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{"sheet":"Title","index":0,"n_rows":9,"n_cols":3,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
[null,null,"Calculation practice activities to accompany\nCHAPTER 10"]
[]
[null,null,"Social Statistics in Action: A Canadian Introduction"]
[null,null,"Andrea M. Noack"]
[]
[null,null,"Oxford University Press, 2018"]
[]
[null,null,"For more information, visit: "]
[null,null,"https://www.oupcanada.com/catalog/9780199015214.html"]

{"sheet":"Pearson's r","index":1,"n_rows":91,"n_cols":11,"rows_kept":91,"cut":false,"hidden":false,"merged":[[2,1,2,11],[0,1,0,11],[45,4,45,5],[44,4,44,5],[25,4,25,5],[24,4,24,5],[23,4,23,5],[5,3,6,3],[5,2,6,2],[5,1,6,1],[31,4,31,5],[32,4,32,5],[33,4,33,5],[42,4,42,5],[43,4,43,5],[39,4,39,5],[40,4,40,5],[41,4,41,5],[37,4,37,5],[38,4,38,5],[26,4,26,5],[27,4,27,5],[28,4,28,5],[29,4,29,5],[30,4,30,5],[5,5,5,7],[18,1,18,2],[23,8,23,9],[24,8,24,9],[25,8,25,9],[20,5,20,7],[26,8,26,9],[27,8,27,9],[28,8,28,9],[29,8,29,9],[30,8,30,9],[31,8,31,9],[32,8,32,9],[33,8,33,9],[37,8,37,9],[38,8,38,9],[39,8,39,9],[40,8,40,9],[41,8,41,9],[42,8,42,9],[43,8,43,9],[44,8,44,9],[45,8,45,9],[46,4,46,5],[46,8,46,9],[47,4,47,5],[47,8,47,9],[51,4,51,5],[51,8,51,9],[52,4,52,5],[52,8,52,9],[53,4,53,5],[53,8,53,9],[54,4,54,5],[54,8,54,9],[55,4,55,5],[55,8,55,9],[56,4,56,5],[56,8,56,9],[57,4,57,5],[57,8,57,9],[61,4,61,5],[61,8,61,9],[58,4,58,5],[58,8,58,9],[59,4,59,5],[59,8,59,9],[60,4,60,5],[60,8,60,9]]}
[null,"PRACTICE CALCULATING PEARSON'S CORRELATION COEFFICIENTS"]
[]
[null,"Using the values in the yellow highlighted cells, calculate the sum of products, the sum of squares X, the sum of squares Y. \nThen, calculate Pearson's correlation coefficient, the degrees of freedom and the t-statistic. \nKeep two decimal places throughout your calculations. \nTo check your answers, click on the 'Show Correlation Coefficient' and/or 'Show T-Statistic' buttons."]
[]
[]
[null,"Case #","Value on \nVariable X","Value on \nVariable Y",null,"Means"]
[null,null,null,null,null,"Mean of Variable X (x-bar):",null,11.9]
[null,1,13,18,null,"Mean of Variable Y (y-bar):",null,13.2]
[null,2,18,3]
[null,3,26,18,null,"Pearson's Correlation Coefficient"]
[null,4,1,5,null,"Sum of Products:",null,"hidden"]
[null,5,23,12,null,"Sum of Squares X:",null,"hidden"]
[null,6,10,2,null,"Sum of Squares Y:",null,"hidden"]
[null,7,11,15,null,"Correlation Coefficient:",null,"hidden"]
[null,8,4,25]
[null,9,9,15,null,"T-statistic for Pearson's Correlation Coefficient"]
[null,10,4,19,null,"Number of Cases (n):",null,10]
[null,null,null,null,null,"Degrees of Freedom:",null,"hidden"]
[null,"Need some help?",null,null,null,"T-statistic:",null,"hidden"]
[]
[null,null,null,null,null,"If the t-statistic is beyond +/-2.31 then p<0.05."]
[]
[null,"SUM OF PRODUCTS CALCULATION"]
[null,"Case #","Value on \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X\n",null,"Value on \nVariable Y\n","Mean of \nVariable Y\n","(Value-Mean)\nVariable Y\n",null,"(Value-Mean Variable X) x (Value-Mean Variable Y)\n"]
[null,1,13,11.9,"13 - 11.9 = ?",null,18,13.2,"18 - 13.2 = ?",null,"1.1 x 4.8 = ?"]
[null,2,18,11.9,"18 - 11.9 = ?",null,3,13.2,"3 - 13.2 = ?",null,"6.1 x -10.2 = ?"]
[null,3,26,11.9,"26 - 11.9 = ?",null,18,13.2,"18 - 13.2 = ?",null,"14.1 x 4.8 = ?"]
[null,4,1,11.9,"1 - 11.9 = ?",null,5,13.2,"5 - 13.2 = ?",null,"-10.9 x -8.2 = ?"]
[null,5,23,11.9,"23 - 11.9 = ?",null,12,13.2,"12 - 13.2 = ?",null,"11.1 x -1.2 = ?"]
[null,6,10,11.9,"10 - 11.9 = ?",null,2,13.2,"2 - 13.2 = ?",null,"-1.9 x -11.2 = ?"]
[null,7,11,11.9,"11 - 11.9 = ?",null,15,13.2,"15 - 13.2 = ?",null,"-0.9 x 1.8 = ?"]
[null,8,4,11.9,"4 - 11.9 = ?",null,25,13.2,"25 - 13.2 = ?",null,"-7.9 x 11.8 = ?"]
[null,9,9,11.9,"9 - 11.9 = ?",null,15,13.2,"15 - 13.2 = ?",null,"-2.9 x 1.8 = ?"]
[null,10,4,11.9,"4 - 11.9 = ?",null,19,13.2,"19 - 13.2 = ?",null,"-7.9 x 5.8 = ?"]
[null,null,null,null,null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Value on \nVariable X\n","Mean of \nVariable X\n","(Value-Mean)\nVariable X\n",null,"(Value-Mean)2 Variable X\n"]
[null,1,13,11.9,"13 - 11.9 = ?",null,"1.1 x 1.1 = ?"]
[null,2,18,11.9,"18 - 11.9 = ?",null,"6.1 x 6.1 = ?"]
[null,3,26,11.9,"26 - 11.9 = ?",null,"14.1 x 14.1 = ?"]
[null,4,1,11.9,"1 - 11.9 = ?",null,"-10.9 x -10.9 = ?"]
[null,5,23,11.9,"23 - 11.9 = ?",null,"11.1 x 11.1 = ?"]
[null,6,10,11.9,"10 - 11.9 = ?",null,"-1.9 x -1.9 = ?"]
[null,7,11,11.9,"11 - 11.9 = ?",null,"-0.9 x -0.9 = ?"]
[null,8,4,11.9,"4 - 11.9 = ?",null,"-7.9 x -7.9 = ?"]
[null,9,9,11.9,"9 - 11.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,10,4,11.9,"4 - 11.9 = ?",null,"-7.9 x -7.9 = ?"]
[null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"SUM OF SQUARES Y CALCULATION"]
[null,"Case #","Value on\nVariable Y\n","Mean of \nVariable Y\n","(Value-Mean)\nVariable Y\n",null,"(Value-Mean)2 Variable Y\n"]
[null,1,18,13.2,"18 - 13.2 = ?",null,"4.8 x 4.8 = ?"]
[null,2,3,13.2,"3 - 13.2 = ?",null,"-10.2 x -10.2 = ?"]
[null,3,18,13.2,"18 - 13.2 = ?",null,"4.8 x 4.8 = ?"]
[null,4,5,13.2,"5 - 13.2 = ?",null,"-8.2 x -8.2 = ?"]
[null,5,12,13.2,"12 - 13.2 = ?",null,"-1.2 x -1.2 = ?"]
[null,6,2,13.2,"2 - 13.2 = ?",null,"-11.2 x -11.2 = ?"]
[null,7,15,13.2,"15 - 13.2 = ?",null,"1.8 x 1.8 = ?"]
[null,8,25,13.2,"25 - 13.2 = ?",null,"11.8 x 11.8 = ?"]
[null,9,15,13.2,"15 - 13.2 = ?",null,"1.8 x 1.8 = ?"]
[null,10,19,13.2,"19 - 13.2 = ?",null,"5.8 x 5.8 = ?"]
[null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"PEARSON'S CORRELATION COEFFICIENT CALCULATION"]
[null,"Correlation Coefficient Numerator"]
[null,null,null,"= -37.8"]
[null,"Correlation Coefficient Denominator"]
[null,null,null,"= square root of 616.9 x square root of 523.6"]
[null,null,null,"= ? x ?"]
[null,null,null,"= ?"]
[null,"Correlation Coefficient"]
[null,null,null,"= -37.8 ÷ 568.34"]
[null,null,null,"= ?"]
[]
[null,"T-STATISTIC CALCULATION"]
[null,"Degrees of Freedom"]
[null,null,null,"= 10 - 2"]
[null,null,null,"= ?"]
[null,"T-Statistic Fraction Numerator"]
[null,null,null,"= 10 - 2"]
[null,null,null,"= ?"]
[null,"T-Statistic Fraction Denominator"]
[null,null,null,"= 1 - (-0.07²)"]
[null,null,null,"= ? - ?"]
[null,null,null,"= ?"]
[null,"T-Statistic"]
[null,null,null,"= -0.07 x [square root of (8 ÷ 1)]"]
[null,null,null,"= ? x (square root of ?)"]
[null,null,null,"= ? x ?"]
[null,null,null,"= ?"]

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[null,"PRACTICE CALCULATING SPEARMAN'S RANK-ORDER CORRELATION COEFFICIENTS"]
[]
[null,"Use the values in the yellow highlighted cells to find the rank of each case on Variable X and Variable Y. Then, use the ranks to calculate \nthe sum of products, the sum of squares X, the sum of squares Y, followed by Spearman's correlation coefficient, the degrees of freedom and the t-statistic. \nKeep two decimal places throughout your calculations. \nTo check your answers, click on the 'Show Ranks', 'Show Correlation Coefficient' and/or 'Show T-Statistic' buttons."]
[]
[]
[null,"Case #","Value on\nVariable X","Rank of Case on Variable X","Value on\nVariable Y","Rank of Case on Variable Y",null,"Means"]
[null,null,null,null,null,null,null,"Mean of Variable X Ranks (x-bar):",null,5.5]
[null,1,30,"hidden",46,"hidden",null,"Mean of Variable Y Ranks (y-bar):",null,5.5]
[null,2,10,"hidden",9,"hidden"]
[null,3,21,"hidden",41,"hidden",null,"Spearman's Correlation Coefficient"]
[null,4,4,"hidden",27,"hidden",null,"Sum of Products (for ranks):",null,"hidden"]
[null,5,16,"hidden",31,"hidden",null,"Sum of Squares X (for ranks):",null,"hidden"]
[null,6,10,"hidden",20,"hidden",null,"Sum of Squares Y (for ranks):",null,"hidden"]
[null,7,21,"hidden",42,"hidden",null,"Correlation Coefficient:",null,"hidden"]
[null,8,21,"hidden",49,"hidden"]
[null,9,28,"hidden",20,"hidden",null,"T-statistic for Spearman's Correlation Coefficient"]
[null,10,3,"hidden",20,"hidden",null,"Number of Cases (n):",null,10]
[null,null,null,null,null,null,null,"Degrees of Freedom:",null,"hidden"]
[null,null,null,null,null,null,null,"T-statistic:",null,"hidden"]
[null,"Need some help?"]
[null,null,null,null,null,null,null,"If the t-statistic is beyond +/-2.10 then p<0.05."]
[]
[null,"SUM OF PRODUCTS CALCULATION"]
[null,"Case #","Rank of Case on \nVariable X\n","Mean of \nVariable X Ranks\n","(Rank-Mean)\nVariable X\n","Rank of Case on\nVariable Y\n","Mean of \nVariable Y Ranks\n",null,"(Rank-Mean)\nVariable Y\n","(Rank-Mean Variable X) x (Rank-Mean Variable Y)\n"]
[null,1,"?",5.5,"10 - 5.5 = ?","?",5.5,null,"9 - 5.5 = ?","4.5 x 3.5 = ?"]
[null,2,"?",5.5,"3.5 - 5.5 = ?","?",5.5,null,"1 - 5.5 = ?","-2 x -4.5 = ?"]
[null,3,"?",5.5,"7 - 5.5 = ?","?",5.5,null,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,4,"?",5.5,"2 - 5.5 = ?","?",5.5,null,"5 - 5.5 = ?","-3.5 x -0.5 = ?"]
[null,5,"?",5.5,"5 - 5.5 = ?","?",5.5,null,"6 - 5.5 = ?","-0.5 x 0.5 = ?"]
[null,6,"?",5.5,"3.5 - 5.5 = ?","?",5.5,null,"3 - 5.5 = ?","-2 x -2.5 = ?"]
[null,7,"?",5.5,"7 - 5.5 = ?","?",5.5,null,"8 - 5.5 = ?","1.5 x 2.5 = ?"]
[null,8,"?",5.5,"7 - 5.5 = ?","?",5.5,null,"10 - 5.5 = ?","1.5 x 4.5 = ?"]
[null,9,"?",5.5,"9 - 5.5 = ?","?",5.5,null,"3 - 5.5 = ?","3.5 x -2.5 = ?"]
[null,10,"?",5.5,"1 - 5.5 = ?","?",5.5,null,"3 - 5.5 = ?","-4.5 x -2.5 = ?"]
[null,null,null,null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Rank of Case on \nVariable X\n","Mean of \nVariable X Ranks\n","(Rank-Mean)\nVariable X\n","(Rank-Mean)2 Variable X\n"]
[null,1,"?",5.5,"10 - 5.5 = ?","4.5 x 4.5 = ?"]
[null,2,"?",5.5,"3.5 - 5.5 = ?","-2 x -2 = ?"]
[null,3,"?",5.5,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,4,"?",5.5,"2 - 5.5 = ?","-3.5 x -3.5 = ?"]
[null,5,"?",5.5,"5 - 5.5 = ?","-0.5 x -0.5 = ?"]
[null,6,"?",5.5,"3.5 - 5.5 = ?","-2 x -2 = ?"]
[null,7,"?",5.5,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,8,"?",5.5,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,9,"?",5.5,"9 - 5.5 = ?","3.5 x 3.5 = ?"]
[null,10,"?",5.5,"1 - 5.5 = ?","-4.5 x -4.5 = ?"]
[null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"SUM OF SQUARES Y CALCULATION"]
[null,"Case #","Rank of Case on \nVariable Y\n","Mean of \nVariable Y\n","(Rank-Mean)\nVariable Y\n","(Rank-Mean)2 Variable Y\n"]
[null,1,"?",5.5,"9 - 5.5 = ?","3.5 x 3.5 = ?"]
[null,2,"?",5.5,"1 - 5.5 = ?","-4.5 x -4.5 = ?"]
[null,3,"?",5.5,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,4,"?",5.5,"5 - 5.5 = ?","-0.5 x -0.5 = ?"]
[null,5,"?",5.5,"6 - 5.5 = ?","0.5 x 0.5 = ?"]
[null,6,"?",5.5,"3 - 5.5 = ?","-2.5 x -2.5 = ?"]
[null,7,"?",5.5,"8 - 5.5 = ?","2.5 x 2.5 = ?"]
[null,8,"?",5.5,"10 - 5.5 = ?","4.5 x 4.5 = ?"]
[null,9,"?",5.5,"3 - 5.5 = ?","-2.5 x -2.5 = ?"]
[null,10,"?",5.5,"3 - 5.5 = ?","-2.5 x -2.5 = ?"]
[null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"SPEARMAN'S CORRELATION COEFFICIENT CALCULATION"]
[null,"Correlation Coefficient Numerator"]
[null,null,null,"= 46.5"]
[null,"Correlation Coefficient Denominator"]
[null,null,null,"= square root of 80 x square root of 80.5"]
[null,null,null,"= ? x ?"]
[null,null,null,"= ?"]
[null,"Correlation Coefficient"]
[null,null,null,"= 46.5 ÷ 80.19"]
[null,null,null,"= ?"]
[]
[null,"T-STATISTIC CALCULATION"]
[null,"Degrees of Freedom"]
[null,null,null,"= 10 - 2"]
[null,null,null,"= ?"]
[null,"T-Statistic Fraction Numerator"]
[null,null,null,"= 10 - 2"]
[null,null,null,"= ?"]
[null,"T-Statistic Fraction Denominator"]
[null,null,null,"= 1 - (0.58²)"]
[null,null,null,"= ? - ?"]
[null,null,null,"= ?"]
[null,"T-Statistic"]
[null,null,null,"= 0.58 x [square root of (8 ÷ 0.66)]"]
[null,null,null,"= ? x (square root of ?)"]
[null,null,null,"= ? x ?"]
[null,null,null,"= ?"]

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[null,"PRACTICE CALCULATING PEARSON'S CORRELATION COEFFICIENTS"]
[]
[null,"Then calculate the sum of products, the sum of squares X, the sum of squares Y and the correlation coefficient. \nKeep two decimal places in your calculations.\nTo check your answers, click on the 'Show Correlation Coefficient' and/or 'Show T-Statistic' buttons."]
[]
[]
[null,"Case #","Value of \nVariable X","Value of \nVariable Y",null,"Means",null,null,{"$f":"COUNTIF(J8:J19,0)","v":10},null," ",{"$f":"IFERROR(ROUND(AVERAGE(D8:D19),2),\"error\")","v":13.2}]
[null,null,null,null,null,"Mean of Variable X",null,{"$f":"ROUND(AVERAGE(C8:C17),2)","v":11.9}]
[null,1,13,18,null,"Mean of Variable Y",null,{"$f":"ROUND(AVERAGE(D8:D17),2)","v":13.2},{"$f":"COUNTIF(J8:J19,1)","v":1},{"$f":"COUNTBLANK(C8:D8)","v":0},{"$f":"IF(ISNUMBER(C8),ROUND(C8-$K$6,2),0)","v":{"$error":"#VALUE!"}},{"$f":"IF(ISNUMBER(D8),ROUND(D8-$L$6,2),0)","v":4.8},{"$f":"ROUND(K8*K8,2)","v":{"$error":"#VALUE!"}},{"$f":"ROUND(L8*L8,2)","v":23.04},{"$f":"IF(AND(ISNUMBER(C8),ISNUMBER(D8)),ROUND(K8*L8,2),0)","v":{"$error":"#VALUE!"}},null,null,null,{"$f":"RANDBETWEEN(1,30)","v":24},{"$f":"RANDBETWEEN(1,30)","v":29}]
[null,2,18,3,null,null,null,null,null,{"$f":"COUNTBLANK(C9:D9)","v":0},{"$f":"IF(ISNUMBER(C9),ROUND(C9-$K$6,2),0)","v":{"$error":"#VALUE!"}},{"$f":"IF(ISNUMBER(D9),ROUND(D9-$L$6,2),0)","v":-10.199999999999999},{"$f":"ROUND(K9*K9,2)","v":{"$error":"#VALUE!"}},104.04,{"$f":"IF(AND(ISNUMBER(C9),ISNUMBER(D9)),ROUND(K9*L9,2),0)","v":{"$error":"#VALUE!"}},null,{"$f":"ROUND(O8*O8,2)","v":{"$error":"#VALUE!"}},{"$f":"ROUND(P8*P8,2)","v":0},{"$f":"RANDBETWEEN(1,30)","v":14},17]
[null,3,26,18,null,"Pearson's Correlation Coefficient",null,null,{"$f":"IFERROR(ROUND(SUM(O8:O19),2),\"error\")","v":"error"},0,{"$error":"#VALUE!"},4.8,{"$error":"#VALUE!"},23.04,{"$error":"#VALUE!"},null,{"$f":"ROUND(O9*O9,2)","v":{"$error":"#VALUE!"}},0,2,1]
[null,4,1,5,null,"Sum of Products",null,{"$f":"N35","v":-37.799999999999997},{"$f":"IFERROR(ROUND(SUM(M8:M19),2),\"error\")","v":"error"},0,{"$error":"#VALUE!"},-8.1999999999999993,{"$error":"#VALUE!"},67.239999999999995,{"$error":"#VALUE!"},null,{"$error":"#VALUE!"},0,30,26]
[null,5,23,12,null,"Sum of Squares X",null,{"$f":"I49","v":616.9},{"$f":"IFERROR(ROUND(SUM(N8:N19),2),\"error\")","v":523.6},0,{"$error":"#VALUE!"},-1.2,{"$error":"#VALUE!"},1.44,{"$error":"#VALUE!"},null,{"$error":"#VALUE!"},0,17,17]
[null,6,10,2,null,"Sum of Squares Y",null,{"$f":"I63","v":523.6},null,0,{"$error":"#VALUE!"},-11.2,{"$error":"#VALUE!"},125.44,{"$error":"#VALUE!"},null,{"$error":"#VALUE!"},0,24,14]
[null,7,11,15,null,"Correlation coefficient (r)",null,{"$f":"G74","v":-7.0000000000000007E-2},{"$f":"IFERROR(ROUND(I10/I16,2),\"error\")","v":"error"},0,{"$error":"#VALUE!"},1.8,{"$error":"#VALUE!"},3.24,{"$error":"#VALUE!"},null,{"$error":"#VALUE!"},0,24,23]
[null,8,4,25,null,null,null,null,{"$f":"IFERROR(ROUND(I11*I12,2),\"error\")","v":"error"},0,{"$error":"#VALUE!"},11.8,{"$error":"#VALUE!"},139.24,{"$error":"#VALUE!"},null,{"$error":"#VALUE!"},0,9,21]
[null,9,9,15,null,"T-statistic for Pearson's Correlation Coefficient",null,null,{"$f":"IFERROR(ROUND(SQRT(I15),2),\"error\")","v":"error"},0,{"$error":"#VALUE!"},1.8,{"$error":"#VALUE!"},3.24,{"$error":"#VALUE!"},null,{"$error":"#VALUE!"},0,16,20]
[null,10,4,19,null,"Number of Cases",null,10,null,0,{"$error":"#VALUE!"},5.8,{"$error":"#VALUE!"},33.64,{"$error":"#VALUE!"},null,{"$error":"#VALUE!"},0,25,12]
[null,null,null,null,null,"Degrees of Freedom",null,{"$f":"H17-2","v":8},null,2,0,0,0,0,0,null,{"$error":"#VALUE!"},0]
[null,"Need some help?",null,null,null,"T-statistic",null,{"$f":"G91","v":-0.2},"`",{"$f":"COUNTBLANK(D19:D19)","v":1},{"$f":"IF(ISNUMBER(#REF!),ROUND(#REF!-$K$6,2),0)","v":0},0,0,0,{"$f":"IF(AND(ISNUMBER(#REF!),ISNUMBER(D19)),ROUND(K19*L19,2),0)","v":0}]
[]
[null,null,null,null,null,"If the T-statistic is greater than 2.10 then p<0.05."]
[]
[null,"SUM OF PRODUCTS CALCULATION"]
[null,"Case #","Value of \nVariable X","Mean of \nVariable X","Value-Mean\nVariable X",null,"Value of \nVariable Y","Mean of \nVariable Y","Value-Mean\nVariable X",null,"(Value-Mean Variable X) x (Value-Mean Variable Y)"]
[null,1,{"$f":"C8","v":13},{"$f":"$H$7","v":11.9},{"$f":"CONCATENATE(C25,\" - \",D25,\" = \",L25)","v":"13 - 11.9 = 1.1"},null,{"$f":"D8","v":18},{"$f":"$H$8","v":13.2},{"$f":"CONCATENATE(G25,\" - \",H25,\" = \",M25)","v":"18 - 13.2 = 4.8"},null,{"$f":"CONCATENATE(L25,\" x \",M25,\" = \",N25)","v":"1.1 x 4.8 = 5.28"},{"$f":"ROUND(C25-D25,2)","v":1.1000000000000001},{"$f":"ROUND(G25-H25,2)","v":4.8},{"$f":"ROUND(L25*M25,2)","v":5.28},{"$f":"CONCATENATE(C25,\" - \",D25,\" = ?\")","v":"13 - 11.9 = ?"},null,{"$f":"CONCATENATE(G25,\" - \",H25,\" = ?\")","v":"18 - 13.2 = ?"},null,{"$f":"CONCATENATE(L25,\" x \",M25,\" = ?\")","v":"1.1 x 4.8 = ?"}]
[null,2,18,{"$f":"$H$7","v":11.9},{"$f":"CONCATENATE(C26,\" - \",D26,\" = \",L26)","v":"18 - 11.9 = 6.1"},null,3,{"$f":"$H$8","v":13.2},{"$f":"CONCATENATE(G26,\" - \",H26,\" = \",M26)","v":"3 - 13.2 = -10.2"},null,{"$f":"CONCATENATE(L26,\" x \",M26,\" = \",N26)","v":"6.1 x -10.2 = -62.22"},{"$f":"ROUND(C26-D26,2)","v":6.1},{"$f":"ROUND(G26-H26,2)","v":-10.199999999999999},{"$f":"ROUND(L26*M26,2)","v":-62.22},"18 - 11.9 = ?",null,{"$f":"CONCATENATE(G26,\" - \",H26,\" = ?\")","v":"3 - 13.2 = ?"},null,{"$f":"CONCATENATE(L26,\" x \",M26,\" = ?\")","v":"6.1 x -10.2 = ?"}]
[null,3,26,11.9,"26 - 11.9 = 14.1",null,18,13.2,"18 - 13.2 = 4.8",null,"14.1 x 4.8 = 67.68",14.1,4.8,67.680000000000007,"26 - 11.9 = ?",null,"18 - 13.2 = ?",null,"14.1 x 4.8 = ?"]
[null,4,1,11.9,"1 - 11.9 = -10.9",null,5,13.2,"5 - 13.2 = -8.2",null,"-10.9 x -8.2 = 89.38",-10.9,-8.1999999999999993,89.38,"1 - 11.9 = ?",null,"5 - 13.2 = ?",null,"-10.9 x -8.2 = ?"]
[null,5,23,11.9,"23 - 11.9 = 11.1",null,12,13.2,"12 - 13.2 = -1.2",null,"11.1 x -1.2 = -13.32",11.1,-1.2,-13.32,"23 - 11.9 = ?",null,"12 - 13.2 = ?",null,"11.1 x -1.2 = ?"]
[null,6,10,11.9,"10 - 11.9 = -1.9",null,2,13.2,"2 - 13.2 = -11.2",null,"-1.9 x -11.2 = 21.28",-1.9,-11.2,21.28,"10 - 11.9 = ?",null,"2 - 13.2 = ?",null,"-1.9 x -11.2 = ?"]
[null,7,11,11.9,"11 - 11.9 = -0.9",null,15,13.2,"15 - 13.2 = 1.8",null,"-0.9 x 1.8 = -1.62",-0.9,1.8,-1.62,"11 - 11.9 = ?",null,"15 - 13.2 = ?",null,"-0.9 x 1.8 = ?"]
[null,8,4,11.9,"4 - 11.9 = -7.9",null,25,13.2,"25 - 13.2 = 11.8",null,"-7.9 x 11.8 = -93.22",-7.9,11.8,-93.22,"4 - 11.9 = ?",null,"25 - 13.2 = ?",null,"-7.9 x 11.8 = ?"]
[null,9,9,11.9,"9 - 11.9 = -2.9",null,15,13.2,"15 - 13.2 = 1.8",null,"-2.9 x 1.8 = -5.22",-2.9,1.8,-5.22,"9 - 11.9 = ?",null,"15 - 13.2 = ?",null,"-2.9 x 1.8 = ?"]
[null,10,4,11.9,"4 - 11.9 = -7.9",null,19,13.2,"19 - 13.2 = 5.8",null,"-7.9 x 5.8 = -45.82",-7.9,5.8,-45.82,"4 - 11.9 = ?",null,"19 - 13.2 = ?",null,"-7.9 x 5.8 = ?"]
[null,null,null,null,null,null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",N35)","v":"'= -37.8"},null,null,{"$f":"ROUND(SUM(N25:N34),2)","v":-37.799999999999997}]
[]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Value of \nVariable X","Mean of \nVariable X","Value-Mean\nVariable X",null,"(Value-Mean)2 Variable X"]
[null,1,{"$f":"C8","v":13},{"$f":"$H$7","v":11.9},{"$f":"CONCATENATE(C39,\" - \",D39,\" = \",H39)","v":"13 - 11.9 = 1.1"},null,{"$f":"CONCATENATE(H39,\" x \",H39,\" = \",I39)","v":"1.1 x 1.1 = 1.21"},{"$f":"ROUND(C39-D39,2)","v":1.1000000000000001},{"$f":"ROUND(H39*H39,2)","v":1.21},null,null,null,null,null,null,{"$f":"CONCATENATE(C39,\" - \",D39,\" = ?\")","v":"13 - 11.9 = ?"},null,{"$f":"CONCATENATE(H39,\" x \",H39,\" = ?\")","v":"1.1 x 1.1 = ?"}]
[null,2,18,{"$f":"$H$7","v":11.9},{"$f":"CONCATENATE(C40,\" - \",D40,\" = \",H40)","v":"18 - 11.9 = 6.1"},null,{"$f":"CONCATENATE(H40,\" x \",H40,\" = \",I40)","v":"6.1 x 6.1 = 37.21"},{"$f":"ROUND(C40-D40,2)","v":6.1},{"$f":"ROUND(H40*H40,2)","v":37.21},null,null,null,null,null,null,{"$f":"CONCATENATE(C40,\" - \",D40,\" = ?\")","v":"18 - 11.9 = ?"},null,{"$f":"CONCATENATE(H40,\" x \",H40,\" = ?\")","v":"6.1 x 6.1 = ?"}]
[null,3,26,11.9,"26 - 11.9 = 14.1",null,"14.1 x 14.1 = 198.81",14.1,198.81,null,null,null,null,null,null,"26 - 11.9 = ?",null,"14.1 x 14.1 = ?"]
[null,4,1,11.9,"1 - 11.9 = -10.9",null,"-10.9 x -10.9 = 118.81",-10.9,118.81,null,null,null,null,null,null,"1 - 11.9 = ?",null,"-10.9 x -10.9 = ?"]
[null,5,23,11.9,"23 - 11.9 = 11.1",null,"11.1 x 11.1 = 123.21",11.1,123.21,null,null,null,null,null,null,"23 - 11.9 = ?",null,"11.1 x 11.1 = ?"]
[null,6,10,11.9,"10 - 11.9 = -1.9",null,"-1.9 x -1.9 = 3.61",-1.9,3.61,null,null,null,null,null,null,"10 - 11.9 = ?",null,"-1.9 x -1.9 = ?"]
[null,7,11,11.9,"11 - 11.9 = -0.9",null,"-0.9 x -0.9 = 0.81",-0.9,0.81,null,null,null,null,null,null,"11 - 11.9 = ?",null,"-0.9 x -0.9 = ?"]
[null,8,4,11.9,"4 - 11.9 = -7.9",null,"-7.9 x -7.9 = 62.41",-7.9,62.41,null,null,null,null,null,null,"4 - 11.9 = ?",null,"-7.9 x -7.9 = ?"]
[null,9,9,11.9,"9 - 11.9 = -2.9",null,"-2.9 x -2.9 = 8.41",-2.9,8.41,null,null,null,null,null,null,"9 - 11.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,10,4,11.9,{"$f":"CONCATENATE(C48,\" - \",D48,\" = \",H48)","v":"4 - 11.9 = -7.9"},null,"-7.9 x -7.9 = 62.41",-7.9,62.41,null,null,null,null,null,null,"4 - 11.9 = ?",null,"-7.9 x -7.9 = ?"]
[null,null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",I49)","v":"'= 616.9"},null,{"$f":"ROUND(SUM(I39:J48),2)","v":616.9}]
[]
[null,"SUM OF SQUARES Y CALCULATION"]
[null,"Case #","Value of \nVariable Y","Mean of \nVariable Y","Value-Mean\nVariable Y",null,"(Value-Mean)2 Variable Y"]
[null,1,{"$f":"D8","v":18},{"$f":"$H$8","v":13.2},{"$f":"CONCATENATE(C53,\" - \",D53,\" = \",H53)","v":"18 - 13.2 = 4.8"},null,{"$f":"CONCATENATE(H53,\" x \",H53,\" = \",I53)","v":"4.8 x 4.8 = 23.04"},{"$f":"ROUND(C53-D53,2)","v":4.8},{"$f":"ROUND(H53*H53,2)","v":23.04},null,null,null,null,null,null,{"$f":"CONCATENATE(C53,\" - \",D53,\" = ?\")","v":"18 - 13.2 = ?"},null,{"$f":"CONCATENATE(H53,\" x \",H53,\" = ?\")","v":"4.8 x 4.8 = ?"}]
[null,2,3,{"$f":"$H$8","v":13.2},{"$f":"CONCATENATE(C54,\" - \",D54,\" = \",H54)","v":"3 - 13.2 = -10.2"},null,{"$f":"CONCATENATE(H54,\" x \",H54,\" = \",I54)","v":"-10.2 x -10.2 = 104.04"},-10.199999999999999,104.04,null,null,null,null,null,null,{"$f":"CONCATENATE(C54,\" - \",D54,\" = ?\")","v":"3 - 13.2 = ?"},null,{"$f":"CONCATENATE(H54,\" x \",H54,\" = ?\")","v":"-10.2 x -10.2 = ?"}]
[null,3,18,13.2,"18 - 13.2 = 4.8",null,"4.8 x 4.8 = 23.04",4.8,23.04,null,null,null,null,null,null,{"$f":"CONCATENATE(C55,\" - \",D55,\" = ?\")","v":"18 - 13.2 = ?"},null,"4.8 x 4.8 = ?"]
[null,4,5,13.2,"5 - 13.2 = -8.2",null,"-8.2 x -8.2 = 67.24",-8.1999999999999993,67.239999999999995,null,null,null,null,null,null,"5 - 13.2 = ?",null,"-8.2 x -8.2 = ?"]
[null,5,12,13.2,"12 - 13.2 = -1.2",null,"-1.2 x -1.2 = 1.44",-1.2,1.44,null,null,null,null,null,null,"12 - 13.2 = ?",null,"-1.2 x -1.2 = ?"]
[null,6,2,13.2,"2 - 13.2 = -11.2",null,"-11.2 x -11.2 = 125.44",-11.2,125.44,null,null,null,null,null,null,"2 - 13.2 = ?",null,"-11.2 x -11.2 = ?"]
[null,7,15,13.2,"15 - 13.2 = 1.8",null,"1.8 x 1.8 = 3.24",1.8,3.24,null,null,null,null,null,null,"15 - 13.2 = ?",null,"1.8 x 1.8 = ?"]
[null,8,25,13.2,"25 - 13.2 = 11.8",null,"11.8 x 11.8 = 139.24",11.8,139.24,null,null,null,null,null,null,"25 - 13.2 = ?",null,"11.8 x 11.8 = ?"]
[null,9,15,13.2,"15 - 13.2 = 1.8",null,"1.8 x 1.8 = 3.24",1.8,3.24,null,null,null,null,null,null,"15 - 13.2 = ?",null,"1.8 x 1.8 = ?"]
[null,10,19,13.2,"19 - 13.2 = 5.8",null,"5.8 x 5.8 = 33.64",5.8,33.64,null,null,null,null,null,null,"19 - 13.2 = ?",null,"5.8 x 5.8 = ?"]
[null,null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",I63)","v":"'= 523.6"},null,{"$f":"ROUND(SUM(I53:J62),2)","v":523.6},null,null,null,null,null,null," -  = ?",null," x  = ?"]
[]
[null,"PEARSON'S CORRELATION COEFFICIENT CALCULATION"]
[null,"Correlation Coefficient Numerator"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",N35)","v":"'= -37.8"}]
[null,"Correlation Coefficient Denominator"]
[null,null,null,{"$f":"CONCATENATE(\"'= square root of \",I49,\" x square root of \",I63)","v":"'= square root of 616.9 x square root of 523.6"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \", G70,\" x \",H70)","v":"'= 24.84 x 22.88"},null,null,{"$f":"ROUND(SQRT(I49),2)","v":24.84},{"$f":"ROUND(SQRT(I63),2)","v":22.88}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G71)","v":"'= 568.34"},null,null,{"$f":"ROUND(G70*H70,2)","v":568.34}]
[null,"Correlation Coefficient"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",N35,\" ÷ \",G71)","v":"'= -37.8 ÷ 568.34"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74)","v":"'= -0.07"},null,null,{"$f":"ROUND(N35/G71,2)","v":-7.0000000000000007E-2}]
[]
[null,"T-STATISTIC CALCULATION"]
[null,"Degrees of Freedom"]
[null,null,null,{"$f":"CONCATENATE(\"'= 10 - 2\")","v":"'= 10 - 2"}]
[null,null,null,{"$f":"CONCATENATE(\"'= 8\")","v":"'= 8"}]
[null,"T-Statistic Fraction Numerator"]
[null,null,null,{"$f":"CONCATENATE(\"'= 10 - 2\")","v":"'= 10 - 2"}]
[null,null,null,{"$f":"CONCATENATE(\"'= 8\")","v":"'= 8"}]
[null,"T-Statistic Fraction Denominator"]
[null,null,null,{"$f":"CONCATENATE(\"'= 1 - (\",G74,G84,\")\")","v":"'= 1 - (-0.07²)"},null,null,"²"]
[null,null,null,{"$f":"CONCATENATE(\"'= 1 - \",G85)","v":"'= 1 - 0"},null,null,{"$f":"ROUND(G74*G74,2)","v":0}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G86)","v":"'= 1"},null,null,{"$f":"1-G85","v":1}]
[null,"T-Statistic"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74,\" x [square root of (8 ÷ \",G86,\")]\")","v":"'= -0.07 x [square root of (8 ÷ 1)]"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74,\" x (square root of \",G89,\")\")","v":"'= -0.07 x (square root of 8)"},null,null,{"$f":"ROUND(8/G86,2)","v":8}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74,\" x \",G90)","v":"'= -0.07 x 2.83"},null,null,{"$f":"ROUND(SQRT(G89),2)","v":2.83}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G91)","v":"'= -0.2"},null,null,{"$f":"ROUND(G74*G90,2)","v":-0.2}]

{"sheet":"Spearman's rho-A","index":4,"n_rows":91,"n_cols":19,"rows_kept":91,"cut":false,"hidden":true,"merged":[[57,8,57,9],[58,8,58,9],[59,8,59,9],[60,8,60,9],[61,8,61,9],[56,8,56,9],[42,8,42,9],[43,8,43,9],[44,8,44,9],[45,8,45,9],[46,8,46,9],[47,8,47,9],[51,8,51,9],[52,8,52,9],[53,8,53,9],[54,8,54,9],[55,8,55,9],[41,8,41,9],[31,6,31,7],[31,9,31,10],[32,6,32,7],[32,9,32,10],[33,6,33,7],[33,9,33,10],[34,9,34,10],[37,8,37,9],[38,8,38,9],[39,8,39,9],[40,8,40,9],[28,6,28,7],[28,9,28,10],[29,6,29,7],[29,9,29,10],[30,6,30,7],[30,9,30,10],[25,6,25,7],[25,9,25,10],[26,6,26,7],[26,9,26,10],[27,6,27,7],[27,9,27,10],[19,1,19,2],[20,7,20,9],[23,6,23,7],[23,9,23,10],[24,6,24,7],[24,9,24,10],[0,1,0,13],[2,1,2,13],[5,1,6,1],[5,2,6,2],[5,3,6,3],[5,4,6,4],[5,5,6,5],[5,7,5,9],[24,17,24,18],[25,17,25,18],[26,17,26,18],[27,17,27,18],[28,17,28,18],[29,17,29,18],[30,17,30,18],[31,17,31,18],[32,17,32,18],[33,17,33,18]]}
[null,"PRACTICE CALCULATING SPEARMAN'S RANK-ORDER CORRELATION COEFFICIENTS"]
[]
[null,"Then calculate the sum of products, the sum of squares X, the sum of squares Y and the correlation coefficient. \nKeep two decimal places in your calculations.\nTo check your answers, click on the 'Show Correlation Coefficient' and/or 'Show T-Statistic' buttons."]
[]
[]
[null,"Case #","Value of \nVariable X","Rank of Case on Variable X","Value of \nVariable Y","Rank of Case on Variable Y",null,"Means"]
[null,null,null,null,null,null,null,"Mean of Variable X Ranks",null,{"$f":"ROUND(AVERAGE(D8:D17),2)","v":5.5}]
[null,1,30,{"$f":"_xlfn.RANK.AVG(C8,$C$8:$C$17,1)","v":10},46,{"$f":"_xlfn.RANK.AVG(E8,$E$8:$E$17,1)","v":9},null,"Mean of Variable Y Ranks",null,{"$f":"ROUND(AVERAGE(F8:F17),2)","v":5.5},null,{"$f":"RANDBETWEEN(1,30)","v":24},null,{"$f":"IF(L8<15,RANDBETWEEN(1,30),RANDBETWEEN(1,50))","v":38}]
[null,2,10,{"$f":"_xlfn.RANK.AVG(C9,$C$8:$C$17,1)","v":3.5},9,{"$f":"_xlfn.RANK.AVG(E9,$E$8:$E$17,1)","v":1},null,null,null,null,null,{"$f":"RANDBETWEEN(1,30)","v":6},null,{"$f":"IF(L9<15,RANDBETWEEN(1,30),RANDBETWEEN(1,50))","v":20}]
[null,3,21,7,41,7,null,"Spearman's Correlation Coefficient",null,null,null,16,null,1]
[null,4,4,2,27,5,null,"Sum of Products (for ranks)",null,{"$f":"N35","v":46.5},null,6,null,19]
[null,5,16,5,31,6,null,"Sum of Squares X (for ranks)",null,{"$f":"H49","v":80},null,2,null,22]
[null,6,10,3.5,20,3,null,"Sum of Squares Y (for ranks)",null,{"$f":"H63","v":80.5},null,14,null,28]
[null,7,21,7,42,8,null,"Correlation coefficient (ρ)",null,{"$f":"G74","v":0.57999999999999996},null,16,null,39]
[null,8,21,7,49,10,null,null,null,null,null,23,null,48]
[null,9,28,9,20,3,null,"T-statistic for Spearman's Correlation Coefficient",null,null,null,20,null,20]
[null,10,3,1,20,3,null,"Number of Cases",null,{"$f":"10","v":10},null,23,null,21]
[null,null,null,null,null,null,null,"Degrees of Freedom",null,{"$f":"J17-2","v":8}]
[null,null,null,null,null,null,null,"T-statistic",null,{"$f":"G91","v":2.02}]
[null,"Need some help?"]
[null,null,null,null,null,null,null,"If the T-statistic is greater than +/-2.10 then p<0.05."]
[]
[null,"SUM OF PRODUCTS CALCULATION"]
[null,"Case #","Rank of Case on \nVariable X","Mean of \nVariable X Ranks","(Rank-Mean)\nVariable X","Rank of Case on\nVariable Y","Mean of \nVariable Y Ranks",null,"(Rank-Mean)\nVariable Y","(Rank-Mean Variable X) x (Rank-Mean Variable Y)"]
[null,1,{"$f":"D8","v":10},{"$f":"$J$7","v":5.5},{"$f":"CONCATENATE(C25,\" - \",D25,\" = \",L25)","v":"10 - 5.5 = 4.5"},{"$f":"F8","v":9},{"$f":"$J$8","v":5.5},null,{"$f":"CONCATENATE(F25,\" - \",G25,\" = \",M25)","v":"9 - 5.5 = 3.5"},{"$f":"CONCATENATE(L25,\" x \",M25,\" = \",N25)","v":"4.5 x 3.5 = 15.75"},{"$f":"CONCATENATE(L25,\" x \",M25,\" = \",N25)","v":"4.5 x 3.5 = 15.75"},{"$f":"ROUND(C25-D25,2)","v":4.5},{"$f":"ROUND(F25-G25,2)","v":3.5},{"$f":"ROUND(L25*M25,2)","v":15.75},null,{"$f":"CONCATENATE(C25,\" - \",D25,\" = ?\")","v":"10 - 5.5 = ?"},{"$f":"CONCATENATE(F25,\" - \",G25,\" = ?\")","v":"9 - 5.5 = ?"},{"$f":"CONCATENATE(L25,\" x \",M25,\" = ?\")","v":"4.5 x 3.5 = ?"},{"$f":"CONCATENATE(T25,\" x \",U25,\" = \",V25)","v":" x  = "}]
[null,2,3.5,{"$f":"$J$7","v":5.5},{"$f":"CONCATENATE(C26,\" - \",D26,\" = \",L26)","v":"3.5 - 5.5 = -2"},1,{"$f":"$J$8","v":5.5},null,{"$f":"CONCATENATE(F26,\" - \",G26,\" = \",M26)","v":"1 - 5.5 = -4.5"},{"$f":"CONCATENATE(L26,\" x \",M26,\" = \",N26)","v":"-2 x -4.5 = 9"},{"$f":"CONCATENATE(L26,\" x \",M26,\" = \",N26)","v":"-2 x -4.5 = 9"},{"$f":"ROUND(C26-D26,2)","v":-2},{"$f":"ROUND(F26-G26,2)","v":-4.5},{"$f":"ROUND(L26*M26,2)","v":9},null,{"$f":"CONCATENATE(C26,\" - \",D26,\" = ?\")","v":"3.5 - 5.5 = ?"},{"$f":"CONCATENATE(F26,\" - \",G26,\" = ?\")","v":"1 - 5.5 = ?"},{"$f":"CONCATENATE(L26,\" x \",M26,\" = ?\")","v":"-2 x -4.5 = ?"},{"$f":"CONCATENATE(T26,\" x \",U26,\" = \",V26)","v":" x  = "}]
[null,3,7,5.5,"7 - 5.5 = 1.5",7,5.5,null,"7 - 5.5 = 1.5","1.5 x 1.5 = 2.25","1.5 x 1.5 = 2.25",1.5,1.5,2.25,null,"7 - 5.5 = ?","7 - 5.5 = ?","1.5 x 1.5 = ?"," x  = "]
[null,4,2,5.5,"2 - 5.5 = -3.5",5,5.5,null,"5 - 5.5 = -0.5","-3.5 x -0.5 = 1.75","-3.5 x -0.5 = 1.75",-3.5,-0.5,1.75,null,"2 - 5.5 = ?","5 - 5.5 = ?","-3.5 x -0.5 = ?"," x  = "]
[null,5,5,5.5,"5 - 5.5 = -0.5",6,5.5,null,"6 - 5.5 = 0.5","-0.5 x 0.5 = -0.25","-0.5 x 0.5 = -0.25",-0.5,0.5,-0.25,null,"5 - 5.5 = ?","6 - 5.5 = ?","-0.5 x 0.5 = ?"," x  = "]
[null,6,3.5,5.5,"3.5 - 5.5 = -2",3,5.5,null,"3 - 5.5 = -2.5","-2 x -2.5 = 5","-2 x -2.5 = 5",-2,-2.5,5,null,"3.5 - 5.5 = ?","3 - 5.5 = ?","-2 x -2.5 = ?"," x  = "]
[null,7,7,5.5,"7 - 5.5 = 1.5",8,5.5,null,"8 - 5.5 = 2.5","1.5 x 2.5 = 3.75","1.5 x 2.5 = 3.75",1.5,2.5,3.75,null,"7 - 5.5 = ?","8 - 5.5 = ?","1.5 x 2.5 = ?"," x  = "]
[null,8,7,5.5,"7 - 5.5 = 1.5",10,5.5,null,"10 - 5.5 = 4.5","1.5 x 4.5 = 6.75","1.5 x 4.5 = 6.75",1.5,4.5,6.75,null,"7 - 5.5 = ?","10 - 5.5 = ?","1.5 x 4.5 = ?"," x  = "]
[null,9,9,5.5,"9 - 5.5 = 3.5",3,5.5,null,"3 - 5.5 = -2.5","3.5 x -2.5 = -8.75","3.5 x -2.5 = -8.75",3.5,-2.5,-8.75,null,"9 - 5.5 = ?","3 - 5.5 = ?","3.5 x -2.5 = ?"," x  = "]
[null,10,1,5.5,"1 - 5.5 = -4.5",3,5.5,null,"3 - 5.5 = -2.5","-4.5 x -2.5 = 11.25","-4.5 x -2.5 = 11.25",-4.5,-2.5,11.25,null,"1 - 5.5 = ?","3 - 5.5 = ?","-4.5 x -2.5 = ?"," x  = "]
[null,null,null,null,null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",N35)","v":"'= 46.5"},{"$f":"CONCATENATE(\"'= \",N35)","v":"'= 46.5"},null,null,{"$f":"ROUND(SUM(N25:N34),2)","v":46.5}]
[]
[null,"SUM OF SQUARES X CALCULATION"]
[null,"Case #","Rank of Case on \nVariable X","Mean of \nVariable X Ranks","(Rank-Mean)\nVariable X","(Rank-Mean)2 Variable X"]
[null,1,{"$f":"D8","v":10},{"$f":"$J$7","v":5.5},{"$f":"CONCATENATE(C39,\" - \",D39,\" = \",G39)","v":"10 - 5.5 = 4.5"},{"$f":"CONCATENATE(G39,\" x \",G39,\" = \",H39)","v":"4.5 x 4.5 = 20.25"},{"$f":"ROUND(C39-D39,2)","v":4.5},{"$f":"ROUND(G39*G39,2)","v":20.25},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C39,\" - \",D39,\" = ?\")","v":"10 - 5.5 = ?"},{"$f":"CONCATENATE(G39,\" x \",G39,\" = ?\")","v":"4.5 x 4.5 = ?"}]
[null,2,3.5,{"$f":"$J$7","v":5.5},{"$f":"CONCATENATE(C40,\" - \",D40,\" = \",G40)","v":"3.5 - 5.5 = -2"},{"$f":"CONCATENATE(G40,\" x \",G40,\" = \",H40)","v":"-2 x -2 = 4"},{"$f":"ROUND(C40-D40,2)","v":-2},{"$f":"ROUND(G40*G40,2)","v":4},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C40,\" - \",D40,\" = ?\")","v":"3.5 - 5.5 = ?"},{"$f":"CONCATENATE(G40,\" x \",G40,\" = ?\")","v":"-2 x -2 = ?"}]
[null,3,7,5.5,"7 - 5.5 = 1.5","1.5 x 1.5 = 2.25",1.5,2.25,null,null,null,null,null,null,null,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,4,2,5.5,"2 - 5.5 = -3.5","-3.5 x -3.5 = 12.25",-3.5,12.25,null,null,null,null,null,null,null,"2 - 5.5 = ?","-3.5 x -3.5 = ?"]
[null,5,5,5.5,"5 - 5.5 = -0.5","-0.5 x -0.5 = 0.25",-0.5,0.25,null,null,null,null,null,null,null,"5 - 5.5 = ?","-0.5 x -0.5 = ?"]
[null,6,3.5,5.5,"3.5 - 5.5 = -2","-2 x -2 = 4",-2,4,null,null,null,null,null,null,null,"3.5 - 5.5 = ?","-2 x -2 = ?"]
[null,7,7,5.5,"7 - 5.5 = 1.5","1.5 x 1.5 = 2.25",1.5,2.25,null,null,null,null,null,null,null,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,8,7,5.5,"7 - 5.5 = 1.5","1.5 x 1.5 = 2.25",1.5,2.25,null,null,null,null,null,null,null,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,9,9,5.5,"9 - 5.5 = 3.5","3.5 x 3.5 = 12.25",3.5,12.25,null,null,null,null,null,null,null,"9 - 5.5 = ?","3.5 x 3.5 = ?"]
[null,10,1,5.5,"1 - 5.5 = -4.5","-4.5 x -4.5 = 20.25",-4.5,20.25,null,null,null,null,null,null,null,"1 - 5.5 = ?","-4.5 x -4.5 = ?"]
[null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",H49)","v":"'= 80"},null,{"$f":"ROUND(SUM(H39:H48),2)","v":80}]
[]
[null,"SUM OF SQUARES Y CALCULATION"]
[null,"Case #","Rank of Case on \nVariable Y","Mean of \nVariable Y Ranks","(Rank-Mean)\nVariable Y","(Rank-Mean)2 Variable Y"]
[null,1,{"$f":"F8","v":9},{"$f":"$J$8","v":5.5},{"$f":"CONCATENATE(C53,\" - \",D53,\" = \",G53)","v":"9 - 5.5 = 3.5"},{"$f":"CONCATENATE(G53,\" x \",G53,\" = \",H53)","v":"3.5 x 3.5 = 12.25"},{"$f":"ROUND(C53-D53,2)","v":3.5},{"$f":"ROUND(G53*G53,2)","v":12.25},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C53,\" - \",D53,\" = ?\")","v":"9 - 5.5 = ?"},{"$f":"CONCATENATE(G53,\" x \",G53,\" = ?\")","v":"3.5 x 3.5 = ?"}]
[null,2,1,{"$f":"$J$8","v":5.5},{"$f":"CONCATENATE(C54,\" - \",D54,\" = \",G54)","v":"1 - 5.5 = -4.5"},{"$f":"CONCATENATE(G54,\" x \",G54,\" = \",H54)","v":"-4.5 x -4.5 = 20.25"},{"$f":"ROUND(C54-D54,2)","v":-4.5},{"$f":"ROUND(G54*G54,2)","v":20.25},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C54,\" - \",D54,\" = ?\")","v":"1 - 5.5 = ?"},{"$f":"CONCATENATE(G54,\" x \",G54,\" = ?\")","v":"-4.5 x -4.5 = ?"}]
[null,3,7,5.5,"7 - 5.5 = 1.5","1.5 x 1.5 = 2.25",1.5,2.25,null,null,null,null,null,null,null,"7 - 5.5 = ?","1.5 x 1.5 = ?"]
[null,4,5,5.5,"5 - 5.5 = -0.5","-0.5 x -0.5 = 0.25",-0.5,0.25,null,null,null,null,null,null,null,"5 - 5.5 = ?","-0.5 x -0.5 = ?"]
[null,5,6,5.5,"6 - 5.5 = 0.5","0.5 x 0.5 = 0.25",0.5,0.25,null,null,null,null,null,null,null,"6 - 5.5 = ?","0.5 x 0.5 = ?"]
[null,6,3,5.5,"3 - 5.5 = -2.5","-2.5 x -2.5 = 6.25",-2.5,6.25,null,null,null,null,null,null,null,"3 - 5.5 = ?","-2.5 x -2.5 = ?"]
[null,7,8,5.5,"8 - 5.5 = 2.5","2.5 x 2.5 = 6.25",2.5,6.25,null,null,null,null,null,null,null,"8 - 5.5 = ?","2.5 x 2.5 = ?"]
[null,8,10,5.5,"10 - 5.5 = 4.5","4.5 x 4.5 = 20.25",4.5,20.25,null,null,null,null,null,null,null,"10 - 5.5 = ?","4.5 x 4.5 = ?"]
[null,9,3,5.5,"3 - 5.5 = -2.5","-2.5 x -2.5 = 6.25",-2.5,6.25,null,null,null,null,null,null,null,"3 - 5.5 = ?","-2.5 x -2.5 = ?"]
[null,10,3,5.5,"3 - 5.5 = -2.5","-2.5 x -2.5 = 6.25",-2.5,6.25,null,null,null,null,null,null,null,"3 - 5.5 = ?","-2.5 x -2.5 = ?"]
[null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",H63)","v":"'= 80.5"},null,{"$f":"ROUND(SUM(H53:H62),2)","v":80.5}]
[]
[null,"SPEARMAN'S CORRELATION COEFFICIENT CALCULATION"]
[null,"Correlation Coefficient Numerator"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",N35)","v":"'= 46.5"}]
[null,"Correlation Coefficient Denominator"]
[null,null,null,{"$f":"CONCATENATE(\"'= square root of \",H49,\" x square root of \",H63)","v":"'= square root of 80 x square root of 80.5"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \", G70,\" x \",H70)","v":"'= 8.94 x 8.97"},null,null,{"$f":"ROUND(SQRT(H49),2)","v":8.94},{"$f":"ROUND(SQRT(H63),2)","v":8.9700000000000006}]
[null,null,null,{"$f":"IF(H63=H49,CONCATENATE(\"'= \",G71,\" (when two square roots of the same number are multiplied, the result is the original number)\"),CONCATENATE(\"'= \",G71))","v":"'= 80.19"},null,null,{"$f":"IF(H49=H63,H49,ROUND(G70*H70,2))","v":80.19}]
[null,"Correlation Coefficient"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",N35,\" ÷ \",G71)","v":"'= 46.5 ÷ 80.19"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74)","v":"'= 0.58"},null,null,{"$f":"ROUND(N35/G71,2)","v":0.57999999999999996}]
[]
[null,"T-STATISTIC CALCULATION"]
[null,"Degrees of Freedom"]
[null,null,null,{"$f":"CONCATENATE(\"'= 10 - 2\")","v":"'= 10 - 2"}]
[null,null,null,{"$f":"CONCATENATE(\"'= 8\")","v":"'= 8"}]
[null,"T-Statistic Fraction Numerator"]
[null,null,null,{"$f":"CONCATENATE(\"'= 10 - 2\")","v":"'= 10 - 2"}]
[null,null,null,{"$f":"CONCATENATE(\"'= 8\")","v":"'= 8"}]
[null,"T-Statistic Fraction Denominator"]
[null,null,null,{"$f":"CONCATENATE(\"'= 1 - (\",G74,G84,\")\")","v":"'= 1 - (0.58²)"},null,null,"²"]
[null,null,null,{"$f":"CONCATENATE(\"'= 1 - \",G85)","v":"'= 1 - 0.34"},null,null,{"$f":"ROUND(G74*G74,2)","v":0.34}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G86)","v":"'= 0.66"},null,null,{"$f":"1-G85","v":0.65999999999999992}]
[null,"T-Statistic"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74,\" x [square root of (8 ÷ \",G86,\")]\")","v":"'= 0.58 x [square root of (8 ÷ 0.66)]"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74,\" x (square root of \",G89,\")\")","v":"'= 0.58 x (square root of 12.12)"},null,null,{"$f":"ROUND(8/G86,2)","v":12.12}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G74,\" x \",G90)","v":"'= 0.58 x 3.48"},null,null,{"$f":"ROUND(SQRT(G89),2)","v":3.48}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G91)","v":"'= 2.02"},null,null,{"$f":"ROUND(G74*G90,2)","v":2.02}]