y) =",null,161.60606770451261]
[11,69.742697145918896,154.65949081048038,8.2167493363511424E-2,48.254930544702511,1.9912274318340806,8.2167493363511424E-2,48.254930544702511,1.9912274318340806,null,null,"Upper Trim Cutoff for (X-medx)2 = ",null,{"$f":"_xlfn.PERCENTILE.INC(D$4:D$1003,(1000-$N$11)/999)","v":34.004189373552066},null,"Notes:"]
[12,69.923511910794829,155.01069183161337,1.1200827787280465E-2,43.498982904821411,0.69801476806637952,0,43.498982904821411,0.69801476806637952,null,null,"Upper Trim Cutoff for (Y-medy)2 = ",null,{"$f":"_xlfn.PERCENTILE.INC(E$4:E$1003,(1000-$N$11)/999)","v":731.15980051699989}]
[13,71.272442551537864,167.92486667662297,1.5452893494758475,39.927220449942915,7.854878007675933,1.5452893494758475,39.927220449942915,7.854878007675933,null,null,"Upper Trim of (X-Xmed)∙(Y-Ymed) = ",null,{"$f":"_xlfn.PERCENTILE.INC(F$4:F$1003,(1000-$N$11)/999)","v":112.65452327012295}]
[14,68.209184553223238,170.8602725769386,3.3129872339883248,85.640307820832874,-16.844145764189108,3.3129872339883248,85.640307820832874,-16.844145764189108,null,null,"Lower Trim Cutoff for (X-medx)2 = ",null,{"$f":"_xlfn.PERCENTILE.INC($D$4:$D$1003,($N$11-1)/999)","v":3.6477098488472387E-2}]
[15,71.98267048709441,177.2631871840758,3.8154770437592869,245.14539039731719,30.583436848143343,3.8154770437592869,245.14539039731719,30.583436848143343,null,null,"Lower Trim Cutoff for (Y-medy)2 = ",null,{"$f":"_xlfn.PERCENTILE.INC(E$4:E$1003,($N$11-1)/999)","v":0.42761489642463085}]
[16,64.969503845277544,170.46052364202347,25.602001356561669,78.401389949321384,-44.802148294907091,25.602001356561669,78.401389949321384,0,null,null,"Lower Trim of (X-Xmed)∙(Y-Ymed) = ",null,{"$f":"_xlfn.PERCENTILE.INC(F$4:F$1003,($N$11-1)/999)","v":-30.061577241029028}]
[17,67.564203137894168,158.22159030710421,6.0769287098311136,11.454687253568361,8.3432198720485644,6.0769287098311136,11.454687253568361,8.3432198720485644,null,null,"Sum of trimmed (X-medx)2 = ",null,6372.1604607558656]
[18,72.348110751484867,168.08445955367756,5.3766705566287083,41.969560951326862,15.021867481829052,5.3766705566287083,41.969560951326862,15.021867481829052,null,null,"Sum of trimmed (Y-medy)2 = ",null,140129.63249975679]
[19,73.399997728692298,186.43821871981902,11.361293924917451,616.63572404698311,83.700535873446242,11.361293924917451,616.63572404698311,83.700535873446242,null,null,"Sum of Trimmed (X-Xmed)∙(Y-Ymed) = ",null,13978.282655536088]
[20,70.630878832697576,145.0970574458735,0.36184190028824548,272.54741971985129,-9.9307137845216857,0.36184190028824548,272.54741971985129,-9.9307137845216857]
[21,70.119676553511951,138.10299892045091,8.1596316443900887E-3,552.39424226833535,-2.1230481717077438,0,552.39424226833535,-2.1230481717077438]
[22,66.187165277180767,144.01836436558077,14.762351739284552,309.32730873827438,67.575132513082607,14.762351739284552,309.32730873827438,67.575132513082607]
[23,73.781440690017263,194.19555847709682,14.078215507689913,1062.0749088163516,122.278859381443,14.078215507689913,0,0]
[24,67.094982124804702,159.50283587727762,8.6104906131340062,4.4235841190942455,6.1716472301865783,8.6104906131340062,4.4235841190942455,6.1716472301865783]
[25,69.938280213559452,159.32747874166122,8.2929545283098594E-3,5.1919676616281603,0.20750120898524327,0,5.1919676616281603,0.20750120898524327]
[26,69.152185366445423,169.67875714103042,0.76941055617557685,65.168314738466165,-7.0810443642126897,0.76941055617557685,65.168314738466165,-7.0810443642126897]
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[975,65.699545273898138,176.36856795111959,18.747173237442951,217.93141353107103,-63.91868242812744,18.747173237442951,217.93141353107103,0]
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[995,67.046078942109119,175.42135129542331,8.8998815874651882,190.86206069728632,-41.214678692735696,8.8998815874651882,190.86206069728632,0]
[996,72.697270897329361,164.5742158186199,7.1178239296137118,8.8099032272786832,7.9187966263003169,7.1178239296137118,8.8099032272786832,7.9187966263003169]
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{"sheet":"Univariate Alpha-Winsorized","index":13,"n_rows":1007,"n_cols":18,"rows_kept":1007,"cut":false,"hidden":false,"merged":[[18,7,18,8],[19,7,19,8],[20,7,20,8],[21,7,21,8],[0,0,0,13],[5,7,5,8],[6,7,6,8],[15,7,15,8],[16,7,16,8],[17,7,17,8],[13,7,14,9],[4,7,4,9],[4,12,5,13],[15,12,15,13],[16,12,31,13]]}
["Calculating the Univariate Alpha-Winsorized Pearson Correlation Coefficient"]
[]
[]
[]
["Observation\nNumber","X","Y","Winsorized\nX","Winsorized\nY",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Alpha-Trimmed Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,{"$f":"IF($B6>$J$20,$J$20,IF($B6<$J$19,$J$19,$B6))","v":69.5902475889052},{"$f":"IF($C6>$J$22,$J$22,IF($C6<$J$21,$J$21,$C6))","v":179.20354047781973},null,null,"Calculated Winsorized =",null,{"$f":"CORREL(D6:D1005,E6:E1005)","v":0.46265286898467034}]
[2,75.900421131737588,148.6347709869498,74.743989925406638,148.6347709869498,null,null,"VBA Winsorized = ",null,{"$f":"UVWCorr(B6:B1005,C6:C1005,J16)","v":0.46265286898467034},null,null,"U1(0,1), U2(0,1)",{"$f":"UVWCorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003,J16)","v":1.8500969835349931E-2}]
[3,68.70319256856132,148.28328151641921,68.70319256856132,148.28328151641921,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"UVWCorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003,J16)","v":-2.2571911874744971E-2}]
[4,70.30671508908884,161.11898050586314,70.30671508908884,161.11898050586314,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"UVWCorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003,J16)","v":0.46265286898467034}]
[5,67.375076704515038,167.57356788815855,67.375076704515038,167.57356788815855,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"UVWCorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003,J16)","v":0.44503848127878531}]
[6,70.303701168768001,166.7573260094741,70.303701168768001,166.7573260094741,null,null,null,null,null,null,null,"(X, Y) with duplicates",{"$f":"UVWCorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003,J16)","v":0.46265293303142091}]
[7,72.04643599739471,158.14029467085311,72.04643599739471,158.14029467085311,null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"UVWCorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003,J16)","v":0.44506055844077563}]
[8,69.659038619402779,151.45915754274174,69.659038619402779,151.45915754274174]
[9,74.291448615158941,185.99290055062283,74.291448615158941,185.59305559336852,null,null,"Intermediate Calculations for\nthe Alpha-Winsorized Correlation"]
[10,65.649488474075483,147.60307841115861,65.649488474075483,147.60307841115861]
[11,69.742697145918896,154.65949081048038,69.742697145918896,154.65949081048038,null,null,"Alpha-Winsorizing Factor =",null,0.1,null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,69.923511910794829,155.01069183161337,null,null,"Sample Size = ",null,{"$f":"COUNT(A6:A1005)","v":1000}]
[13,71.272442551537864,167.92486667662297,71.272442551537864,167.92486667662297,null,null,"Number of Obs to Winsorize = ",null,{"$f":"FLOOR(J16*J17,2)","v":100}]
[14,68.209184553223238,170.8602725769386,68.209184553223238,170.8602725769386,null,null,"Lower X Cutoff Value = ",null,{"$f":"SMALL($B$6:$B$1005,$J$18/2+1)","v":65.080364936359004}]
[15,71.98267048709441,177.2631871840758,71.98267048709441,177.2631871840758,null,null,"Upper X Cutoff Value = ",null,{"$f":"LARGE($B$6:$B$1005,$J$18/2+1)","v":74.743989925406638}]
[16,64.969503845277544,170.46052364202347,65.080364936359004,170.46052364202347,null,null,"Lower Y Cutoff Value = ",null,{"$f":"SMALL($C$6:$C$1005,$J$18/2+1)","v":139.47275443564163}]
[17,67.564203137894168,158.22159030710421,67.564203137894168,158.22159030710421,null,null,"Upper Y Cutoff Value = ",null,{"$f":"LARGE($C$6:$C$1005,$J$18/2+1)","v":185.59305559336852}]
[18,72.348110751484867,168.08445955367756,72.348110751484867,168.08445955367756]
[19,73.399997728692298,186.43821871981902,73.399997728692298,185.59305559336852]
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[961,68.05782941410915,151.65312405222787,{"$f":"IF($B966>$J$20,$J$20,IF($B966<$J$19,$J$19,$B966))","v":68.05782941410915},{"$f":"IF($C966>$J$22,$J$22,IF($C966<$J$21,$J$21,$C966))","v":151.65312405222787}]
[962,74.532793813216188,166.7535982937145,74.532793813216188,166.7535982937145]
[963,75.867124862587389,165.09075729274707,74.743989925406638,165.09075729274707]
[964,71.815451773933574,159.08227108793085,71.815451773933574,159.08227108793085]
[965,61.877655199001573,152.08396733094887,65.080364936359004,152.08396733094887]
[966,66.379785682903631,150.33862786018673,66.379785682903631,150.33862786018673]
[967,65.901947342454605,154.63298294101941,65.901947342454605,154.63298294101941]
[968,65.574685680426299,163.58129464849748,65.574685680426299,163.58129464849748]
[969,71.752799741851916,175.89650736672533,71.752799741851916,175.89650736672533]
[970,73.13332135243401,152.16529383619647,73.13332135243401,152.16529383619647]
[971,72.964746306546573,148.03734757981741,72.964746306546573,148.03734757981741]
[972,68.038318517381001,157.17792523673273,68.038318517381001,157.17792523673273]
[973,68.762819020043068,148.21777155657355,68.762819020043068,148.21777155657355]
[974,65.791081929103797,162.06889297833703,65.791081929103797,162.06889297833703]
[975,65.699545273898138,176.36856795111959,65.699545273898138,176.36856795111959]
[976,68.216240483735447,138.40648196607015,68.216240483735447,139.47275443564163]
[977,74.587220858248571,172.08428897963017,74.587220858248571,172.08428897963017]
[978,68.428636847793811,145.5348927737291,68.428636847793811,145.5348927737291]
[979,67.756280153305298,158.96612397358521,67.756280153305298,158.96612397358521]
[980,70.279184098712946,157.59822278867134,70.279184098712946,157.59822278867134]
[981,66.8461146376833,161.70316698036402,66.8461146376833,161.70316698036402]
[982,69.669277531813009,159.38863900911079,69.669277531813009,159.38863900911079]
[983,68.884915246787671,164.22129551633441,68.884915246787671,164.22129551633441]
[984,66.757432806439581,153.7354942686037,66.757432806439581,153.7354942686037]
[985,72.94978173730965,189.24947866394663,72.94978173730965,185.59305559336852]
[986,71.413441301612423,166.77684133938783,71.413441301612423,166.77684133938783]
[987,66.276002573263611,154.27064541676046,66.276002573263611,154.27064541676046]
[988,74.474437496857064,184.91105210852731,74.474437496857064,184.91105210852731]
[989,73.229245627942007,179.50437979620904,73.229245627942007,179.50437979620904]
[990,67.661299683710098,174.30074290262405,67.661299683710098,174.30074290262405]
[991,67.995205008986574,140.13194335022001,67.995205008986574,140.13194335022001]
[992,71.613955307897157,177.92968103285378,71.613955307897157,177.92968103285378]
[993,66.616217191886477,144.35468838738177,66.616217191886477,144.35468838738177]
[994,71.281143270425275,159.86075365638786,71.281143270425275,159.86075365638786]
[995,67.046078942109119,175.42135129542331,67.046078942109119,175.42135129542331]
[996,72.697270897329361,164.5742158186199,72.697270897329361,164.5742158186199]
[997,73.063577091851528,185.76517555171091,73.063577091851528,185.59305559336852]
[998,70.595973984843269,168.74073257871854,70.595973984843269,168.74073257871854]
[999,72.863123673420617,179.89831295341651,72.863123673420617,179.89831295341651]
[1000,71.912624388221161,159.94124718472298,71.912624388221161,159.94124718472298]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(R906:R1005)","v":1}]

{"sheet":"Median Correlation Coefficient","index":14,"n_rows":1005,"n_cols":16,"rows_kept":1005,"cut":false,"hidden":false,"merged":[[2,14,3,15],[13,14,13,15],[14,14,29,15],[0,0,0,15],[13,9,13,10],[14,9,14,10],[15,9,15,10],[3,9,3,10],[4,9,4,10],[10,9,10,10],[11,9,11,10],[12,9,12,10],[2,9,2,11],[8,9,9,11]]}
["Calculating the Median Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","|X-Xmed|","|Y-Ymed|","|u|","|v|",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Median Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,0.43909828518724225,17.597472773307118,{"$f":"ABS(($B4-$L$11)/(SQRT(2)*$L$13)+($C4-$L$12)/(SQRT(2)*$L$14))","v":1.1649291158623063},{"$f":"ABS(($B4-$L$11)/(SQRT(2)*$L$13)-($C4-$L$12)/(SQRT(2)*$L$14))","v":1.4757782857750756},null,null,"Calculated Median Correlation = ",null,{"$f":"(L15^2-L16^2)/(L15^2+L16^2)","v":0.46942908792741195}]
[2,75.900421131737588,148.6347709869498,5.8710752576451455,12.971296717562808,1.1048962437629331,3.0513916122831417,null,null,"VBA Median Correlation = ",null,{"$f":"medcorr(B4:B1003,C4:C1003)","v":0.46942908792741195},null,null,"U1(0,1), U2(0,1)",{"$f":"medcorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":4.5616848833694545E-2}]
[3,68.70319256856132,148.28328151641921,1.3261533055311219,13.322786188093403,1.4690295643814801,0.53021092603121245,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"medcorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-3.3998232284133748E-2}]
[4,70.30671508908884,161.11898050586314,0.27736921499639777,0.48708719864947625,6.1631887328624402E-2,0.13472504037884855,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"medcorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.46942908792741195}]
[5,67.375076704515038,167.57356788815855,2.6542691695774039,5.9675001836459387,0.49176657812210617,1.3872600451232069,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"medcorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.5991544461343119}]
[6,70.303701168768001,166.7573260094741,0.27435529467555853,5.1512583049614875,0.48361504211257911,0.2893917474925517,null,null,"Intermediate Calculations for\nthe Median Correlation",null,null,null,null,"(X, Y) with duplicates",{"$f":"medcorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.46941081119530359}]
[7,72.04643599739471,158.14029467085311,2.0170901233022676,3.4657730336595023,0.45393548112174759,0.97401541647827927,null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"medcorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.5991544461343119}]
[8,69.659038619402779,151.45915754274174,0.37030725468966352,10.146910161770876,0.89240660171992048,0.63025640296914942,null,null,"Median of X = ",null,70.029345874092442]
[9,74.291448615158941,185.99290055062283,4.2621027410664993,24.386832846110224,3.3383923447958566,0.32113824967111193,null,null,"Median of Y = ",null,161.60606770451261]
[10,65.649488474075483,147.60307841115861,4.3798574000169594,14.002989293354005,2.6009643265820905,0.49965137395749371,null,null,"MAD of X = ",null,1.9976850840580553]
[11,69.742697145918896,154.65949081048038,0.28664872817354592,6.9465768940322334,0.62267078036216383,0.41974464237621967,null,null,"MAD of Y = ",null,9.4242113473348752,null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,0.10583396329761285,6.5953758728992398,0.5323181094954863,0.45739547656920926,null,null,"Median of |u| = ",null,1.1860672811606083]
[13,71.272442551537864,167.92486667662297,1.243096677445422,6.3187989721103577,0.91411532602518575,3.4094648785570059E-2,null,null,"Median of |v| = ",null,0.71269994884293619]
[14,68.209184553223238,170.8602725769386,1.8201613208692038,9.2542048724259871,5.0081125606679211E-2,1.3386209691595923]
[15,71.98267048709441,177.2631871840758,1.9533246130019677,15.657119479563192,1.8661721159742211,0.48336249224061334]
[16,64.969503845277544,170.46052364202347,5.0598420288148986,8.8544559375108634,1.1266397724512993,2.4553548460796124]
[17,67.564203137894168,158.22159030710421,2.4651427361982741,3.3844773974084035,1.1265098205653963,0.61862924992075308]
[18,72.348110751484867,168.08445955367756,2.3187648773924252,6.4783918491649501,1.3068365562233835,0.334677796429938]
[19,73.399997728692298,186.43821871981902,3.3706518545998563,24.832151015306408,3.0562642461151022,0.67009156812227144]
[20,70.630878832697576,145.0970574458735,0.60153295860513367,16.509010258639108,1.0257649472780428,1.4516058743903919]
[21,70.119676553511951,138.10299892045091,9.0330679419508897E-2,23.503068784061696,1.731481984111843,1.7954294365671337]
[22,66.187165277180767,144.01836436558077,3.8421805969116747,17.587703338931846,2.6796108003547721,4.0369417048370382E-2]
[23,73.781440690017263,194.19555847709682,3.7520948159248206,32.589490772584213,3.7733209293673822,1.1171147944085973]
[24,67.094982124804702,159.50283587727762,2.9343637492877406,2.1032318272349926,1.1964637688516584,0.88084913912122209]
[25,69.938280213559452,159.32747874166122,9.1065660532990478E-2,2.2785889628513871,0.20319839581146379,0.13873063098708735]
[26,69.152185366445423,169.67875714103042,0.87716050764701947,8.0726894365178055,0.29521847376484289,0.91618335766564973]
[27,69.979041938513163,169.26417290074878,5.0303935579279369E-2,7.6581051962361641,0.55678856289471534,0.59240003564618937]
[28,65.231388920735938,150.1850862026223,4.7979569533565041,11.42098150189031,2.5552258433329791,0.84137347518196703]
[29,69.189918454669353,162.13540998077724,0.83942741942308885,0.52934227626462871,0.2574093097415161,0.33684333330493976]
[30,70.721846699211568,179.8605006679764,0.69250082511912581,18.254432963463785,1.6147657262667989,1.1245262652759767]
[31,73.086466808676647,167.34548500243301,3.057120934584205,5.7394172979203972,1.5127414424049737,0.65147449032912164]
[32,72.420047763828379,176.77910111575324,2.3907018897359364,15.173033411240624,1.9846661283598328,0.29222568164661411]
[33,64.432162861783951,134.40751922342531,5.5971830123084914,27.1985484810873,4.0219269520171661,5.9534585843336929E-2]
[34,70.274805760558294,157.56549297529213,0.24545988646585215,4.0405747292204808,0.21628409987095543,0.39005157865365236]
[35,68.139313698476599,139.42832188855618,1.8900321756158434,22.177745815956428,2.3330171996292295,0.99501394906294827]
[36,74.470459052628982,176.30621399227613,4.4411131785365399,14.700146287763516,2.674954907271359,0.46902536231237968]
[37,66.394209385680298,143.0109075725224,3.6351364884121438,18.595160131990212,2.6819151885364043,0.10850691512289568]
[38,71.518807312755527,168.23805683123777,1.4894614386630849,6.6319891267251592,1.0248182876113741,2.9610452933730491E-2]
[39,71.110333645128406,154.63128579463387,1.0809877710359643,6.9747819098787431,0.14069418874439305,0.90595372777697025]
[40,69.828091828731687,178.51054410827797,0.20125404536075564,16.904476403765358,1.1971210765906064,1.3395940833237132]
[41,71.003847780521227,174.76476874014267,0.97450190642878454,13.15870103563006,1.3322464974330981,0.64237108932799725]
[42,68.1622931523939,165.52786009697638,1.867052721698542,3.9217923924637716,0.36661224967905676,0.95512324394939951]
[43,69.415685455940761,142.51469910413542,0.6136604181516816,19.091368600377194,1.6496551417500072,1.2152288685764965]
[44,70.859628547228837,175.83772864987318,0.83028267313639503,14.231660945360574,1.3617033283102069,0.77392449053281398]
[45,68.009080122378336,170.53613457786034,2.0202657517141063,8.9300668733477266,4.5068812889502818E-2,1.3851301951884563]
[46,71.794560651216031,161.16549604869812,1.7652147771235889,0.44057165581449453,0.59176439862350716,0.65787734833215616]
[47,67.756412972341224,154.8749645974199,2.2729329017512185,6.7311031070927072,1.3095748742647051,0.29949382313524597]
[48,68.650601790017191,159.3540303641403,1.378744084075251,2.2520373403723113,0.65699683559988586,0.31905219149703257]
[49,71.657131082103163,187.63602188388052,1.6277852080107209,26.029954179367905,2.5292260000218039,1.3768742423950391]
[50,68.959977085019389,167.85438772308584,1.069368789073053,6.2483200185732244,9.02998113880219E-2,0.84733396895079383]
[51,68.442374616495457,163.80167125809115,1.5869712575969857,2.1956035535785361,0.39699120098927076,0.72646729279438749]
[52,72.648912335845125,164.46518267301462,2.619566461752683,2.8591149685020127,1.1417517189517363,0.7127079490470084]
[53,64.166896838800838,157.77140207039417,5.8624490352916041,3.8346656341184371,2.3628088643335743,1.7873722631085891]
[54,69.536771215104523,160.63787952561177,0.49257465898791963,0.96818817890084574,0.24699724923422633,0.1017092454886296]
[55,68.527943015374262,142.84776624718435,1.5014028587181798,18.758301457328258,1.9388928796748841,0.87601049529438402]
[56,68.51182490133948,133.19711497110532,1.5175209727529619,28.40895273340729,2.668694863247886,1.5944020440347042]
[57,70.280391459192344,179.51517039635146,0.25104558509990227,17.909102691838854,1.432596435409077,1.25487469435219]
[58,68.951489511797746,154.59362077552515,1.0778563622946962,7.0124469289874583,0.90767136384035529,0.14462863102342011]
[59,76.136784956699003,167.10277102493976,6.107439082606561,5.4967033204271445,2.5742304324192942,1.7493855623721464]
[60,72.688035466243065,162.41746850306819,2.6586895921506226,0.81140079855558156,1.001958086288643,0.88019786980515247]
[61,71.298523340915253,165.1235083392898,1.2691774668228106,3.5174406347771878,0.71315860813195087,0.18532534259818623]
[62,73.963927281617615,175.8806819278384,3.9345814075251724,14.274614223325784,2.4637333162173469,0.32165985370102712]
[63,68.344540439240092,174.45744958845057,1.6848054348523505,12.851381883937961,0.36789143552292758,1.5606093042913018]
[64,69.957820123806584,161.43502210065782,7.1525750285857725E-2,0.17104560385479317,3.8151175994835008E-2,1.2483774889261216E-2]
[65,71.614451687242948,154.64146323085288,1.5851058131505056,6.9646044736597332,{"$f":"ABS(($B68-$L$11)/(SQRT(2)*$L$13)+($C68-$L$12)/(SQRT(2)*$L$14))","v":3.850861205338818E-2},{"$f":"ABS(($B68-$L$11)/(SQRT(2)*$L$13)-($C68-$L$12)/(SQRT(2)*$L$14))","v":1.083629284776767}]
[66,72.772605588350714,185.80687969088467,2.7432597142582722,24.200811986372059,2.7868206698156643,0.84479531057588708]
[67,67.591612056114627,168.3994951627237,2.437733817977815,6.7934274582110845,0.35315101402864946,1.3725845657938924]
[68,70.625426373375404,181.36657414654795,0.59608049928296225,19.760506442035336,1.6936384941261298,1.2716575056914219]
[69,70.565968480146978,152.49502206578686,0.53662260605453582,9.1110456387257557,0.49366509073340314,0.87355428018297732]
[70,70.668860911057024,160.93867359067352,0.6395150369645819,0.66739411383909442,0.17628955597125512,0.2764398786299393]
[71,69.85923457942225,173.28389861247075,0.17011129467019259,11.677830907958139,0.81598469943713825,0.93641093776432038]
[72,72.802644538910101,153.65404410185471,2.7732986648176592,7.9520236026579028,0.3849981061590223,1.5782926124807681]
[73,69.226041710772179,159.7414200297961,0.80330416332026289,1.8646476747165082,0.42424616045852986,0.14443388403104124]
[74,66.619838657451766,177.71154978949872,3.4095072166406766,16.105482084986107,1.5686377635113491E-3,2.4152480436222881]
[75,66.122648506831055,170.86176001047457,3.9066973672613869,9.2556923059619578,0.68836401314560125,2.077289314777909]
[76,75.298482284810035,167.9362434322129,5.2691364107175929,6.3301757277002935,2.3400383902636608,1.3901211997020995]
[77,78.776806264444375,177.53874289601023,8.7474603903519323,15.932675191497623,4.2917205808927337,1.9008356028013527]
[78,76.093564133764687,178.34848587336288,6.0642182596722449,16.742418168850264,3.4027076309638247,0.89031121192493967]
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[949,68.005617591003997,148.32134224269456,2.0237282830884453,13.284725461818056,1.7130896281184698,0.28043940344545792]
[950,71.624995487172498,174.24375688216597,1.5956496130800559,12.637689177653357,1.5130178845319251,0.38341575573732622]
[951,74.973795398985601,193.23656188137949,4.9444495248931588,31.630494176866875,4.1234161347490579,0.62311089025642752]
[952,71.873045801006441,168.03200020950018,1.8436999269139989,6.4259325049875713,1.1347450290961969,0.17045840982195021]
[953,68.336302393893561,187.04256961076453,1.693043480198881,25.43650190625192,1.3092479822010099,2.5077977789091177]
[954,66.726307931796228,133.8178904718269,3.3030379422962142,27.788177232685712,3.2541246372420343,0.9158176176294901]
[955,68.193220209947654,155.13575229669999,1.8361256641447881,6.4703154078126204,1.135394107491527,0.16444731254853118]
[956,66.345021385320479,140.46873245451278,3.6843244887719635,21.137335249999836,2.8900675371089704,0.2818377906965428]
[957,65.998474633827485,171.19216310318342,4.0308712402649576,9.5860953986708068,0.70752654901919543,2.1460327139765818]
[958,71.732056793810898,166.46134629439925,1.7027109197184558,4.8552785898866375,0.96699259422889627,0.23840103596983975]
[959,67.276418676790001,161.98905061000559,2.7529271973024407,0.38298290549298031,0.94569907098473061,1.003170152557874]
[960,71.610127043785425,130.00738042447429,1.5807811696929832,31.59868728003832,1.8113388290833314,2.9304151976081179]
[961,68.05782941410915,151.65312405222787,1.9715164599832917,9.9529436522847448,{"$f":"ABS(($B964-$L$11)/(SQRT(2)*$L$13)+($C964-$L$12)/(SQRT(2)*$L$14))","v":1.4446220804901029},{"$f":"ABS(($B964-$L$11)/(SQRT(2)*$L$13)-($C964-$L$12)/(SQRT(2)*$L$14))","v":4.8933972088960553E-2}]
[962,74.532793813216188,166.7535982937145,4.5034479391237454,5.1475305892018923,1.9802780401826288,1.2078306380943518]
[963,75.867124862587389,165.09075729274707,5.8377789884949465,3.4846895882344597,2.327817571010983,1.8048989845411312]
[964,71.815451773933574,159.08227108793085,1.7861058998411323,2.5237966165817625,0.44285290267408073,0.8215782168989797]
[965,61.877655199001573,152.08396733094887,8.1516906750908689,9.5221003735637453,3.5998490837388837,2.1709461236646734]
[966,66.379785682903631,150.33862786018673,3.6495601911888116,11.267439844325878,2.1372154149319544,0.44640377523173946]
[967,65.901947342454605,154.63298294101941,4.1273985316378372,6.9730847634932047,1.9841433495176355,0.93775010973762529]
[968,65.574685680426299,163.58129464849748,4.4546601936661432,1.9752269439848646,1.4285822810537654,1.7249882751466414]
[969,71.752799741851916,175.89650736672533,1.7234538677594742,14.290439662212719,1.6822631807559265,0.46218507467192316]
[970,73.13332135243401,152.16529383619647,3.1039754783415674,9.4407738683161426,0.39034326380832673,1.8070422269152902]
[971,72.964746306546573,148.03734757981741,2.9354004324541307,13.568720124695204,2.0950519005689783E-2,2.0570962841168781]
[972,68.038318517381001,157.17792523673273,1.9910273567114416,4.4281424677798782,1.0369975755208944,0.37250280739098285]
[973,68.762819020043068,148.21777155657355,1.2665268540493742,13.388296147939059,1.4528392708028399,0.55623175823741033]
[974,65.791081929103797,162.06889297833703,4.2382639449886454,0.4628252738244214,1.4654628105032388,1.534915176874101]
[975,65.699545273898138,176.36856795111959,4.3298006001943037,14.762500246606976,0.42494634653885455,2.6402328351203908]
[976,68.216240483735447,138.40648196607015,1.8131053903569949,23.199585738442465,2.3824574960677469,1.0989127304203352]
[977,74.587220858248571,172.08428897963017,4.557874984156129,10.478221275117562,2.3995095676543374,0.82712944048240711]
[978,68.428636847793811,145.5348927737291,1.600709026298631,16.071174930783513,1.7724261549721967,0.63924233512506012]
[979,67.756280153305298,158.96612397358521,2.2730657207871445,2.6399437309273992,1.0026586379441884,0.60650408552796331]
[980,70.279184098712946,157.59822278867134,0.24983822462050398,4.0078449158412752,0.21227858338825259,0.38914560235792739]
[981,66.8461146376833,161.70316698036402,3.1832312364091422,9.7099275851405764E-2,1.1194609150362096,1.1340318014207238]
[982,69.669277531813009,159.38863900911079,0.3600683422794333,2.2174286954018214,0.29382650761338391,3.8924702971399688E-2]
[983,68.884915246787671,164.22129551633441,1.1444306273047715,2.6152278118217964,0.20886337954979933,0.60130901811451731]
[984,66.757432806439581,153.7354942686037,3.2719130676528607,7.8705734359089092,1.7486724293113338,0.56760047681702841]
[985,72.94978173730965,189.24947866394663,2.9204358632172074,27.643410959434021,3.1078356843580681,1.0403826915106102]
[986,71.413441301612423,166.77684133938783,1.3840954275199806,5.1707736348752178,0.87788633859318432,0.10195104460492682]
[987,66.276002573263611,154.27064541676046,3.7533433008288313,7.3354222877521522,1.8789281048020654,0.77816186530058717]
[988,74.474437496857064,184.91105210852731,4.4450916227646218,23.304984404014704,3.3219916240679295,0.17519490967544771]
[989,73.229245627942007,179.50437979620904,3.1998997538495644,17.898312091696425,2.4755723348926155,0.21027953862479798]
[990,67.661299683710098,174.30074290262405,2.3680461903823442,12.69467519811144,0.11429158880322932,1.7906934729088659]
[991,67.995205008986574,140.13194335022001,2.0341408651058686,21.474124354292599,2.3312330255948255,0.89121146155212216]
[992,71.613955307897157,177.92968103285378,1.5846094338047152,16.323613328341168,1.7856681662145677,0.66388166931651416]
[993,66.616217191886477,144.35468838738177,3.413128682205965,17.251379317130841,2.5025075755906263,8.6264439462764964E-2]
[994,71.281143270425275,159.86075365638786,1.251797396332833,1.7453140481247544,0.31213763961454721,0.57404250427532599]
[995,67.046078942109119,175.42135129542331,2.9832669319833229,13.815283590910695,1.939362148618784E-2,2.0925391296057154]
[996,72.697270897329361,164.5742158186199,2.6679250232369185,2.9681481141072936,1.1670497165338434,0.72164424297241681]
[997,73.063577091851528,185.76517555171091,3.0342312177590856,24.1591078471983,2.886684743846418,0.7386730408136355]
[998,70.595973984843269,168.74073257871854,0.56662811075082686,7.1346648742059244,0.73588555207642203,0.33475468042879863]
[999,72.863123673420617,179.89831295341651,2.8337777993281748,18.292245248903896,2.3755358249938885,0.36943034393337992]
[1000,71.912624388221161,159.94124718472298,1.8832785141287189,1.6648205197896289,0.54169814557829543,0.79152401123753036]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(O904:O1003)","v":0}]

{"sheet":"MAD Correlation (Gideon)","index":15,"n_rows":1003,"n_cols":16,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[2,14,3,15],[13,14,13,15],[14,14,29,15],[0,0,0,10],[3,9,3,10],[4,9,4,10],[10,9,10,10],[11,9,11,10],[2,9,2,11],[8,9,9,11],[13,9,13,10],[14,9,14,10],[15,9,15,10],[12,9,12,10]]}
["Calculating the MAD-G Correlation Coefficient (Gideon)"]
[]
["Observation\nNumber","X","Y","|X-Xmed|","|Y-Ymed|","|X()+Y()|","|X() - Y()|",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"MAD-G Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[{"$f":"'Simulated Data'!A4","v":1},{"$f":"'Simulated Data'!F4","v":69.5902475889052},{"$f":"'Simulated Data'!G4","v":179.20354047781973},{"$f":"ABS(B4-$L$11)","v":0.43909828518724225},{"$f":"ABS(C4-$L$12)","v":17.597472773307118},{"$f":"ABS(($B4-$L$11)/$L$13+($C4-$L$12)/$L$14)","v":1.6474585548557723},{"$f":"ABS(($B4-$L$11)/$L$13-($C4-$L$12)/$L$14)","v":2.087065666798829},null,null,"Calculated MAD-G Correlation = ",null,{"$f":"0.5*(L15-L16)","v":0.33472125067401182}]
[{"$f":"'Simulated Data'!A5","v":2},{"$f":"'Simulated Data'!F5","v":75.900421131737588},{"$f":"'Simulated Data'!G5","v":148.6347709869498},{"$f":"ABS(B5-$L$11)","v":5.8710752576451455},{"$f":"ABS(C5-$L$12)","v":12.971296717562808},{"$f":"ABS(($B5-$L$11)/$L$13+($C5-$L$12)/$L$14)","v":1.5625592529446291},{"$f":"ABS(($B5-$L$11)/$L$13-($C5-$L$12)/$L$14)","v":4.3153194022023245},null,null,"VBA MAD-G Correlation = ",null,{"$f":"MADCorr_G(B4:B1003,C4:C1003)","v":0.33472125067401182},null,null,"U1(0,1), U2(0,1)",{"$f":"MADCorr_G('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":2.6829437615448759E-2}]
[{"$f":"'Simulated Data'!A6","v":3},{"$f":"'Simulated Data'!F6","v":68.70319256856132},{"$f":"'Simulated Data'!G6","v":148.28328151641921},1.3261533055311219,13.322786188093403,2.0775215334753288,0.7498314825117387,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"MADCorr_G('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-2.2737159365861515E-2}]
[{"$f":"'Simulated Data'!A7","v":4},{"$f":"'Simulated Data'!F7","v":70.30671508908884},{"$f":"'Simulated Data'!G7","v":161.11898050586314},0.27736921499639777,0.48708719864947625,8.7160650934791112E-2,0.19052997929503049,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"MADCorr_G('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.33472125067401182}]
[{"$f":"'Simulated Data'!A8","v":5},{"$f":"'Simulated Data'!F8","v":67.375076704515038},{"$f":"'Simulated Data'!G8","v":167.57356788815855},2.6542691695774039,5.9675001836459387,0.69546296430209076,1.9618819703515511,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"MADCorr_G('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.37800000000000006}]
[{"$f":"'Simulated Data'!A9","v":6},{"$f":"'Simulated Data'!F9","v":70.303701168768001},{"$f":"'Simulated Data'!G9","v":166.7573260094741},0.27435529467555853,5.1512583049614875,0.68393495152324491,0.40926173414281686,null,null,"Intermediate Calculations for\nthe MAD-G Correlation",null,null,null,null,"(X, Y) with duplicates",{"$f":"MADCorr_G('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.33471365899970984}]
[{"$f":"'Simulated Data'!A10","v":7},{"$f":"'Simulated Data'!F10","v":72.04643599739471},{"$f":"'Simulated Data'!G10","v":158.14029467085311},2.0170901233022676,3.4657730336595023,0.64196171384473166,1.3774658119440613,null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"MADCorr_G('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.37800000000000006}]
[{"$f":"'Simulated Data'!A11","v":8},{"$f":"'Simulated Data'!F11","v":69.659038619402779},{"$f":"'Simulated Data'!G11","v":151.45915754274174},0.37030725468966352,10.146910161770876,1.2620535193035964,0.89131715285145363,null,null,"Median of X = ",null,{"$f":"MEDIAN(B4:B1003)","v":70.029345874092442}]
[{"$f":"'Simulated Data'!A12","v":9},{"$f":"'Simulated Data'!F12","v":74.291448615158941},{"$f":"'Simulated Data'!G12","v":185.99290055062283},4.2621027410664993,24.386832846110224,4.7211997305328186,0.4541580680816435,null,null,"Median of Y = ",null,{"$f":"MEDIAN(C4:C1003)","v":161.60606770451261}]
[{"$f":"'Simulated Data'!A13","v":10},{"$f":"'Simulated Data'!F13","v":65.649488474075483},{"$f":"'Simulated Data'!G13","v":147.60307841115861},4.3798574000169594,14.002989293354005,3.678319025900997,0.70661374950903899,null,null,"MAD of X = ",null,{"$f":"MEDIAN(D4:D1003)","v":1.9976850840580553}]
[{"$f":"'Simulated Data'!A14","v":11},{"$f":"'Simulated Data'!F14","v":69.742697145918896},{"$f":"'Simulated Data'!G14","v":154.65949081048038},0.28664872817354592,6.9465768940322334,0.88058946248161074,0.59360856598189449,null,null,"MAD of Y = ",null,{"$f":"MEDIAN(E4:E1003)","v":9.4242113473348752},null,null,"Notes:"]
[{"$f":"'Simulated Data'!A15","v":12},{"$f":"'Simulated Data'!F15","v":69.923511910794829},{"$f":"'Simulated Data'!G15","v":155.01069183161337},0.10583396329761285,6.5953758728992398,0.75281148994532288,0.64685488633228094,null,null,"Median of |X()+Y()| = ",null,{"$f":"MEDIAN(F4:F1003)","v":1.6773524349043152}]
[{"$f":"'Simulated Data'!A16","v":13},{"$f":"'Simulated Data'!F16","v":71.272442551537864},{"$f":"'Simulated Data'!G16","v":167.92486667662297},1.243096677445422,6.3187989721103577,1.2927542916379209,4.8217114716900489E-2,null,null,"Median of |X()-Y()| =",null,{"$f":"MEDIAN(G4:G1003)","v":1.0079099335562915}]
[{"$f":"'Simulated Data'!A17","v":14},{"$f":"'Simulated Data'!F17","v":68.209184553223238},{"$f":"'Simulated Data'!G17","v":170.8602725769386},1.8201613208692038,9.2542048724259871,7.0825407051876343E-2,1.8930959294625123]
[{"$f":"'Simulated Data'!A18","v":15},{"$f":"'Simulated Data'!F18","v":71.98267048709441},{"$f":"'Simulated Data'!G18","v":177.2631871840758},1.9533246130019677,15.657119479563192,2.6391659161332397,0.68357779206913527]
[{"$f":"'Simulated Data'!A19","v":16},{"$f":"'Simulated Data'!F19","v":64.969503845277544},{"$f":"'Simulated Data'!G19","v":170.46052364202347},5.0598420288148986,8.8544559375108634,1.5933092461095653,3.4723961237642911]
[{"$f":"'Simulated Data'!A20","v":17},{"$f":"'Simulated Data'!F20","v":67.564203137894168},{"$f":"'Simulated Data'!G20","v":158.22159030710421},2.4651427361982741,3.3844773974084035,1.5931254663900654,0.87487387531862382]
[{"$f":"'Simulated Data'!A21","v":18},{"$f":"'Simulated Data'!F21","v":72.348110751484867},{"$f":"'Simulated Data'!G21","v":168.08445955367756},2.3187648773924252,6.4783918491649501,1.8481459816160586,0.47330587873636021]
[{"$f":"'Simulated Data'!A22","v":19},{"$f":"'Simulated Data'!F22","v":73.399997728692298},{"$f":"'Simulated Data'!G22","v":186.43821871981902},3.3706518545998563,24.832151015306408,4.3222103470519597,0.94765258367037108]
[{"$f":"'Simulated Data'!A23","v":20},{"$f":"'Simulated Data'!F23","v":70.630878832697576},{"$f":"'Simulated Data'!G23","v":145.0970574458735},0.60153295860513367,16.509010258639108,1.4506507002475306,2.0528807147833477]
[{"$f":"'Simulated Data'!A24","v":21},{"$f":"'Simulated Data'!F24","v":70.119676553511951},{"$f":"'Simulated Data'!G24","v":138.10299892045091},9.0330679419508897E-2,23.503068784061696,2.4486853049356441,2.539120659477125]
[{"$f":"'Simulated Data'!A25","v":22},{"$f":"'Simulated Data'!F25","v":66.187165277180767},{"$f":"'Simulated Data'!G25","v":144.01836436558077},3.8421805969116747,17.587703338931846,3.7895419357431424,5.7090977094900852E-2]
[{"$f":"'Simulated Data'!A26","v":23},{"$f":"'Simulated Data'!F26","v":73.781440690017263},{"$f":"'Simulated Data'!G26","v":194.19555847709682},3.7520948159248206,32.589490772584213,5.3362816334976033,1.5798388929802698]
[{"$f":"'Simulated Data'!A27","v":24},{"$f":"'Simulated Data'!F27","v":67.094982124804702},{"$f":"'Simulated Data'!G27","v":159.50283587727762},2.9343637492877406,2.1032318272349926,1.6920552887980431,1.2457087989498974]
[{"$f":"'Simulated Data'!A28","v":25},{"$f":"'Simulated Data'!F28","v":69.938280213559452},{"$f":"'Simulated Data'!G28","v":159.32747874166122},9.1065660532990478E-2,2.2785889628513871,0.28736592720902843,0.19619473985851607]
[{"$f":"'Simulated Data'!A29","v":26},{"$f":"'Simulated Data'!F29","v":69.152185366445423},{"$f":"'Simulated Data'!G29","v":169.67875714103042},0.87716050764701947,8.0726894365178055,0.41750196946132667,1.2956789300312821]
[{"$f":"'Simulated Data'!A30","v":27},{"$f":"'Simulated Data'!F30","v":69.979041938513163},{"$f":"'Simulated Data'!G30","v":169.26417290074878},5.0303935579279369E-2,7.6581051962361641,0.78741793701993146,0.83778016476114581]
[{"$f":"'Simulated Data'!A31","v":28},{"$f":"'Simulated Data'!F31","v":65.231388920735938},{"$f":"'Simulated Data'!G31","v":150.1850862026223},4.7979569533565041,11.42098150189031,3.6136350425677284,1.1898817796233203]
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[{"$f":"'Simulated Data'!A968","v":965},{"$f":"'Simulated Data'!F968","v":61.877655199001573},{"$f":"'Simulated Data'!G968","v":152.08396733094887},8.1516906750908689,9.5221003735637453,5.0909553967198882,3.0701814512678793]
[{"$f":"'Simulated Data'!A969","v":966},{"$f":"'Simulated Data'!F969","v":66.379785682903631},{"$f":"'Simulated Data'!G969","v":150.33862786018673},3.6495601911888116,11.267439844325878,3.0224790255096114,0.6313102732272764]
[{"$f":"'Simulated Data'!A970","v":967},{"$f":"'Simulated Data'!F970","v":65.901947342454605},{"$f":"'Simulated Data'!G970","v":154.63298294101941},4.1273985316378372,6.9730847634932047,2.8060024345802201,1.3261789233078076]
[{"$f":"'Simulated Data'!A971","v":968},{"$f":"'Simulated Data'!F971","v":65.574685680426299},{"$f":"'Simulated Data'!G971","v":163.58129464849748},4.4546601936661432,1.9752269439848646,2.0203204368321277,2.4395018136469524]
[{"$f":"'Simulated Data'!A972","v":969},{"$f":"'Simulated Data'!F972","v":71.752799741851916},{"$f":"'Simulated Data'!G972","v":175.89650736672533},1.7234538677594742,14.290439662212719,2.3790794057059328,0.65362840092745556]
[{"$f":"'Simulated Data'!A973","v":970},{"$f":"'Simulated Data'!F973","v":73.13332135243401},{"$f":"'Simulated Data'!G973","v":152.16529383619647},3.1039754783415674,9.4407738683161426,0.55202873765871452,2.5555436250844834]
[{"$f":"'Simulated Data'!A974","v":971},{"$f":"'Simulated Data'!F974","v":72.964746306546573},{"$f":"'Simulated Data'!G974","v":148.03734757981741},2.9354004324541307,13.568720124695204,2.9628508116601893E-2,2.9091734641053866]
[{"$f":"'Simulated Data'!A975","v":972},{"$f":"'Simulated Data'!F975","v":68.038318517381001},{"$f":"'Simulated Data'!G975","v":157.17792523673273},1.9910273567114416,4.4281424677798782,1.4665360354496668,0.52679852223438073]
[{"$f":"'Simulated Data'!A976","v":973},{"$f":"'Simulated Data'!F976","v":68.762819020043068},{"$f":"'Simulated Data'!G976","v":148.21777155657355},1.2665268540493742,13.388296147939059,2.0546250007176141,0.78663049632197823]
[{"$f":"'Simulated Data'!A977","v":974},{"$f":"'Simulated Data'!F977","v":65.791081929103797},{"$f":"'Simulated Data'!G977","v":162.06889297833703},4.2382639449886454,0.4628252738244214,2.0724773817670732,2.1706978602276514]
[{"$f":"'Simulated Data'!A978","v":975},{"$f":"'Simulated Data'!F978","v":65.699545273898138},{"$f":"'Simulated Data'!G978","v":176.36856795111959},4.3298006001943037,14.762500246606976,0.60096488655614522,3.7338530832500245]
[{"$f":"'Simulated Data'!A979","v":976},{"$f":"'Simulated Data'!F979","v":68.216240483735447},{"$f":"'Simulated Data'!G979","v":138.40648196607015},1.8131053903569949,23.199585738442465,3.3693037027164525,1.554097287224887]
[{"$f":"'Simulated Data'!A980","v":977},{"$f":"'Simulated Data'!F980","v":74.587220858248571},{"$f":"'Simulated Data'!G980","v":172.08428897963017},4.557874984156129,10.478221275117562,3.3934189736207663,1.16973767256829]
[{"$f":"'Simulated Data'!A981","v":978},{"$f":"'Simulated Data'!F981","v":68.428636847793811},{"$f":"'Simulated Data'!G981","v":145.5348927737291},1.600709026298631,16.071174930783513,2.5065891066664778,0.90402517997690712]
[{"$f":"'Simulated Data'!A982","v":979},{"$f":"'Simulated Data'!F982","v":67.756280153305298},{"$f":"'Simulated Data'!G982","v":158.96612397358521},2.2730657207871445,2.6399437309273992,1.417973444211206,0.85772630338833744]
[{"$f":"'Simulated Data'!A983","v":980},{"$f":"'Simulated Data'!F983","v":70.279184098712946},{"$f":"'Simulated Data'!G983","v":157.59822278867134},0.24983822462050398,4.0078449158412752,0.30020725162901485,0.55033498859242835]
[{"$f":"'Simulated Data'!A984","v":981},{"$f":"'Simulated Data'!F984","v":66.8461146376833},{"$f":"'Simulated Data'!G984","v":161.70316698036402},3.1832312364091422,9.7099275851405764E-2,1.583156808590803,1.6037631537315802]
[{"$f":"'Simulated Data'!A985","v":982},{"$f":"'Simulated Data'!F985","v":69.669277531813009},{"$f":"'Simulated Data'!G985","v":159.38863900911079},0.3600683422794333,2.2174286954018214,0.41553343205156901,5.5047842853497758E-2]
[{"$f":"'Simulated Data'!A986","v":983},{"$f":"'Simulated Data'!F986","v":68.884915246787671},{"$f":"'Simulated Data'!G986","v":164.22129551633441},1.1444306273047715,2.6152278118217964,0.29537742404240558,0.85037936859479957]
[{"$f":"'Simulated Data'!A987","v":984},{"$f":"'Simulated Data'!F987","v":66.757432806439581},{"$f":"'Simulated Data'!G987","v":153.7354942686037},3.2719130676528607,7.8705734359089092,2.4729962656799955,0.80270829232407725]
[{"$f":"'Simulated Data'!A988","v":985},{"$f":"'Simulated Data'!F988","v":72.94978173730965},{"$f":"'Simulated Data'!G988","v":189.24947866394663},2.9204358632172074,27.643410959434021,4.3951433744462491,1.4713233123925287]
[{"$f":"'Simulated Data'!A989","v":986},{"$f":"'Simulated Data'!F989","v":71.413441301612423},{"$f":"'Simulated Data'!G989","v":166.77684133938783},1.3840954275199806,5.1707736348752178,1.2415187662605405,0.1441805499783918]
[{"$f":"'Simulated Data'!A990","v":987},{"$f":"'Simulated Data'!F990","v":66.276002573263611},{"$f":"'Simulated Data'!G990","v":154.27064541676046},3.7533433008288313,7.3354222877521522,2.6572056085350568,1.100487063629636]
[{"$f":"'Simulated Data'!A991","v":988},{"$f":"'Simulated Data'!F991","v":74.474437496857064},{"$f":"'Simulated Data'!G991","v":184.91105210852731},4.4450916227646218,23.304984404014704,4.6980056088466906,0.24776301732174755]
[{"$f":"'Simulated Data'!A992","v":989},{"$f":"'Simulated Data'!F992","v":73.229245627942007},{"$f":"'Simulated Data'!G992","v":179.50437979620904},3.1998997538495644,17.898312091696425,3.5009879706407667,0.29738017541274653]
[{"$f":"'Simulated Data'!A993","v":990},{"$f":"'Simulated Data'!F993","v":67.661299683710098},{"$f":"'Simulated Data'!G993","v":174.30074290262405},2.3680461903823442,12.69467519811144,0.16163271495069576,2.5324229954406965]
[{"$f":"'Simulated Data'!A994","v":991},{"$f":"'Simulated Data'!F994","v":67.995205008986574},{"$f":"'Simulated Data'!G994","v":140.13194335022001},2.0341408651058686,21.474124354292599,3.2968613618482667,1.2603633358693591]
[{"$f":"'Simulated Data'!A995","v":992},{"$f":"'Simulated Data'!F995","v":71.613955307897157},{"$f":"'Simulated Data'!G995","v":177.92968103285378},1.5846094338047152,16.323613328341168,2.5253161385585354,0.93887046055830436]
[{"$f":"'Simulated Data'!A996","v":993},{"$f":"'Simulated Data'!F996","v":66.616217191886477},{"$f":"'Simulated Data'!G996","v":144.35468838738177},3.413128682205965,17.251379317130841,3.5390801533416765,0.12199634023875516]
[{"$f":"'Simulated Data'!A997","v":994},{"$f":"'Simulated Data'!F997","v":71.281143270425275},{"$f":"'Simulated Data'!G997","v":159.86075365638786},1.251797396332833,1.7453140481247544,0.44142928327001812,0.81181869492478143]
[{"$f":"'Simulated Data'!A998","v":995},{"$f":"'Simulated Data'!F998","v":67.046078942109119},{"$f":"'Simulated Data'!G998","v":175.42135129542331},2.9832669319833229,13.815283590910695,2.742672252929701E-2,2.9592972168847949]
[{"$f":"'Simulated Data'!A999","v":996},{"$f":"'Simulated Data'!F999","v":72.697270897329361},{"$f":"'Simulated Data'!G999","v":164.5742158186199},2.6679250232369185,2.9681481141072936,1.6504575370858374,1.0205590756200569]
[{"$f":"'Simulated Data'!A1000","v":997},{"$f":"'Simulated Data'!F1000","v":73.063577091851528},{"$f":"'Simulated Data'!G1000","v":185.76517555171091},3.0342312177590856,24.1591078471983,4.0823887150431082,1.0446414324780182]
[{"$f":"'Simulated Data'!A1001","v":998},{"$f":"'Simulated Data'!F1001","v":70.595973984843269},{"$f":"'Simulated Data'!G1001","v":168.74073257871854},0.56662811075082686,7.1346648742059244,1.0406993281008885,0.47341460913027839]
[{"$f":"'Simulated Data'!A1002","v":999},{"$f":"'Simulated Data'!F1002","v":72.863123673420617},{"$f":"'Simulated Data'!G1002","v":179.89831295341651},2.8337777993281748,18.292245248903896,3.3595149816095162,0.52245340274274277]
[{"$f":"'Simulated Data'!A1003","v":1000},{"$f":"'Simulated Data'!F1003","v":71.912624388221161},{"$f":"'Simulated Data'!G1003","v":159.94124718472298},1.8832785141287189,1.6648205197896289,0.76607686418918064,1.1193839916360695]

{"sheet":"MAD Correlation (Shevylakov)","index":16,"n_rows":1003,"n_cols":18,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[2,16,3,17],[13,16,13,17],[14,16,29,17],[0,0,0,17],[11,11,11,12],[17,11,17,12],[12,11,12,12],[13,11,13,12],[3,11,3,12],[4,11,4,12],[14,11,14,12],[15,11,15,12],[10,11,10,12],[16,11,16,12],[2,11,2,13],[8,11,9,13]]}
["Calculating the MAD-S Correlation Coefficient (Shevylakov)"]
[]
["Observation\nNumber","X","Y","|X-Xmed|","|Y-Ymed|","U","V","|U-Umed|","|V-Vmed|",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"MAD-S Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,0.43909828518724225,17.597472773307118,{"$f":"(($B4-$N$11)/(SQRT(2)*$N$13))+(($C4-$N$12)/(SQRT(2)*$N$14))","v":1.1649291158623063},{"$f":"(($B4-$N$11)/(SQRT(2)*$N$13))-(($C4-$N$12)/(SQRT(2)*$N$14))","v":-1.4757782857750756},{"$f":"ABS($F4-$N$15)","v":1.1626173306786312},{"$f":"ABS($G4-$N$16)","v":1.4179004686058267},null,null,"Calculated MAD-S Correlation = ",null,{"$f":"(N17^2-N18^2)/(N17^2+N18^2)","v":0.46439911913394605}]
[2,75.900421131737588,148.6347709869498,5.8710752576451455,12.971296717562808,{"$f":"(($B5-$N$11)/(SQRT(2)*$N$13))+(($C5-$N$12)/(SQRT(2)*$N$14))","v":1.1048962437629331},{"$f":"(($B5-$N$11)/(SQRT(2)*$N$13))-(($C5-$N$12)/(SQRT(2)*$N$14))","v":3.0513916122831417},{"$f":"ABS($F5-$N$15)","v":1.1025844585792579},{"$f":"ABS($G5-$N$16)","v":3.1092694294523904},null,null,"VBA MAD-S Correlation = ",null,{"$f":"MADCorr_S(B4:B1003,C4:C1003)","v":0.46439911913394605},null,null,"U1(0,1), U2(0,1)",{"$f":"MADCorr_S('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":2.7595657030367902E-2}]
[3,68.70319256856132,148.28328151641921,1.3261533055311219,13.322786188093403,-1.4690295643814801,0.53021092603121245,1.4713413495651553,0.58808874320046134,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"MADCorr_S('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-1.7387554705960019E-2}]
[4,70.30671508908884,161.11898050586314,0.27736921499639777,0.48708719864947625,6.1631887328624402E-2,0.13472504037884855,5.9320102144949351E-2,0.19260285754809739,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"MADCorr_S('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.46439911913394605}]
[5,67.375076704515038,167.57356788815855,2.6542691695774039,5.9675001836459387,-0.49176657812210617,-1.3872600451232069,0.4940783633057812,1.329382227953958,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"MADCorr_S('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.6058814558058927}]
[6,70.303701168768001,166.7573260094741,0.27435529467555853,5.1512583049614875,0.48361504211257911,-0.2893917474925517,0.48130325692890408,0.23151393032330286,null,null,"Intermediate Calculations for\nthe MAD-S Correlation",null,null,null,null,"(X, Y) with duplicates",{"$f":"MADCorr_S('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.46441531550567605}]
[7,72.04643599739471,158.14029467085311,2.0170901233022676,3.4657730336595023,0.45393548112174759,0.97401541647827927,0.45162369593807256,1.0318932336475282,null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"MADCorr_S('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.6058814558058927}]
[8,69.659038619402779,151.45915754274174,0.37030725468966352,10.146910161770876,-0.89240660171992048,0.63025640296914942,0.89471838690359551,0.6881342201383982,null,null,"Median of X = ",null,{"$f":"MEDIAN(B4:B1003)","v":70.029345874092442}]
[9,74.291448615158941,185.99290055062283,4.2621027410664993,24.386832846110224,3.3383923447958566,-0.32113824967111193,3.3360805596121814,0.2632604325018631,null,null,"Median of Y = ",null,{"$f":"MEDIAN(C4:C1003)","v":161.60606770451261}]
[10,65.649488474075483,147.60307841115861,4.3798574000169594,14.002989293354005,-2.6009643265820905,-0.49965137395749371,2.6032761117657657,0.44177355678824487,null,null,"MAD of X = ",null,{"$f":"MEDIAN(D4:D1003)","v":1.9976850840580553}]
[11,69.742697145918896,154.65949081048038,0.28664872817354592,6.9465768940322334,-0.62267078036216383,0.41974464237621967,0.62498256554583886,0.4776224595454685,null,null,"MAD of Y = ",null,{"$f":"MEDIAN(E4:E1003)","v":9.4242113473348752},null,null,"Notes:"]
[12,69.923511910794829,155.01069183161337,0.10583396329761285,6.5953758728992398,-0.5323181094954863,0.45739547656920926,0.53462989467916133,0.51527329373845809,null,null,"Median of U = ",null,{"$f":"MEDIAN(F4:F1003)","v":2.3117851836750494E-3}]
[13,71.272442551537864,167.92486667662297,1.243096677445422,6.3187989721103577,0.91411532602518575,-3.4094648785570059E-2,0.91180354084151072,2.3783168383678777E-2,null,null,"Median of V = ",null,{"$f":"MEDIAN(G4:G1003)","v":-5.7877817169248835E-2}]
[14,68.209184553223238,170.8602725769386,1.8201613208692038,9.2542048724259871,5.0081125606679211E-2,-1.3386209691595923,4.776934042300416E-2,1.2807431519903434,null,null,"MAD of U = ",null,{"$f":"MEDIAN(H4:H1003)","v":1.1837554959769332}]
[15,71.98267048709441,177.2631871840758,1.9533246130019677,15.657119479563192,1.8661721159742211,-0.48336249224061334,1.8638603307905459,0.4254846750713645,null,null,"MAD of V = ",null,{"$f":"MEDIAN(I4:I1003)","v":0.71590091943248502}]
[16,64.969503845277544,170.46052364202347,5.0598420288148986,8.8544559375108634,-1.1266397724512993,-2.4553548460796124,1.1289515576349745,2.3974770289103637]
[17,67.564203137894168,158.22159030710421,2.4651427361982741,3.3844773974084035,-1.1265098205653963,-0.61862924992075308,1.1288216057490714,0.56075143275150419]
[18,72.348110751484867,168.08445955367756,2.3187648773924252,6.4783918491649501,1.3068365562233835,0.334677796429938,1.3045247710397083,0.39255561359918684]
[19,73.399997728692298,186.43821871981902,3.3706518545998563,24.832151015306408,3.0562642461151022,-0.67009156812227144,3.053952460931427,0.61221375095302255]
[20,70.630878832697576,145.0970574458735,0.60153295860513367,16.509010258639108,-1.0257649472780428,1.4516058743903919,1.0280767324617179,1.5094836915596408]
[21,70.119676553511951,138.10299892045091,9.0330679419508897E-2,23.503068784061696,-1.731481984111843,1.7954294365671337,1.7337937692955181,1.8533072537363826]
[22,66.187165277180767,144.01836436558077,3.8421805969116747,17.587703338931846,-2.6796108003547721,-4.0369417048370382E-2,2.6819225855384472,1.7508400120878453E-2]
[23,73.781440690017263,194.19555847709682,3.7520948159248206,32.589490772584213,3.7733209293673822,-1.1171147944085973,3.771009144183707,1.0592369772393484]
[24,67.094982124804702,159.50283587727762,2.9343637492877406,2.1032318272349926,-1.1964637688516584,-0.88084913912122209,1.1987755540353335,0.8229713219519732]
[25,69.938280213559452,159.32747874166122,9.1065660532990478E-2,2.2785889628513871,-0.20319839581146379,0.13873063098708735,0.20551018099513885,0.19660844815633619]
[26,69.152185366445423,169.67875714103042,0.87716050764701947,8.0726894365178055,0.29521847376484289,-0.91618335766564973,0.29290668858116786,0.85830554049640084]
[27,69.979041938513163,169.26417290074878,5.0303935579279369E-2,7.6581051962361641,0.55678856289471534,-0.59240003564618937,0.55447677771104031,0.53452221847694048]
[28,65.231388920735938,150.1850862026223,4.7979569533565041,11.42098150189031,-2.5552258433329791,-0.84137347518196703,2.5575376285166542,0.78349565801271814]
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[962,74.532793813216188,166.7535982937145,4.5034479391237454,5.1475305892018923,{"$f":"(($B965-$N$11)/(SQRT(2)*$N$13))+(($C965-$N$12)/(SQRT(2)*$N$14))","v":1.9802780401826288},{"$f":"(($B965-$N$11)/(SQRT(2)*$N$13))-(($C965-$N$12)/(SQRT(2)*$N$14))","v":1.2078306380943518},{"$f":"ABS($F965-$N$15)","v":1.9779662549989536},{"$f":"ABS($G965-$N$16)","v":1.2657084552636007}]
[963,75.867124862587389,165.09075729274707,5.8377789884949465,3.4846895882344597,2.327817571010983,1.8048989845411312,2.3255057858273078,1.8627768017103801]
[964,71.815451773933574,159.08227108793085,1.7861058998411323,2.5237966165817625,0.44285290267408073,0.8215782168989797,0.4405411174904057,0.87945603406822848]
[965,61.877655199001573,152.08396733094887,8.1516906750908689,9.5221003735637453,-3.5998490837388837,-2.1709461236646734,3.6021608689225588,2.1130683064954248]
[966,66.379785682903631,150.33862786018673,3.6495601911888116,11.267439844325878,-2.1372154149319544,-0.44640377523173946,2.1395272001156296,0.38852595806249063]
[967,65.901947342454605,154.63298294101941,4.1273985316378372,6.9730847634932047,-1.9841433495176355,-0.93775010973762529,1.9864551347013106,0.8798722925683764]
[968,65.574685680426299,163.58129464849748,4.4546601936661432,1.9752269439848646,-1.4285822810537654,-1.7249882751466414,1.4308940662374405,1.6671104579773925]
[969,71.752799741851916,175.89650736672533,1.7234538677594742,14.290439662212719,1.6822631807559265,-0.46218507467192316,1.6799513955722514,0.40430725750267432]
[970,73.13332135243401,152.16529383619647,3.1039754783415674,9.4407738683161426,0.39034326380832673,1.8070422269152902,0.3880314786246517,1.864920044084539]
[971,72.964746306546573,148.03734757981741,2.9354004324541307,13.568720124695204,2.0950519005689783E-2,2.0570962841168781,1.8638733822014732E-2,2.1149741012861267]
[972,68.038318517381001,157.17792523673273,1.9910273567114416,4.4281424677798782,-1.0369975755208944,-0.37250280739098285,1.0393093607045696,0.31462499022173401]
[973,68.762819020043068,148.21777155657355,1.2665268540493742,13.388296147939059,-1.4528392708028399,0.55623175823741033,1.4551510559865151,0.61410957540665922]
[974,65.791081929103797,162.06889297833703,4.2382639449886454,0.4628252738244214,-1.4654628105032388,-1.534915176874101,1.4677745956869139,1.4770373597048521]
[975,65.699545273898138,176.36856795111959,4.3298006001943037,14.762500246606976,-0.42494634653885455,-2.6402328351203908,0.42725813172252958,2.5823550179511421]
[976,68.216240483735447,138.40648196607015,1.8131053903569949,23.199585738442465,-2.3824574960677469,1.0989127304203352,2.3847692812514221,1.1567905475895841]
[977,74.587220858248571,172.08428897963017,4.557874984156129,10.478221275117562,2.3995095676543374,0.82712944048240711,2.3971977824706623,0.88500725765165589]
[978,68.428636847793811,145.5348927737291,1.600709026298631,16.071174930783513,-1.7724261549721967,0.63924233512506012,1.7747379401558718,0.6971201522943089]
[979,67.756280153305298,158.96612397358521,2.2730657207871445,2.6399437309273992,-1.0026586379441884,-0.60650408552796331,1.0049704231278636,0.54862626835871442]
[980,70.279184098712946,157.59822278867134,0.24983822462050398,4.0078449158412752,-0.21227858338825259,0.38914560235792739,0.21459036857192765,0.44702341952717622]
[981,66.8461146376833,161.70316698036402,3.1832312364091422,9.7099275851405764E-2,-1.1194609150362096,-1.1340318014207238,1.1217727002198847,1.0761539842514749]
[982,69.669277531813009,159.38863900911079,0.3600683422794333,2.2174286954018214,-0.29382650761338391,3.8924702971399688E-2,0.29613829279705894,9.6802520140648524E-2]
[983,68.884915246787671,164.22129551633441,1.1444306273047715,2.6152278118217964,-0.20886337954979933,-0.60130901811451731,0.21117516473347439,0.54343120094526842]
[984,66.757432806439581,153.7354942686037,3.2719130676528607,7.8705734359089092,-1.7486724293113338,-0.56760047681702841,1.750984214495009,0.50972265964777952]
[985,72.94978173730965,189.24947866394663,2.9204358632172074,27.643410959434021,3.1078356843580681,-1.0403826915106102,3.105523899174393,0.98250487434136136]
[986,71.413441301612423,166.77684133938783,1.3840954275199806,5.1707736348752178,0.87788633859318432,0.10195104460492682,0.87557455340950929,0.15982886177417566]
[987,66.276002573263611,154.27064541676046,3.7533433008288313,7.3354222877521522,-1.8789281048020654,-0.77816186530058717,1.8812398899857405,0.72028404813133839]
[988,74.474437496857064,184.91105210852731,4.4450916227646218,23.304984404014704,3.3219916240679295,-0.17519490967544771,3.3196798388842543,0.11731709250619887]
[989,73.229245627942007,179.50437979620904,3.1998997538495644,17.898312091696425,2.4755723348926155,-0.21027953862479798,2.4732605497089404,0.15240172145554914]
[990,67.661299683710098,174.30074290262405,2.3680461903823442,12.69467519811144,0.11429158880322932,-1.7906934729088659,0.11197980361955427,1.732815655739617]
[991,67.995205008986574,140.13194335022001,2.0341408651058686,21.474124354292599,-2.3312330255948255,0.89121146155212216,2.3335448107785006,0.94908927872137094]
[992,71.613955307897157,177.92968103285378,1.5846094338047152,16.323613328341168,1.7856681662145677,-0.66388166931651416,1.7833563810308926,0.60600385214726527]
[993,66.616217191886477,144.35468838738177,3.413128682205965,17.251379317130841,-2.5025075755906263,8.6264439462764964E-2,2.5048193607743015,0.1441422566320138]
[994,71.281143270425275,159.86075365638786,1.251797396332833,1.7453140481247544,0.31213763961454721,0.57404250427532599,0.30982585443087218,0.63192032144457477]
[995,67.046078942109119,175.42135129542331,2.9832669319833229,13.815283590910695,-1.939362148618784E-2,-2.0925391296057154,2.1705406669862891E-2,2.0346613124364668]
[996,72.697270897329361,164.5742158186199,2.6679250232369185,2.9681481141072936,1.1670497165338434,0.72164424297241681,1.1647379313501682,0.7795220601416657]
[997,73.063577091851528,185.76517555171091,3.0342312177590856,24.1591078471983,2.886684743846418,-0.7386730408136355,2.8843729586627429,0.6807952236443866]
[998,70.595973984843269,168.74073257871854,0.56662811075082686,7.1346648742059244,0.73588555207642203,-0.33475468042879863,0.733573766892747,0.2768768632595498]
[999,72.863123673420617,179.89831295341651,2.8337777993281748,18.292245248903896,2.3755358249938885,-0.36943034393337992,2.3732240398102133,0.31155252676413109]
[1000,71.912624388221161,159.94124718472298,1.8832785141287189,1.6648205197896289,0.54169814557829543,0.79152401123753036,0.5393863603946204,0.84940182840677925]

{"sheet":"Absolute Value Correlation","index":17,"n_rows":1003,"n_cols":18,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[9,11,10,13],[0,0,0,17],[2,11,2,13],[2,16,3,17],[3,11,3,12],[4,11,4,12],[17,16,26,17],[11,11,11,12],[12,11,12,12],[13,11,13,12],[14,11,14,12],[16,16,16,17]]}
["Calculating the Absolute Value Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","X-Xmean","Y-Ymean","|X-Xmean|","|Y-Ymean|","|x/x()+y/y()|","|x/x()-y/y()|",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Absolute Value Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,{"$f":"(B4-$N$12)","v":-0.400779448653239},{"$f":"(C4-$N$13)","v":17.172738348625586},{"$f":"ABS(D4)","v":0.400779448653239},{"$f":"ABS(E4)","v":17.172738348625586},{"$f":"ABS($D4/$N$14+$E4/$N$15)","v":1.3792354265906802E-3},{"$f":"ABS($D4/$N$14-$E4/$N$15)","v":1.7155516963835472E-3},null,null,"Calculated AV Correlation = ",null,{"$f":"0.5*(SUM(H4:H1003)-SUM(I4:I1003))","v":0.34282995929938309}]
[2,75.900421131737588,148.6347709869498,{"$f":"(B5-$N$12)","v":5.9093940941791487},{"$f":"(C5-$N$13)","v":-13.39603114224434},{"$f":"ABS(D5)","v":5.9093940941791487},{"$f":"ABS(E5)","v":13.39603114224434},{"$f":"ABS($D5/$N$14+$E5/$N$15)","v":1.2723665247859029E-3},{"$f":"ABS($D5/$N$14-$E5/$N$15)","v":3.68653390079426E-3},null,null,"VBA AV Correlation = ",null,{"$f":"AVCorr(B4:B1003,C4:C1003)","v":0.34282995929938309},null,null,"U1(0,1), U2(0,1)",{"$f":"AVCorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":1.183643995440542E-2}]
[3,68.70319256856132,148.28328151641921,-1.2878344689971186,-13.747520612774935,1.2878344689971186,13.747520612774935,1.779102221456789E-3,6.9840887208664452E-4,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"AVCorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":-1.5027443580606259E-2}]
[4,70.30671508908884,161.11898050586314,0.31568805153040103,-0.91182162333100791,0.31568805153040103,0.91182162333100791,5.0293656700375381E-5,2.1461770106922872E-4,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"AVCorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.34282995929938309}]
[5,67.375076704515038,167.57356788815855,-2.6159503330434006,5.542765758964407,2.6159503330434006,5.542765758964407,5.9814942448770884E-4,1.5970396275681283E-3,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"AVCorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.35205199999999925}]
[6,70.303701168768001,166.7573260094741,0.31267413120956178,4.7265238802799558,0.31267413120956178,4.7265238802799558,5.5708664200015902E-4,2.9470443197793494E-4,null,null,null,null,null,null,null,"(X, Y) with duplicates",{"$f":"AVCorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.34283004089848046}]
[7,72.04643599739471,158.14029467085311,2.0554089598362708,-3.890507458341034,2.0554089598362708,3.890507458341034,5.1183970746856511E-4,1.2129679806348924E-3,null,null,"Intermediate Calculations for\nthe Absolute Value Correlation",null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"AVCorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.35207799999999939}]
[8,69.659038619402779,151.45915754274174,-0.33198841815566027,-10.571644586452408,0.33198841815566027,10.571644586452408,1.0918800551167631E-3,8.1329015540074657E-4]
[9,74.291448615158941,185.99290055062283,4.3004215776005026,23.962098421428692,4.3004215776005026,23.962098421428692,3.9635273979098835E-3,3.5480507351065517E-4,null,null,"Mean X = ",null,{"$f":"AVERAGE(B4:B1003)","v":69.991027037558439}]
[10,65.649488474075483,147.60307841115861,-4.3415385634829562,-14.427723718035537,4.3415385634829562,14.427723718035537,3.1216599234720173E-3,5.2156594486785159E-4,null,null,"Mean Y = ",null,{"$f":"AVERAGE(C4:C1003)","v":162.03080212919414}]
[11,69.742697145918896,154.65949081048038,-0.24832989163954267,-7.3713113187137651,0.24832989163954267,7.3713113187137651,7.6840457583847942E-4,5.600171869268825E-4,null,null,"Sum of |X-Xmean| = ",null,{"$f":"SUM(F4:F1003)","v":2383.3485599734677}]
[12,69.923511910794829,155.01069183161337,-6.7515126763609601E-2,-7.0201102975807714,6.7515126763609601E-2,7.0201102975807714,6.6089285832128595E-4,6.0423716985215066E-4,null,null,"Sum of |Y-Ymean| = ",null,{"$f":"SUM(G4:G1003)","v":11097.847875314812}]
[13,71.272442551537864,167.92486667662297,1.2814155139794252,5.894064547428826,1.2814155139794252,5.894064547428826,1.0687532024640342E-3,6.5536456402065166E-6]
[14,68.209184553223238,170.8602725769386,-1.7818424843352005,8.8294704477444554,1.7818424843352005,8.8294704477444554,4.7980602672556484E-5,1.5432234842719115E-3,null,null,null,null,null,null,null,"Notes:"]
[15,71.98267048709441,177.2631871840758,1.9916434495359709,15.232385054881661,1.9916434495359709,15.232385054881661,2.208202314892607E-3,5.3690380406283338E-4]
[16,64.969503845277544,170.46052364202347,-5.0215231922808954,8.4297215128293317,5.0215231922808954,8.4297215128293317,1.3473377051706362E-3,2.8665009893565274E-3]
[17,67.564203137894168,158.22159030710421,-2.4268238996642708,-3.8092118220899351,2.4268238996642708,3.8092118220899351,1.3614800698417665E-3,6.7500249961612848E-4]
[18,72.348110751484867,168.08445955367756,2.3570837139264285,6.0536574244834185,2.3570837139264285,6.0536574244834185,1.5344601585339625E-3,4.4349955202777633E-4]
[19,73.399997728692298,186.43821871981902,3.4089706911338595,24.407416590624877,3.4089706911338595,24.407416590624877,3.6296209844715391E-3,7.6896455478690285E-4]
[20,70.630878832697576,145.0970574458735,0.63985179513913693,-16.93374468332064,0.63985179513913693,16.93374468332064,1.2573908558185121E-3,1.7943259947947932E-3]
[21,70.119676553511951,138.10299892045091,0.12864951595351215,-23.927803208743228,0.12864951595351215,23.927803208743228,2.1020975047298623E-3,2.2100544507797043E-3]
[22,66.187165277180767,144.01836436558077,-3.8038617603776714,-18.012437763613377,3.8038617603776714,18.012437763613377,3.2190725442322278E-3,2.7041110592477451E-5]
[23,73.781440690017263,194.19555847709682,3.7904136524588239,32.164756347902681,3.7904136524588239,32.164756347902681,4.4886609220404139E-3,1.3079145418290192E-3]
[24,67.094982124804702,159.50283587727762,-2.8960449127537373,-2.5279662519165242,2.8960449127537373,2.5279662519165242,1.4429048487336188E-3,9.873271042342487E-4]
[25,69.938280213559452,159.32747874166122,-5.2746823998987225E-2,-2.7033233875329188,5.2746823998987225E-2,2.7033233875329188,2.6572126912658431E-4,2.2145848282261672E-4]
[26,69.152185366445423,169.67875714103042,-0.83884167111301622,7.6479550118362738,0.83884167111301622,7.6479550118362738,3.3717927799686235E-4,1.0410978614560562E-3]
[27,69.979041938513163,169.26417290074878,-1.1985099045276115E-2,7.2333707715546325,1.1985099045276115E-2,7.2333707715546325,6.4675271441088299E-4,6.5681007592867087E-4]
[28,65.231388920735938,150.1850862026223,-4.7596381168225008,-11.845715926571842,4.7596381168225008,11.845715926571842,3.0644267651820942E-3,9.2964963367706964E-4]
[29,69.189918454669353,162.13540998077724,-0.8011085828890856,0.10460785158309704,0.8011085828890856,0.10460785158309704,3.26701369561598E-4,3.4555328621397501E-4]
[30,70.721846699211568,179.8605006679764,0.73081966165312906,17.829698538782253,0.73081966165312906,17.829698538782253,1.9132263028762465E-3,1.2999549803960257E-3]
[31,73.086466808676647,167.34548500243301,3.0954397711182082,5.3146828732388656,3.0954397711182082,5.3146828732388656,1.7776707294130997E-3,8.1988451122922421E-4]
[32,72.420047763828379,176.77910111575324,2.4290207262699397,14.748298986559092,2.4290207262699397,14.748298986559092,2.3480962690078343E-3,3.0977022046965426E-4]
[33,64.432162861783951,134.40751922342531,-5.5588641757744881,-27.623282905768832,5.5588641757744881,27.623282905768832,4.8214423006959963E-3,1.5669097633547397E-4]
[34,70.274805760558294,157.56549297529213,0.2837787229998554,-4.4653091539020124,0.2837787229998554,4.4653091539020124,2.8329088023374576E-4,5.2142535016878086E-4]
[35,68.139313698476599,139.42832188855618,-1.8517133390818401,-22.602480240637959,1.8517133390818401,22.602480240637959,2.8135920541412555E-3,1.2597166620312117E-3]
[36,74.470459052628982,176.30621399227613,4.4794320150705431,14.275411863081985,4.4794320150705431,14.275411863081985,3.1657924964086297E-3,5.9314741720636411E-4]
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{"sheet":"Footrule Correlation","index":18,"n_rows":1005,"n_cols":16,"rows_kept":1005,"cut":false,"hidden":false,"merged":[[0,0,0,14],[2,8,2,10],[2,13,3,14],[3,8,3,9],[4,8,4,9],[14,13,29,14],[8,8,9,10],[10,8,10,9],[12,8,12,9],[11,8,11,9],[13,13,13,14]]}
["Calculating Spearman's Footrule Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","Xrnk","Yrnk","|Xrnk-Yrnk|",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Footrule Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[1,69.5902475889052,179.20354047781973,452,892,{"$f":"ABS(D4-E4)","v":440},null,null,"Calculated Footrule =",null,{"$f":"1-3*(K13/(K12-1))","v":0.28939528939528936}]
[2,75.900421131737588,148.6347709869498,977,171,{"$f":"ABS(D5-E5)","v":806},null,null,"VBA Footrule = ",null,{"$f":"footcorr(B4:B1003,C4:C1003)","v":0.28939528939528936},null,null,"U1(0,1), U2(0,1)",{"$f":"footcorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":8.6730086730086864E-3}]
[3,68.70319256856132,148.28328151641921,350,162,188,null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"footcorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":2.4900024900020856E-4}]
[4,70.30671508908884,161.11898050586314,544,482,62,null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"footcorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.28939528939528936}]
[5,67.375076704515038,167.57356788815855,190,656,466,null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"footcorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.28939528939528936}]
[6,70.303701168768001,166.7573260094741,543,634,91,null,null,"Intermediate Calculations for\nthe Absolute Value Correlation",null,null,null,null,"(X, Y) with duplicates",{"$f":"footcorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.28940728940728944}]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(P904:P1003)","v":0}]

{"sheet":"Greatest Deviation Correlation","index":19,"n_rows":1005,"n_cols":21,"rows_kept":1005,"cut":false,"hidden":false,"merged":[[8,9,9,11],[0,0,0,15],[2,9,2,11],[2,14,3,15],[3,9,3,10],[4,9,4,10],[10,9,10,10],[11,9,11,10],[12,9,12,10],[13,14,13,15],[14,14,29,15],[13,9,13,10]]}
["Calculating Greatest Deviation Rank Correlation Coefficient"]
[]
["Observation\nNumber","X","Y","Xrnk","Yrnk","d+","d-",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,null,"Greatest Deviation Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[930,59.778881710363848,138.64951997561852,1,41,{"$f":"SUM(IF($E$4:$E4>$D4,1,0))","v":1},{"$f":"SUM(IF(1000+1-($E$4:$E4)>$D4,1,0))","v":1},null,null,"Calculated GD Correlation =",null,{"$f":"(L12-L11)/L14","v":0.312},null,null,null,null,null,1,14,{"$f":"SUM(IF($S$4:$S4>$R4,1,0))","v":1},{"$f":"SUM(IF(16+1-($S$4:$S4)>$R4,1,0))","v":1}]
[102,61.706607348992598,143.21613849324444,2,93,{"$f":"SUM(IF($E$4:$E5>$D5,1,0))","v":2},{"$f":"SUM(IF(1000+1-($E$4:$E5)>$D5,1,0))","v":2},null,null,"VBA GD Correlation = ",null,null,null,null,"U1(0,1), U2(0,1)",{"$f":"footcorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003)","v":8.6730086730086864E-3},null,{"$f":"R4+1","v":2},11,{"$f":"SUM(IF($S$4:$S5>$R5,1,0))","v":2},{"$f":"SUM(IF(16+1-($S$4:$S5)>$R5,1,0))","v":2}]
[866,61.734570393264733,133.51516734190585,3,14,{"$f":"SUM(IF($E$4:$E6>$D6,1,0))","v":3},{"$f":"SUM(IF(1000+1-($E$4:$E6)>$D6,1,0))","v":3},null,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"footcorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003)","v":2.4900024900020856E-4},null,{"$f":"R5+1","v":3},16,{"$f":"SUM(IF($S$4:$S6>$R6,1,0))","v":3},{"$f":"SUM(IF(16+1-($S$4:$S6)>$R6,1,0))","v":1}]
[965,61.877655199001573,152.08396733094887,4,236,{"$f":"SUM(IF($E$4:$E7>$D7,1,0))","v":4},{"$f":"SUM(IF(1000+1-($E$4:$E7)>$D7,1,0))","v":4},null,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"footcorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003)","v":0.28939528939528936},null,4,2,{"$f":"SUM(IF($S$4:$S7>$R7,1,0))","v":3},{"$f":"SUM(IF(16+1-($S$4:$S7)>$R7,1,0))","v":2}]
[260,62.73808266150202,142.56237692928903,5,82,{"$f":"SUM(IF($E$4:$E8>$D8,1,0))","v":5},{"$f":"SUM(IF(1000+1-($E$4:$E8)>$D8,1,0))","v":5},null,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"footcorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003)","v":0.28939528939528936},null,5,12,{"$f":"SUM(IF($S$4:$S8>$R8,1,0))","v":4},{"$f":"SUM(IF(16+1-($S$4:$S8)>$R8,1,0))","v":2}]
[302,62.824173201537945,149.13048299698045,6,177,{"$f":"SUM(IF($E$4:$E9>$D9,1,0))","v":6},{"$f":"SUM(IF(1000+1-($E$4:$E9)>$D9,1,0))","v":6},null,null,"Intermediate Calculations for\nthe Greatest Deviation Correlation",null,null,null,null,"(X, Y) with duplicates",{"$f":"footcorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003)","v":0.28940728940728944},null,6,13,{"$f":"SUM(IF($S$4:$S9>$R9,1,0))","v":5},{"$f":"SUM(IF(16+1-($S$4:$S9)>$R9,1,0))","v":1}]
[155,63.165209918698068,123.77153681679405,7,3,{"$f":"SUM(IF($E$4:$E10>$D10,1,0))","v":6},{"$f":"SUM(IF(1000+1-($E$4:$E10)>$D10,1,0))","v":7},null,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"footcorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003)","v":0.28940728940728944},null,7,7,{"$f":"SUM(IF($S$4:$S10>$R10,1,0))","v":5},{"$f":"SUM(IF(16+1-($S$4:$S10)>$R10,1,0))","v":2}]
[522,63.17430187853067,134.56610097899684,8,20,{"$f":"SUM(IF($E$4:$E11>$D11,1,0))","v":7},{"$f":"SUM(IF(1000+1-($E$4:$E11)>$D11,1,0))","v":8},null,null,"Maximum d+ = ",null,{"$f":"MAX(F4:F1003)","v":176},null,null,null,null,null,8,9,{"$f":"SUM(IF($S$4:$S11>$R11,1,0))","v":6},{"$f":"SUM(IF(16+1-($S$4:$S11)>$R11,1,0))","v":2}]
[259,63.293724508537558,136.88877384867516,9,28,{"$f":"SUM(IF($E$4:$E12>$D12,1,0))","v":8},{"$f":"SUM(IF(1000+1-($E$4:$E12)>$D12,1,0))","v":9},null,null,"Maximum d- = ",null,{"$f":"MAX(G4:G1003)","v":332},null,null,null,null,null,9,10,{"$f":"SUM(IF($S$4:$S12>$R12,1,0))","v":6},{"$f":"SUM(IF(16+1-($S$4:$S12)>$R12,1,0))","v":2}]
[848,63.32614218189299,153.22463810559995,10,267,{"$f":"SUM(IF($E$4:$E13>$D13,1,0))","v":9},{"$f":"SUM(IF(1000+1-($E$4:$E13)>$D13,1,0))","v":10},null,null,"# of Observations (n) = ",null,{"$f":"COUNTA(A4:A1003)","v":1000},null,null,null,null,null,10,3,{"$f":"SUM(IF($S$4:$S13>$R13,1,0))","v":5},{"$f":"SUM(IF(16+1-($S$4:$S13)>$R13,1,0))","v":2}]
[355,63.384826231893328,139.97702828817486,11,56,{"$f":"SUM(IF($E$4:$E14>$D14,1,0))","v":10},{"$f":"SUM(IF(1000+1-($E$4:$E14)>$D14,1,0))","v":11},null,null,"Largest integer  of n/2",null,{"$f":"FLOOR(L13/2,1)","v":500},null,null,"Notes:",null,null,11,8,{"$f":"SUM(IF($S$4:$S14>$R14,1,0))","v":4},{"$f":"SUM(IF(16+1-($S$4:$S14)>$R14,1,0))","v":2}]
[798,63.710534533360629,159.93329239615144,12,453,{"$f":"SUM(IF($E$4:$E15>$D15,1,0))","v":11},{"$f":"SUM(IF(1000+1-($E$4:$E15)>$D15,1,0))","v":12},null,null,null,null,null,null,null,null,null,null,12,1,{"$f":"SUM(IF($S$4:$S15>$R15,1,0))","v":3},{"$f":"SUM(IF(16+1-($S$4:$S15)>$R15,1,0))","v":3}]
[464,63.718696610570163,158.43790809605861,13,406,{"$f":"SUM(IF($E$4:$E16>$D16,1,0))","v":12},{"$f":"SUM(IF(1000+1-($E$4:$E16)>$D16,1,0))","v":13},null,null,null,null,null,null,null,null,null,null,13,15,{"$f":"SUM(IF($S$4:$S16>$R16,1,0))","v":3},{"$f":"SUM(IF(16+1-($S$4:$S16)>$R16,1,0))","v":3}]
[339,63.725696957922054,139.47275443564163,14,51,{"$f":"SUM(IF($E$4:$E17>$D17,1,0))","v":12},{"$f":"SUM(IF(1000+1-($E$4:$E17)>$D17,1,0))","v":14},null,null,null,null,null,null,null,null,null,null,14,6,{"$f":"SUM(IF($S$4:$S17>$R17,1,0))","v":2},{"$f":"SUM(IF(16+1-($S$4:$S17)>$R17,1,0))","v":2}]
[587,63.751050285831056,154.08035846372795,15,283,{"$f":"SUM(IF($E$4:$E18>$D18,1,0))","v":13},{"$f":"SUM(IF(1000+1-($E$4:$E18)>$D18,1,0))","v":15},null,null,null,null,null,null,null,null,null,null,15,4,{"$f":"SUM(IF($S$4:$S18>$R18,1,0))","v":1},{"$f":"SUM(IF(16+1-($S$4:$S18)>$R18,1,0))","v":1}]
[350,63.798239301904559,126.03206148672338,16,4,{"$f":"SUM(IF($E$4:$E19>$D19,1,0))","v":13},{"$f":"SUM(IF(1000+1-($E$4:$E19)>$D19,1,0))","v":16},null,null,null,null,null,null,null,null,null,null,16,5,{"$f":"SUM(IF($S$4:$S19>$R19,1,0))","v":0},{"$f":"SUM(IF(16+1-($S$4:$S19)>$R19,1,0))","v":0}]
[847,63.905285849408564,143.2106694203591,17,92,{"$f":"SUM(IF($E$4:$E20>$D20,1,0))","v":14},{"$f":"SUM(IF(1000+1-($E$4:$E20)>$D20,1,0))","v":17},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MAX(T4:T19)","v":6},{"$f":"MAX(U4:U19)","v":3}]
[734,63.935966973490352,150.04129763153719,18,194,{"$f":"SUM(IF($E$4:$E21>$D21,1,0))","v":15},{"$f":"SUM(IF(1000+1-($E$4:$E21)>$D21,1,0))","v":18}]
[790,63.994192888295409,137.76138158117121,19,32,{"$f":"SUM(IF($E$4:$E22>$D22,1,0))","v":16},{"$f":"SUM(IF(1000+1-($E$4:$E22)>$D22,1,0))","v":19},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(U20-T20)/8","v":-0.375}]
[381,64.002307309750904,154.60462713460578,20,296,{"$f":"SUM(IF($E$4:$E23>$D23,1,0))","v":16},{"$f":"SUM(IF(1000+1-($E$4:$E23)>$D23,1,0))","v":20}]
[146,64.139584202718865,159.11634223377763,21,429,{"$f":"SUM(IF($E$4:$E24>$D24,1,0))","v":17},{"$f":"SUM(IF(1000+1-($E$4:$E24)>$D24,1,0))","v":21}]
[365,64.148218074751028,158.53163399860793,22,412,{"$f":"SUM(IF($E$4:$E25>$D25,1,0))","v":18},{"$f":"SUM(IF(1000+1-($E$4:$E25)>$D25,1,0))","v":22}]
[53,64.166896838800838,157.77140207039417,23,382,{"$f":"SUM(IF($E$4:$E26>$D26,1,0))","v":19},{"$f":"SUM(IF(1000+1-($E$4:$E26)>$D26,1,0))","v":23}]
[392,64.198034754494032,142.38171322283631,24,80,{"$f":"SUM(IF($E$4:$E27>$D27,1,0))","v":20},{"$f":"SUM(IF(1000+1-($E$4:$E27)>$D27,1,0))","v":24}]
[452,64.199591200798295,147.28602201146384,25,149,{"$f":"SUM(IF($E$4:$E28>$D28,1,0))","v":21},{"$f":"SUM(IF(1000+1-($E$4:$E28)>$D28,1,0))","v":25}]
[394,64.327840923692278,161.22028722045687,26,486,{"$f":"SUM(IF($E$4:$E29>$D29,1,0))","v":22},{"$f":"SUM(IF(1000+1-($E$4:$E29)>$D29,1,0))","v":26}]
[291,64.329377153871704,136.9310135455159,27,29,{"$f":"SUM(IF($E$4:$E30>$D30,1,0))","v":23},{"$f":"SUM(IF(1000+1-($E$4:$E30)>$D30,1,0))","v":27}]
[520,64.3841726953045,155.06001788003789,28,313,{"$f":"SUM(IF($E$4:$E31>$D31,1,0))","v":23},{"$f":"SUM(IF(1000+1-($E$4:$E31)>$D31,1,0))","v":28}]
[716,64.419510750452119,171.00298356664476,29,739,{"$f":"SUM(IF($E$4:$E32>$D32,1,0))","v":23},{"$f":"SUM(IF(1000+1-($E$4:$E32)>$D32,1,0))","v":29}]
[33,64.432162861783951,134.40751922342531,30,19,{"$f":"SUM(IF($E$4:$E33>$D33,1,0))","v":23},{"$f":"SUM(IF(1000+1-($E$4:$E33)>$D33,1,0))","v":30}]
[337,64.461456499581601,166.5710611102445,31,629,{"$f":"SUM(IF($E$4:$E34>$D34,1,0))","v":24},{"$f":"SUM(IF(1000+1-($E$4:$E34)>$D34,1,0))","v":31}]
[422,64.470749261184338,148.62162514283537,32,170,{"$f":"SUM(IF($E$4:$E35>$D35,1,0))","v":24},{"$f":"SUM(IF(1000+1-($E$4:$E35)>$D35,1,0))","v":32}]
[832,64.562984969897073,150.52740164832412,33,205,{"$f":"SUM(IF($E$4:$E36>$D36,1,0))","v":25},{"$f":"SUM(IF(1000+1-($E$4:$E36)>$D36,1,0))","v":33}]
[820,64.614025605265994,138.86910207320568,34,43,{"$f":"SUM(IF($E$4:$E37>$D37,1,0))","v":26},{"$f":"SUM(IF(1000+1-($E$4:$E37)>$D37,1,0))","v":34}]
[340,64.674241740156788,156.33098784633827,35,343,{"$f":"SUM(IF($E$4:$E38>$D38,1,0))","v":27},{"$f":"SUM(IF(1000+1-($E$4:$E38)>$D38,1,0))","v":35}]
[492,64.694431051599807,158.01999874157147,36,387,{"$f":"SUM(IF($E$4:$E39>$D39,1,0))","v":28},{"$f":"SUM(IF(1000+1-($E$4:$E39)>$D39,1,0))","v":36}]
[772,64.703794797666845,156.99562303431941,37,361,{"$f":"SUM(IF($E$4:$E40>$D40,1,0))","v":29},{"$f":"SUM(IF(1000+1-($E$4:$E40)>$D40,1,0))","v":37}]
[871,64.727359065630679,132.1463650108235,38,11,{"$f":"SUM(IF($E$4:$E41>$D41,1,0))","v":29},{"$f":"SUM(IF(1000+1-($E$4:$E41)>$D41,1,0))","v":38}]
[485,64.778107772883516,147.15992208831364,39,144,{"$f":"SUM(IF($E$4:$E42>$D42,1,0))","v":30},{"$f":"SUM(IF(1000+1-($E$4:$E42)>$D42,1,0))","v":39}]
[447,64.783550086575445,166.10195943376934,40,617,{"$f":"SUM(IF($E$4:$E43>$D43,1,0))","v":31},{"$f":"SUM(IF(1000+1-($E$4:$E43)>$D43,1,0))","v":40}]
[177,64.798215543717106,146.80340340234113,41,139,{"$f":"SUM(IF($E$4:$E44>$D44,1,0))","v":31},{"$f":"SUM(IF(1000+1-($E$4:$E44)>$D44,1,0))","v":41}]
[305,64.801177032824995,139.22164671455997,42,48,{"$f":"SUM(IF($E$4:$E45>$D45,1,0))","v":32},{"$f":"SUM(IF(1000+1-($E$4:$E45)>$D45,1,0))","v":42}]
[810,64.8207646671286,131.26939386613492,43,10,{"$f":"SUM(IF($E$4:$E46>$D46,1,0))","v":31},{"$f":"SUM(IF(1000+1-($E$4:$E46)>$D46,1,0))","v":43}]
[509,64.832578645266253,152.40176655318865,44,246,{"$f":"SUM(IF($E$4:$E47>$D47,1,0))","v":32},{"$f":"SUM(IF(1000+1-($E$4:$E47)>$D47,1,0))","v":44}]
[493,64.854717985183015,154.13453451726659,45,286,{"$f":"SUM(IF($E$4:$E48>$D48,1,0))","v":33},{"$f":"SUM(IF(1000+1-($E$4:$E48)>$D48,1,0))","v":45}]
[247,64.915006638571711,151.8994206235389,46,232,{"$f":"SUM(IF($E$4:$E49>$D49,1,0))","v":34},{"$f":"SUM(IF(1000+1-($E$4:$E49)>$D49,1,0))","v":46}]
[16,64.969503845277544,170.46052364202347,47,727,{"$f":"SUM(IF($E$4:$E50>$D50,1,0))","v":35},{"$f":"SUM(IF(1000+1-($E$4:$E50)>$D50,1,0))","v":47}]
[854,65.007883117155998,164.2952408796948,48,584,{"$f":"SUM(IF($E$4:$E51>$D51,1,0))","v":35},{"$f":"SUM(IF(1000+1-($E$4:$E51)>$D51,1,0))","v":48}]
[454,65.026704184150304,140.30204925197694,49,62,{"$f":"SUM(IF($E$4:$E52>$D52,1,0))","v":36},{"$f":"SUM(IF(1000+1-($E$4:$E52)>$D52,1,0))","v":49}]
[812,65.044236203556807,161.62223192699167,50,501,{"$f":"SUM(IF($E$4:$E53>$D53,1,0))","v":37},{"$f":"SUM(IF(1000+1-($E$4:$E53)>$D53,1,0))","v":50}]
[232,65.080364936359004,166.51706198784535,51,628,{"$f":"SUM(IF($E$4:$E54>$D54,1,0))","v":37},{"$f":"SUM(IF(1000+1-($E$4:$E54)>$D54,1,0))","v":51}]
[945,65.081620831171904,167.23078872947454,52,648,{"$f":"SUM(IF($E$4:$E55>$D55,1,0))","v":38},{"$f":"SUM(IF(1000+1-($E$4:$E55)>$D55,1,0))","v":52}]
[506,65.225829274139301,118.20685120412463,53,1,{"$f":"SUM(IF($E$4:$E56>$D56,1,0))","v":38},{"$f":"SUM(IF(1000+1-($E$4:$E56)>$D56,1,0))","v":53}]
[733,65.231080743004966,139.30404931415893,54,49,{"$f":"SUM(IF($E$4:$E57>$D57,1,0))","v":38},{"$f":"SUM(IF(1000+1-($E$4:$E57)>$D57,1,0))","v":54}]
[28,65.231388920735938,150.1850862026223,55,196,{"$f":"SUM(IF($E$4:$E58>$D58,1,0))","v":39},{"$f":"SUM(IF(1000+1-($E$4:$E58)>$D58,1,0))","v":55}]
[517,65.247553136931771,135.91370970295128,56,25,{"$f":"SUM(IF($E$4:$E59>$D59,1,0))","v":38},{"$f":"SUM(IF(1000+1-($E$4:$E59)>$D59,1,0))","v":56}]
[861,65.271379634769175,165.2250269231609,57,605,{"$f":"SUM(IF($E$4:$E60>$D60,1,0))","v":39},{"$f":"SUM(IF(1000+1-($E$4:$E60)>$D60,1,0))","v":57}]
[904,65.296827744729754,141.16343061145179,58,71,{"$f":"SUM(IF($E$4:$E61>$D61,1,0))","v":40},{"$f":"SUM(IF(1000+1-($E$4:$E61)>$D61,1,0))","v":58}]
[703,65.306185967080395,132.78637829542032,59,12,{"$f":"SUM(IF($E$4:$E62>$D62,1,0))","v":40},{"$f":"SUM(IF(1000+1-($E$4:$E62)>$D62,1,0))","v":59}]
[145,65.368458537561708,150.62044502403535,60,207,{"$f":"SUM(IF($E$4:$E63>$D63,1,0))","v":41},{"$f":"SUM(IF(1000+1-($E$4:$E63)>$D63,1,0))","v":60}]
[170,65.372857365859304,145.88425917197276,61,123,{"$f":"SUM(IF($E$4:$E64>$D64,1,0))","v":42},{"$f":"SUM(IF(1000+1-($E$4:$E64)>$D64,1,0))","v":61}]
[691,65.375896929864496,162.1351638854139,62,521,{"$f":"SUM(IF($E$4:$E65>$D65,1,0))","v":42},{"$f":"SUM(IF(1000+1-($E$4:$E65)>$D65,1,0))","v":62}]
[598,65.381771463745309,145.90727759270729,63,124,{"$f":"SUM(IF($E$4:$E66>$D66,1,0))","v":43},{"$f":"SUM(IF(1000+1-($E$4:$E66)>$D66,1,0))","v":63}]
[134,65.486664403091069,155.40705816954977,64,321,{"$f":"SUM(IF($E$4:$E67>$D67,1,0))","v":44},{"$f":"SUM(IF(1000+1-($E$4:$E67)>$D67,1,0))","v":64}]
[856,65.518809889007301,139.7615845171749,65,54,{"$f":"SUM(IF($E$4:$E68>$D68,1,0))","v":44},{"$f":"SUM(IF(1000+1-($E$4:$E68)>$D68,1,0))","v":65}]
[511,65.556008234454197,166.24511929990354,66,621,{"$f":"SUM(IF($E$4:$E69>$D69,1,0))","v":45},{"$f":"SUM(IF(1000+1-($E$4:$E69)>$D69,1,0))","v":66}]
[968,65.574685680426299,163.58129464849748,67,559,{"$f":"SUM(IF($E$4:$E70>$D70,1,0))","v":46},{"$f":"SUM(IF(1000+1-($E$4:$E70)>$D70,1,0))","v":67}]
[441,65.588977962881302,152.772859227298,68,260,{"$f":"SUM(IF($E$4:$E71>$D71,1,0))","v":47},{"$f":"SUM(IF(1000+1-($E$4:$E71)>$D71,1,0))","v":68}]
[10,65.649488474075483,147.60307841115861,69,153,{"$f":"SUM(IF($E$4:$E72>$D72,1,0))","v":48},{"$f":"SUM(IF(1000+1-($E$4:$E72)>$D72,1,0))","v":69}]
[715,65.67887438957932,163.9351785520895,70,570,{"$f":"SUM(IF($E$4:$E73>$D73,1,0))","v":49},{"$f":"SUM(IF(1000+1-($E$4:$E73)>$D73,1,0))","v":70}]
[99,65.684256326241609,145.87223281078164,71,122,{"$f":"SUM(IF($E$4:$E74>$D74,1,0))","v":49},{"$f":"SUM(IF(1000+1-($E$4:$E74)>$D74,1,0))","v":71}]
[975,65.699545273898138,176.36856795111959,72,846,{"$f":"SUM(IF($E$4:$E75>$D75,1,0))","v":50},{"$f":"SUM(IF(1000+1-($E$4:$E75)>$D75,1,0))","v":72}]
[283,65.730838906065273,149.34197266426088,73,182,{"$f":"SUM(IF($E$4:$E76>$D76,1,0))","v":51},{"$f":"SUM(IF(1000+1-($E$4:$E76)>$D76,1,0))","v":73}]
[294,65.742526507537107,172.65778893959671,74,781,{"$f":"SUM(IF($E$4:$E77>$D77,1,0))","v":52},{"$f":"SUM(IF(1000+1-($E$4:$E77)>$D77,1,0))","v":74}]
[936,65.746470074843629,152.53956857371412,75,253,{"$f":"SUM(IF($E$4:$E78>$D78,1,0))","v":53},{"$f":"SUM(IF(1000+1-($E$4:$E78)>$D78,1,0))","v":75}]
[274,65.78601954551047,172.46433328235415,76,776,{"$f":"SUM(IF($E$4:$E79>$D79,1,0))","v":54},{"$f":"SUM(IF(1000+1-($E$4:$E79)>$D79,1,0))","v":76}]
[974,65.791081929103797,162.06889297833703,77,518,{"$f":"SUM(IF($E$4:$E80>$D80,1,0))","v":55},{"$f":"SUM(IF(1000+1-($E$4:$E80)>$D80,1,0))","v":77}]
[538,65.796854924957373,167.9132704908788,78,660,{"$f":"SUM(IF($E$4:$E81>$D81,1,0))","v":56},{"$f":"SUM(IF(1000+1-($E$4:$E81)>$D81,1,0))","v":78}]
[664,65.806275625891658,141.68392778074374,79,72,{"$f":"SUM(IF($E$4:$E82>$D82,1,0))","v":56},{"$f":"SUM(IF(1000+1-($E$4:$E82)>$D82,1,0))","v":79}]
[158,65.835300916793514,156.72584204569222,80,356,{"$f":"SUM(IF($E$4:$E83>$D83,1,0))","v":56},{"$f":"SUM(IF(1000+1-($E$4:$E83)>$D83,1,0))","v":80}]
[543,65.850000048762297,142.67937372077074,81,84,{"$f":"SUM(IF($E$4:$E84>$D84,1,0))","v":57},{"$f":"SUM(IF(1000+1-($E$4:$E84)>$D84,1,0))","v":81}]
[799,65.874734470513161,164.43036806978321,82,586,{"$f":"SUM(IF($E$4:$E85>$D85,1,0))","v":57},{"$f":"SUM(IF(1000+1-($E$4:$E85)>$D85,1,0))","v":82}]
[654,65.881457515481756,172.1194752380589,83,767,{"$f":"SUM(IF($E$4:$E86>$D86,1,0))","v":58},{"$f":"SUM(IF(1000+1-($E$4:$E86)>$D86,1,0))","v":83}]
[79,65.890898680095972,163.57768387415356,84,558,{"$f":"SUM(IF($E$4:$E87>$D87,1,0))","v":58},{"$f":"SUM(IF(1000+1-($E$4:$E87)>$D87,1,0))","v":84}]
[967,65.901947342454605,154.63298294101941,85,298,{"$f":"SUM(IF($E$4:$E88>$D88,1,0))","v":59},{"$f":"SUM(IF(1000+1-($E$4:$E88)>$D88,1,0))","v":85}]
[669,65.919503042825056,144.43781583923646,86,106,{"$f":"SUM(IF($E$4:$E89>$D89,1,0))","v":60},{"$f":"SUM(IF(1000+1-($E$4:$E89)>$D89,1,0))","v":86}]
[210,65.92729568007276,133.71272972121488,87,16,{"$f":"SUM(IF($E$4:$E90>$D90,1,0))","v":60},{"$f":"SUM(IF(1000+1-($E$4:$E90)>$D90,1,0))","v":87}]
[843,65.948803227494153,135.58820193574715,88,24,{"$f":"SUM(IF($E$4:$E91>$D91,1,0))","v":60},{"$f":"SUM(IF(1000+1-($E$4:$E91)>$D91,1,0))","v":88}]
[351,65.966736967405836,158.30645250581063,89,399,{"$f":"SUM(IF($E$4:$E92>$D92,1,0))","v":61},{"$f":"SUM(IF(1000+1-($E$4:$E92)>$D92,1,0))","v":89}]
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[278,77.459376491510042,192.32485766256121,995,984,{"$f":"SUM(IF($E$4:$E998>$D998,1,0))","v":5},{"$f":"SUM(IF(1000+1-($E$4:$E998)>$D998,1,0))","v":5}]
[872,78.101738260691391,193.01562642203402,996,986,{"$f":"SUM(IF($E$4:$E999>$D999,1,0))","v":4},{"$f":"SUM(IF(1000+1-($E$4:$E999)>$D999,1,0))","v":4}]
[77,78.776806264444375,177.53874289601023,997,864,{"$f":"SUM(IF($E$4:$E1000>$D1000,1,0))","v":3},{"$f":"SUM(IF(1000+1-($E$4:$E1000)>$D1000,1,0))","v":3}]
[505,78.87067039469666,174.8569052469376,998,821,{"$f":"SUM(IF($E$4:$E1001>$D1001,1,0))","v":2},{"$f":"SUM(IF(1000+1-($E$4:$E1001)>$D1001,1,0))","v":2}]
[783,79.299240538345117,172.28788654721851,999,771,{"$f":"SUM(IF($E$4:$E1002>$D1002,1,0))","v":1},{"$f":"SUM(IF(1000+1-($E$4:$E1002)>$D1002,1,0))","v":1}]
[550,79.457861636090044,177.55841409576601,1000,866,{"$f":"SUM(IF($E$4:$E1003>$D1003,1,0))","v":0},{"$f":"SUM(IF(1000+1-($E$4:$E1003)>$D1003,1,0))","v":0}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(Q904:Q1003)","v":0}]

{"sheet":"Percentage Bend Correlation","index":20,"n_rows":1003,"n_cols":22,"rows_kept":1003,"cut":false,"hidden":false,"merged":[[23,16,23,17],[24,16,24,17],[21,16,21,17],[13,16,13,17],[14,16,14,17],[15,16,15,17],[16,16,16,17],[20,16,20,17],[22,16,22,17],[0,0,0,21],[10,16,10,17],[11,16,11,17],[12,16,12,17],[17,16,17,17],[18,16,18,17],[19,16,19,17],[13,20,13,21],[14,20,29,21],[2,16,2,18],[2,20,3,21],[3,16,3,17],[4,16,4,17],[8,16,9,18]]}
["Calculating the Percentage Bend Correlation Coefficient"]
[]
["Obs\nNum","X","Y","|X-Xmed|","|Y-Ymed|","psi(x)","psi(y)","Sx","Sy","a","b","a2","b2","ab",null,null,"Comparison of Manually Calculated\nCorrelation with Macro Calculation",null,null,null,"Percentage Bend Correlation Applied to\nthe Paired Data Series From the\n\"Simulated Data\" Worksheet"]
[{"$f":"'Simulated Data'!A4","v":1},69.5902475889052,179.20354047781973,{"$f":"ABS(B4-$S$14)","v":0.43909828518724225},{"$f":"ABS(C4-$S$15)","v":17.597472773307118},{"$f":"(B4-$S$14)/$S$16","v":-0.11402009622333237},{"$f":"(C4-$S$15)/$S$17","v":0.97483120672056334},{"$f":"AND(F4>=-1,F4<=1)*B4","v":69.5902475889052},{"$f":"AND(G4>=-1,G4<=1)*C4","v":179.20354047781973},{"$f":"IF((B4-$S$24)/$S$16 <=-1,-1,IF((B4-$S$24)/$S$16>=1,1, (B4-$S$24)/$S$16))","v":-0.10349598394360372},{"$f":"IF((C4-$S$25)/$S$17 <=-1,-1,IF((C4-$S$25)/$S$17>=1,1, (C4-$S$25)/$S$17))","v":0.9577755062418416},{"$f":"J4^2","v":1.0711418692454679E-2},{"$f":"K4^2","v":0.91733392035681594},{"$f":"J4*K4","v":-9.9125918415582562E-2},null,null,"Calculated Pct Bend = ",null,{"$f":"SUM(N4:N1003)/(SQRT(SUM(L4:L1003)*SUM(M4:M1003)))","v":0.44705743496276296}]
[{"$f":"'Simulated Data'!A5","v":2},75.900421131737588,148.6347709869498,5.8710752576451455,12.971296717562808,{"$f":"(B5-$S$14)/$S$16","v":1.5245346848158792},{"$f":"(C5-$S$15)/$S$17","v":-0.7185591360080209},{"$f":"AND(F5>=-1,F5<=1)*B5","v":0},{"$f":"AND(G5>=-1,G5<=1)*C5","v":148.6347709869498},{"$f":"IF((B5-$S$24)/$S$16 <=-1,-1,IF((B5-$S$24)/$S$16>=1,1, (B5-$S$24)/$S$16))","v":1},{"$f":"IF((C5-$S$25)/$S$17 <=-1,-1,IF((C5-$S$25)/$S$17>=1,1, (C5-$S$25)/$S$17))","v":-0.73561483648674253},{"$f":"J5^2","v":1},{"$f":"K5^2","v":0.54112918765941698},{"$f":"J5*K5","v":-0.73561483648674253},null,null,"VBA Pct Bend = ",null,{"$f":"PBCorr(B4:B1003,C4:C1003,S11)","v":0.44705743496276296},null,"U1(0,1), U2(0,1)",{"$f":"PBCorr('Simulated Data'!$B$4:$B$1003,'Simulated Data'!$C$4:$C$1003,S11)","v":2.0457527057698821E-2}]
[{"$f":"'Simulated Data'!A6","v":3},68.70319256856132,148.28328151641921,1.3261533055311219,13.322786188093403,-0.34436055116696701,-0.73803027877498983,68.70319256856132,148.28328151641921,-0.33383643888723835,-0.75508597925371146,0.11144676792891282,0.57015483606553641,0.25207521436774216,null,null,null,null,null,null,"N1(0,1), N2(0,1)",{"$f":"PBCorr('Simulated Data'!$D$4:$D$1003,'Simulated Data'!$E$4:$E$1003,S11)","v":-2.2672054873132855E-2}]
[{"$f":"'Simulated Data'!A7","v":4},70.30671508908884,161.11898050586314,0.27736921499639777,0.48708719864947625,7.2024113165901987E-2,-2.6982726880978865E-2,70.30671508908884,161.11898050586314,8.2548225445630632E-2,-4.4038427359700538E-2,6.8142095242226608E-3,1.9393830843156209E-3,-3.635294029959588E-3,null,null,null,null,null,null,"X, Y (Correlated)",{"$f":"PBCorr('Simulated Data'!$F$4:$F$1003,'Simulated Data'!$G$4:$G$1003,S11)","v":0.44705743496276296}]
[{"$f":"'Simulated Data'!A8","v":5},67.375076704515038,167.57356788815855,2.6542691695774039,5.9675001836459387,-0.68923071742078656,0.33057618443670983,67.375076704515038,167.57356788815855,-0.67870660514105785,0.31352048395798815,0.46064265586209979,9.8295093861251098E-2,-0.21278842330930761,null,null,null,null,null,null,"Ranks of (X, Y)",{"$f":"PBCorr('Simulated Data'!$H$4:$H$1003,'Simulated Data'!$I$4:$I$1003,S11)","v":0.43517722005211373}]
[{"$f":"'Simulated Data'!A9","v":6},70.303701168768001,166.7573260094741,0.27435529467555853,5.1512583049614875,7.1241492289017869E-2,0.285359574880093,70.303701168768001,166.7573260094741,8.1765604568746528E-2,0.26830387440137132,6.6856140904926233E-3,7.1986969018786831E-2,2.1938028498565163E-2,null,null,"Intermediate Calculations for\nthe Percentage Bend Correlation",null,null,null,"(X, Y) with duplicates",{"$f":"PBCorr('Simulated Data'!$J$4:$J$1003,'Simulated Data'!$K$4:$K$1003,S11)","v":0.44705752297092943}]
[{"$f":"'Simulated Data'!A10","v":7},72.04643599739471,158.14029467085311,2.0170901233022676,3.4657730336595023,0.5237752405523175,-0.19199027906704047,72.04643599739471,158.14029467085311,0.5342993528320461,-0.20904597954576215,0.28547579843674331,4.3700221564247209E-2,-0.11169313158344187,null,null,null,null,null,null,"Ranks of (X, Y) with duplicates",{"$f":"PBCorr('Simulated Data'!$L$4:$L$1003,'Simulated Data'!$M$4:$M$1003,S11)","v":0.43520193850799666}]
[{"$f":"'Simulated Data'!A11","v":8},69.659038619402779,151.45915754274174,0.37030725468966352,10.146910161770876,-9.6157216359678541E-2,-0.56209916076632871,69.659038619402779,151.45915754274174,-8.5633104079949882E-2,-0.57915486124505033,7.3330285143675287E-3,0.33542035330377351,4.9594828511406328E-2,null,null,"bend = ",null,0.2]
[{"$f":"'Simulated Data'!A12","v":9},74.291448615158941,185.99290055062283,4.2621027410664993,24.386832846110224,1.1067348269030552,1.3509352165344251,0,0,1,1,1,1,1,null,null,"# of Observations = ",null,{"$f":"COUNTA(A4:A1003)","v":1000}]
[{"$f":"'Simulated Data'!A13","v":10},65.649488474075483,147.60307841115861,4.3798574000169594,14.002989293354005,-1.1373120302245208,-0.77571087203165745,0,147.60307841115861,-1,-0.79276657251037908,1,0.62847883848985409,0.79276657251037908,null,null,"Floor of ((1-beta)*n) = ",null,{"$f":"FLOOR((1-S11)*S12,1)","v":800}]
[{"$f":"'Simulated Data'!A14","v":11},69.742697145918896,154.65949081048038,0.28664872817354592,6.9465768940322334,-7.4433712613353561E-2,-0.38481320718156747,69.742697145918896,154.65949081048038,-6.3909600333624902E-2,-0.40186890766028915,4.0844370148036685E-3,0.16149861894407402,2.5683281275079489E-2,null,null,"Median of X = ",null,{"$f":"MEDIAN(B4:B1003)","v":70.029345874092442},null,"Notes:"]
[{"$f":"'Simulated Data'!A15","v":12},69.923511910794829,155.01069183161337,0.10583396329761285,6.5953758728992398,-2.7481771361836896E-2,-0.36535804338373595,69.923511910794829,155.01069183161337,-1.6957659082108247E-2,-0.38241374386245763,2.8756220154500833E-4,0.14624027149490135,6.4848418967322213E-3,null,null,"Median of Y = ",null,{"$f":"MEDIAN(C4:C1003)","v":161.60606770451261}]
[{"$f":"'Simulated Data'!A16","v":13},71.272442551537864,167.92486667662297,1.243096677445422,6.3187989721103577,0.32279334162462336,0.35003676416254981,71.272442551537864,167.92486667662297,0.33331745390435197,0.33298106368382813,0.1111005250772798,0.1108763887720136,0.11098840034545647,null,null,"omegax = ",null,{"$f":"_xlfn.PERCENTILE.EXC(D4:D1003,S13/(S12+1))","v":3.8510604685613998}]
[{"$f":"'Simulated Data'!A17","v":14},68.209184553223238,170.8602725769386,1.8201613208692038,9.2542048724259871,-0.47263898755376915,0.51264677713895157,68.209184553223238,170.8602725769386,-0.46211487527404049,0.49559107666022989,0.21355015794954199,0.24561051526524585,-0.22902000857776958,null,null,"omegay = ",null,{"$f":"_xlfn.PERCENTILE.EXC(E4:E1003,S13/(S12+1))","v":18.051815177836687}]
[{"$f":"'Simulated Data'!A18","v":15},71.98267048709441,177.2631871840758,1.9533246130019677,15.657119479563192,0.50721733116064283,0.86734321869118136,71.98267048709441,177.2631871840758,0.51774144344037143,0.85028751821245974,0.2680562022557193,0.72298886362790404,0.44022908701864999,null,null,"Sum of Sx = ",null,{"$f":"SUM(H4:H1003)","v":56014.159867871589}]
[{"$f":"'Simulated Data'!A19","v":16},64.969503845277544,170.46052364202347,5.0598420288148986,8.8544559375108634,-1.3138827785545135,0.49050224868145215,0,170.46052364202347,-1,0.47344654820273052,1,0.22415163400508042,-0.47344654820273052,null,null,"Sum of Sy = ",null,{"$f":"SUM(I4:I1003)","v":129422.85235475941}]
[{"$f":"'Simulated Data'!A20","v":17},67.564203137894168,158.22159030710421,2.4651427361982741,3.3844773974084035,-0.64012049572390939,-0.18748681858673871,67.564203137894168,158.22159030710421,-0.62959638344418078,-0.20454251906546039,0.39639160604599194,4.1837642105644231E-2,0.12877923026417626,null,null,"i1 of X = ",null,{"$f":"COUNTIF(F4:F1003,\"<-1\")","v":103}]
[{"$f":"'Simulated Data'!A21","v":18},72.348110751484867,168.08445955367756,2.3187648773924252,6.4783918491649501,0.60211074230642292,0.35887758573547035,72.348110751484867,168.08445955367756,0.61263485458615152,0.34182188525674867,0.37532146505379504,0.11684220124047785,0.20941200096863238,null,null,"i2 of X = ",null,{"$f":"COUNTIF(F4:F1003,\">1\")","v":97}]
[{"$f":"'Simulated Data'!A22","v":19},73.399997728692298,186.43821871981902,3.3706518545998563,24.832151015306408,0.8752529029644126,1.3756041024502816,73.399997728692298,0,0.88577701524414132,1,0.7846009207348198,1,0.88577701524414132,null,null,"i1 of Y = ",null,{"$f":"COUNTIF(G4:G1003,\"<-1\")","v":97}]
[{"$f":"'Simulated Data'!A23","v":20},70.630878832697576,145.0970574458735,0.60153295860513367,16.509010258639108,0.15619930237809068,-0.91453463798522738,70.630878832697576,145.0970574458735,0.16672341465781934,-0.93159033846394912,2.779669699516317E-2,0.86786055871937529,-0.15531792229094327,null,null,"i2 of Y = ",null,{"$f":"COUNTIF(G4:G1003,\">1\")","v":103}]
[{"$f":"'Simulated Data'!A24","v":21},70.119676553511951,138.10299892045091,9.0330679419508897E-2,23.503068784061696,2.3456053249990328E-2,-1.3019781419498382,70.119676553511951,0,3.3980165529718977E-2,-1,1.1546516494271018E-3,1,-3.3980165529718977E-2,null,null,"PB Location of X = ",null,{"$f":"(S18+S16*(S21-S20))/(S12-S20-S21)","v":69.988816881325278}]
[{"$f":"'Simulated Data'!A25","v":22},66.187165277180767,144.01836436558077,3.8421805969116747,17.587703338931846,-0.99769417496239876,-0.97429001824289341,66.187165277180767,144.01836436558077,-0.98717006268267016,-0.99134571872161503,0.97450473265690696,0.98276633402767544,0.97862681529061346,null,null,"PB Location of Y = ",null,{"$f":"(S19+S17*(S23-S22))/(S12-S22-S23)","v":161.91395405728304}]
[{"$f":"'Simulated Data'!A26","v":23},73.781440690017263,194.19555847709682,3.7520948159248206,32.589490772584213,0.97430171417860167,1.8053304031495023,73.781440690017263,0,0.98482582645833028,1,0.96988190845933331,1,0.98482582645833028]
[{"$f":"'Simulated Data'!A27","v":24},67.094982124804702,159.50283587727762,2.9343637492877406,2.1032318272349926,-0.76196252259417263,-0.1165108221259244,67.094982124804702,159.50283587727762,-0.75143841031444392,-0.13356652260464608,0.56465968449589854,1.7840015960697432E-2,0.10036701541726349]
[{"$f":"'Simulated Data'!A28","v":25},69.938280213559452,159.32747874166122,9.1065660532990478E-2,2.2785889628513871,-2.3646904865923572E-2,-0.12622492200390736,69.938280213559452,159.32747874166122,-1.3122792586194922E-2,-0.14328062248262904,1.722076852602924E-4,2.0529336779009665E-2,1.880241890460438E-3]
[{"$f":"'Simulated Data'!A29","v":26},69.152185366445423,169.67875714103042,0.87716050764701947,8.0726894365178055,-0.22777115934891853,0.44719544029174074,69.152185366445423,169.67875714103042,-0.21724704706918987,0.43013973981301906,4.7196279460282799E-2,0.18502019576641174,-9.344658830148804E-2]
[{"$f":"'Simulated Data'!A30","v":27},69.979041938513163,169.26417290074878,5.0303935579279369E-2,7.6581051962361641,-1.3062359313737518E-2,0.42422909390510966,69.979041938513163,169.26417290074878,-2.5382470340088678E-3,0.40717339342638803,6.4426980056548145E-6,0.16579017231436016,-1.0335066581918552E-3]
[{"$f":"'Simulated Data'!A31","v":28},65.231388920735938,150.1850862026223,4.7979569533565041,11.42098150189031,-1.245879412313883,-0.63267773292475016,0,150.1850862026223,-1,-0.64973343340347178,1,0.42215353448226373,0.64973343340347178]
[{"$f":"'Simulated Data'!A32","v":29},69.189918454669353,162.13540998077724,0.83942741942308885,0.52934227626462871,-0.21797305606490902,2.9323493014405247E-2,69.189918454669353,162.13540998077724,-0.20744894378518039,1.2267792535683577E-2,4.303506427758693E-2,1.5049873369857368E-4,-2.5449406041032781E-3]
[{"$f":"'Simulated Data'!A33","v":30},70.721846699211568,179.8605006679764,0.69250082511912581,18.254432963463785,0.17982081319481749,1.0112242333322725,70.721846699211568,0,0.19034492547454615,0.99416853285355089,3.6231190653910526E-2,0.98837107171618188,0.18923493529514804]
[{"$f":"'Simulated Data'!A34","v":31},73.086466808676647,167.34548500243301,3.057120934584205,5.7394172979203972,0.79383872560334567,0.31794128409684969,73.086466808676647,167.34548500243301,0.80436283788307439,0.30088558361812801,0.64699957496731297,9.0532134429221506E-2,0.24202118191718253]
[{"$f":"'Simulated Data'!A35","v":32},72.420047763828379,176.77910111575324,2.3907018897359364,15.173033411240624,0.62079053529611439,0.84052674269950878,72.420047763828379,176.77910111575324,0.63131464757584299,0.82347104222078704,0.39855818424381084,0.67810455737618924,0.51986933080852826]
[{"$f":"'Simulated Data'!A36","v":33},64.432162861783951,134.40751922342531,5.5971830123084914,27.1985484810873,-1.4534134319629035,-1.5066932722910111,0,0,-1,-1,1,1,1]
[{"$f":"'Simulated Data'!A37","v":34},70.274805760558294,157.56549297529213,0.24545988646585215,4.0405747292204808,6.3738258193994549E-2,-0.22383204621889441,70.274805760558294,157.56549297529213,7.4262370473723208E-2,-0.24088774669761606,5.5148996683765166E-3,5.8026906509054836E-2,-1.7888895087838759E-2]
[{"$f":"'Simulated Data'!A38","v":35},68.139313698476599,139.42832188855618,1.8900321756158434,22.177745815956428,-0.49078226401412045,-1.2285604299331292,68.139313698476599,0,-0.48025815173439179,-1,0.2306478923073341,1,0.48025815173439179]
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