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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 9"]
[]
[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":"Lambda (2x2)","index":1,"n_rows":24,"n_cols":9,"rows_kept":24,"cut":false,"hidden":false,"merged":[[0,1,0,10],[2,1,2,10],[5,1,5,5],[6,3,6,5],[8,1,10,1],[8,7,8,8],[9,7,9,8]]}
[null,"PRACTICE CALCULATING LAMBDA: 2x2 CROSSTABULATION"]
[]
[null,"Calculate lambda for this crosstabulation. Keep two decimal places throughout your calculations.\nTo check your answer, click on the 'Show Answer' button."]
[]
[]
[null,"FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,"Lambda:","hidden"]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1",13,3,16,null,"Need some help?"]
[null,null,"Attribute 2",12,5,17]
[null,null,"Total",25,8,33]
[]
[null,"LAMBDA CALCULATIONS"]
[null,"E1"]
[null,null,"= 33 - 17"]
[null,null,"= ?"]
[null,"E2"]
[null,null,"= (25 - 13) + (8 - 5)"]
[null,null,"= ? + ?"]
[null,null,"= ?"]
[null,"Lambda"]
[null,null,"= (16 - 15) ÷ 16"]
[null,null,"= ? ÷ ?"]
[null,null,"= ?"]

{"sheet":"Lambda (3x3)","index":2,"n_rows":25,"n_cols":10,"rows_kept":25,"cut":false,"hidden":false,"merged":[[0,1,0,11],[2,1,2,11],[5,1,5,6],[6,3,6,6],[8,1,11,1],[9,8,9,9],[7,8,8,8]]}
[null,"PRACTICE CALCULATING LAMBDA: 3x3 CROSSTABULATION"]
[]
[null,"Calculate lambda for this crosstabulation. Keep two decimal places throughout your calculations.\nTo check your answer, click on the 'Show Answer' button."]
[]
[]
[null,"FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,null,"Lambda:","hidden"]
[null,null,null,"Group 1","Group 2","Group 3","Total",null,"Need some help?"]
[null,"Dependent\n Variable","Attribute 1",9,13,8,30]
[null,null,"Attribute 2",16,11,7,34]
[null,null,"Attribute 3",20,20,3,43]
[null,null,"Total",45,44,18,107]
[]
[null,"LAMBDA CALCULATIONS"]
[null,"E1"]
[null,null,"= 107 - 43"]
[null,null,"= ?"]
[null,"E2"]
[null,null,"= (45 - 20) + (44 - 20) + (18 - 8)"]
[null,null,"= ? + ? + ?"]
[null,null,"= ?"]
[null,"Lambda"]
[null,null,"= (64 - 59) ÷ 64"]
[null,null,"= ? ÷ ?"]
[null,null,"= ?"]

{"sheet":"Gamma (2x2)","index":3,"n_rows":29,"n_cols":9,"rows_kept":29,"cut":false,"hidden":false,"merged":[[13,1,13,2],[15,1,15,2],[17,1,17,2],[0,1,0,10],[2,1,2,10],[5,1,5,5],[6,3,6,5],[8,1,10,1],[9,7,10,8]]}
[null,"PRACTICE CALCULATING GAMMA: 2x2 CROSSTABULATION"]
[]
[null,"Calculate gamma for this crosstabulation. You may also want to find the total number of pairs of cases and the number of tied pairs of cases. \nKeep two decimal places throughout your calculations.\nTo check your answers, click on the 'Show Answers' button."]
[]
[]
[null,"FREQUENCIES",null,null,null,null,null,"Gamma:","hidden"]
[null,null,null,"Independent Variable"]
[null,null,null,"Low Group","High Group","Total",null,"Total Number of Pairs of Cases:","hidden"]
[null,"Dependent\n Variable","Low Attribute",13,29,42,null,"Number of Tied Pairs of Cases:","hidden"]
[null,null,"High Attribute",20,15,35,null,"Need some help?"]
[null,null,"Total",33,44,77]
[]
[null,"GAMMA CALCULATIONS"]
[null,"Concordant pairs of cases",null,"= 13 x 15"]
[null,null,null,"= ?"]
[null,"Discordant pairs of cases",null,"= 29 x 20"]
[null,null,null,"= ?"]
[null,"Gamma"]
[null,null,null,"= (195 - 580) ÷ (195 + 580)"]
[null,null,null,"= ? ÷ ?"]
[null,null,null,"= ?"]
[null,"Total number of pairs of cases"]
[null,null,null,"= [77 x (77 - 1)] ÷ 2"]
[null,null,null,"= (? x ?) ÷ ?"]
[null,null,null,"= ? ÷ ?"]
[null,null,null,"= ?"]
[null,"Number of tied pairs of cases"]
[null,null,null,"= 2926 - 195 - 580"]
[null,null,null,"= ?"]

{"sheet":"Gamma (3x3)","index":4,"n_rows":34,"n_cols":10,"rows_kept":34,"cut":false,"hidden":false,"merged":[[14,1,14,2],[18,1,18,2],[22,1,22,2],[0,1,0,11],[2,1,2,11],[5,1,5,6],[6,3,6,6],[8,1,11,1],[9,8,10,9]]}
[null,"PRACTICE CALCULATING GAMMA: 3x3 CROSSTABULATION"]
[]
[null,"Calculate gamma for this crosstabulation. You may also want to find the total number of pairs of cases and the number of tied pairs of cases. \nKeep two decimal places throughout your calculations.\nTo check your answers, click on the 'Show Answers' button."]
[]
[]
[null,"FREQUENCIES",null,null,null,null,null,null,"Gamma:","hidden"]
[null,null,null,"Independent Variable"]
[null,null,null,"Low Group","Middle Group","High Group","Total",null,"Total Number of Pairs of Cases:","hidden"]
[null,"Dependent\n Variable","Low Attribute",1,13,18,32,null,"Number of Tied Pairs of Cases:","hidden"]
[null,null,"Middle Attribute",2,19,14,35,null,"Need some help?"]
[null,null,"High Attribute",3,28,7,38]
[null,null,"Total",6,60,39,105]
[]
[null,"GAMMA CALCULATIONS"]
[null,"Concordant pairs of cases",null,"= [1 x (19 + 14 + 28 + 7)] + [13 x (14 + 7)] + [2 x (28 + 7)] + [19 x 7]"]
[null,null,null,"= (? x ?) + (? x ?) + (? x ?) + (? x ?)"]
[null,null,null,"= ? + ? + ? + ?"]
[null,null,null,"= ?"]
[null,"Discordant pairs of cases",null,"= [18 x (2 + 19 + 3 + 28)] + [13 x (2 + 3)] + [14 x (3 + 28)] + [19 x 3]"]
[null,null,null,"= (? x ?) + (? x ?) + (? x ?) + (? x ?)"]
[null,null,null,"= ? + ? + ? + ?"]
[null,null,null,"= ?"]
[null,"Gamma"]
[null,null,null,"= (544 - 1492) ÷ (544 + 1492)"]
[null,null,null,"= ? ÷ ?"]
[null,null,null,"= ?"]
[null,"Total number of pairs of cases"]
[null,null,null,"= [105 x (105 - 1)] ÷ 2"]
[null,null,null,"= (? x ?) ÷ ?"]
[null,null,null,"= ? ÷ ?"]
[null,null,null,"= ?"]
[null,"Number of tied pairs of cases"]
[null,null,null,"= 5460 - 544 - 1492"]
[null,null,null,"= ?"]

{"sheet":"Chi-square (2x2)","index":5,"n_rows":33,"n_cols":11,"rows_kept":33,"cut":false,"hidden":false,"merged":[[29,5,29,6],[30,5,30,6],[31,5,31,6],[32,8,32,9],[2,1,2,11],[29,8,29,10],[30,8,30,10],[31,8,31,10],[27,8,27,10],[28,8,28,10],[27,5,27,6],[28,5,28,6],[27,1,27,2],[13,3,13,5],[15,1,17,1],[20,3,20,5],[22,1,24,1],[0,1,0,11],[5,1,5,5],[6,3,6,5],[8,1,10,1],[12,1,12,5],[9,7,10,8],[13,7,14,8]]}
[null,"PRACTICE CALCULATING EXPECTED FREQUENCIES AND THE CHI-SQUARE STATISTIC: 2x2 CROSSTABULATION"]
[]
[null,"Calculate the expected frequencies for each of the yellow highlighted cells. Then, calculate the chi-square statistic. \nKeep two decimal places throughout your calculations.\nTo check your answers, click on the 'Show Expected Frequencies' and/or 'Show Chi-Square statistic' buttons."]
[]
[]
[null,"OBSERVED FREQUENCIES (fo)"]
[null,null,null,"Independent Variable",null,null,null,"Degrees of freedom:",1]
[null,null,null,"Group 1","Group 2","Total",null,"Chi-square statistic:","hidden"]
[null,"Dependent\n Variable","Attribute 1",17,16,33]
[null,null,"Attribute 2",6,17,23,null,"If the chi-square statistic is \nhigher than 3.84, then p<0.05"]
[null,null,"Total",23,33,56]
[]
[null,"EXPECTED FREQUENCIES (fe)"]
[null,null,null,"Independent Variable",null,null,null,"Need some help?"]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1","hidden","hidden",33]
[null,null,"Attribute 2","hidden","hidden",23]
[null,null,"Total",23,33,56]
[]
[null,"EXPECTED FREQUENCY CALCULATIONS"]
[null,null,null,"Independent Variable"]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1","(33 x 23) ÷ 56 = ?","(33 x 33) ÷ 56 = ?",33]
[null,null,"Attribute 2","(23 x 23) ÷ 56 = ?","(23 x 33) ÷ 56 = ?",23]
[null,null,"Total",23,33,56]
[]
[null,"CHI-SQUARE STATISTIC CALCULATIONS"]
[null,"Cell",null,"Observed\nFrequencies","Expected\nFrequencies","Observed-Expected\nFrequencies",null,"(Observed-Expected)2\n","(Observed-Expected)2 ÷ Expected\n"]
[null,"Group 1, Attribute 1",null,17,13.55,"17 - 13.55 = ?",null,"3.45 x 3.45 = ?","11.9 ÷ 13.55 = ?"]
[null,"Group 1, Attribute 2",null,6,9.4499999999999993,"6 - 9.45 = ?",null,"-3.45 x -3.45 = ?","11.9 ÷ 9.45 = ?"]
[null,"Group 2, Attribute 1",null,16,19.45,"16 - 19.45 = ?",null,"-3.45 x -3.45 = ?","11.9 ÷ 19.45 = ?"]
[null,"Group 2, Attribute 2",null,17,13.55,"17 - 13.55 = ?",null,"3.45 x 3.45 = ?","11.9 ÷ 13.55 = ?"]
[null,null,null,null,null,null,null,null,"Column Sum (Σ)",null,"= ?"]

{"sheet":"Chi-square (3x3)","index":6,"n_rows":41,"n_cols":12,"rows_kept":41,"cut":false,"hidden":false,"merged":[[0,1,0,12],[2,1,2,12],[5,1,5,6],[6,3,6,6],[8,1,11,1],[9,8,10,9],[30,1,30,2],[30,5,30,6],[30,9,30,11],[31,5,31,6],[31,9,31,11],[13,1,13,6],[14,3,14,6],[16,1,19,1],[22,3,22,6],[24,1,27,1],[40,9,40,10],[33,1,33,2],[39,1,39,2],[39,5,39,6],[39,9,39,11],[36,1,36,2],[39,7,39,8],[33,7,33,8],[34,7,34,8],[35,7,35,8],[36,7,36,8],[37,7,37,8],[38,9,38,11],[33,5,33,6],[36,5,36,6],[37,5,37,6],[15,8,16,9],[38,5,38,6],[36,9,36,11],[37,9,37,11],[33,9,33,11],[38,7,38,8],[34,5,34,6],[34,9,34,11],[35,5,35,6],[35,9,35,11],[32,5,32,6],[32,9,32,11],[30,7,30,8],[31,7,31,8],[32,7,32,8]]}
[null,"PRACTICE CALCULATING EXPECTED FREQUENCIES AND THE CHI-SQUARE STATISTIC: 3x3 CROSSTABULATION"]
[]
[null,"Calculate the expected frequencies for each of the yellow highlighted cells. Then, calculate the chi-square statistic. \nKeep two decimal places throughout your calculations.\nTo check your answers, click on the 'Show Expected Frequencies' and/or 'Show Chi-Square statistic' buttons."]
[]
[]
[null,"OBSERVED FREQUENCIES (fo)"]
[null,null,null,"Independent Variable",null,null,null,null,"Degrees of freedom:",4]
[null,null,null,"Group 1","Group 2","Group 3","Total",null,"Chi-Square statistic:","hidden"]
[null,"Dependent\n Variable","Attribute 1",18,5,1,24]
[null,null,"Attribute 2",6,20,17,43,null,"If the chi-square statistic is \nhigher than 9.49, p<0.05"]
[null,null,"Attribute 3",3,20,8,31]
[null,null,"Total",27,45,26,98]
[]
[null,"EXPECTED FREQUENCIES (fe)"]
[null,null,null,"Independent Variable"]
[null,null,null,"Group 1","Group 2","Group 3","Total",null,"Need some help?"]
[null,"Dependent\n Variable","Attribute 1","hidden","hidden","hidden",24]
[null,null,"Attribute 2","hidden","hidden","hidden",43]
[null,null,"Attribute 3","hidden","hidden","hidden",31]
[null,null,"Total",27,45,26,98]
[]
[null,"EXPECTED FREQUENCY CALCULATIONS"]
[null,null,null,"Independent Variable"]
[null,null,null,"Group 1","Group 2","Group 3","Total"]
[null,"Dependent\n Variable","Attribute 1","(24 x 27) ÷ 98 = ?","(24 x 45) ÷ 98 = ?","(24 x 26) ÷ 98 = ?",24]
[null,null,"Attribute 2","(43 x 27) ÷ 98 = ?","(43 x 45) ÷ 98 = ?","(43 x 26) ÷ 98 = ?",43]
[null,null,"Attribute 3","(31 x 27) ÷ 98 = ?","(31 x 45) ÷ 98 = ?","(31 x 26) ÷ 98 = ?",31]
[null,null,"Total",{"$f":"D20","v":35},{"$f":"E20","v":27},26,98]
[]
[null,"CHI-SQUARE STATISTIC CALCULATIONS"]
[null,"Cell",null,"Observed\nFrequencies","Expected\nFrequencies","Observed-Expected\nFrequencies",null,"(Observed-Expected)2\n",null,"(Observed-Expected)2 ÷ Expected\n"]
[null,"Group 1, Attribute 1",null,18,6.61,"18 - 6.61 = ?",null,"11.39 x 11.39 = ?",null,"129.73 ÷ 6.61 = ?"]
[null,"Group 1, Attribute 2",null,6,11.85,"6 - 11.85 = ?",null,"-5.85 x -5.85 = ?",null,"34.22 ÷ 11.85 = ?"]
[null,"Group 1, Attribute 3",null,3,8.5399999999999991,"3 - 8.54 = ?",null,"-5.54 x -5.54 = ?",null,"30.69 ÷ 8.54 = ?"]
[null,"Group 2, Attribute 1",null,5,11.02,"5 - 11.02 = ?",null,"-6.02 x -6.02 = ?",null,"36.24 ÷ 11.02 = ?"]
[null,"Group 2, Attribute 2",null,20,19.739999999999998,"20 - 19.74 = ?",null,"0.26 x 0.26 = ?",null,"0.07 ÷ 19.74 = ?"]
[null,"Group 2, Attribute 3",null,20,14.23,"20 - 14.23 = ?",null,"5.77 x 5.77 = ?",null,"33.29 ÷ 14.23 = ?"]
[null,"Group 3, Attribute 1",null,1,6.37,"1 - 6.37 = ?",null,"-5.37 x -5.37 = ?",null,"28.84 ÷ 6.37 = ?"]
[null,"Group 3, Attribute 2",null,17,11.41,"17 - 11.41 = ?",null,"5.59 x 5.59 = ?",null,"31.25 ÷ 11.41 = ?"]
[null,"Group 3, Attribute 3",null,8,8.2200000000000006,"8 - 8.22 = ?",null,"-0.22 x -0.22 = ?",null,"0.05 ÷ 8.22 = ?"]
[null,null,null,null,null,null,null,null,null,"Column Sum (Σ)",null,"= ?"]

{"sheet":"Phi","index":7,"n_rows":17,"n_cols":9,"rows_kept":17,"cut":false,"hidden":false,"merged":[[2,1,2,10],[0,1,0,10],[5,1,5,5],[6,3,6,5],[8,1,10,1],[8,6,9,8]]}
[null,"PRACTICE CALCULATING PHI"]
[]
[null,"Phi is calculated for 2 x 2 crosstabulations. Use the chi-square statistic in the yellow highlighed cell to calculate phi for this crosstabulation. \nKeep two decimal places throughout your calculations.\nTo check your answer, click on the 'Show Answer' button."]
[]
[]
[null,"OBSERVED FREQUENCIES",null,null,null,null,null,"Chi-Square statistic (χ2):",1.8]
[null,null,null,"Independent Variable",null,null,null,"Phi:","hidden"]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1",10,12,22]
[null,null,"Attribute 2",12,6,18]
[null,null,"Total",22,18,40]
[]
[null,"PHI CALCULATIONS"]
[null,"Phi"]
[null,null,"= square root of (1.8 ÷ 40)"]
[null,null,"= square root of ?"]
[null,null,"= ?"]

{"sheet":"Cramér's V","index":8,"n_rows":20,"n_cols":10,"rows_kept":20,"cut":false,"hidden":false,"merged":[[0,1,0,11],[2,1,2,11],[5,1,5,6],[6,3,6,6],[8,1,11,1],[9,8,9,9],[7,8,8,9]]}
[null,"PRACTICE CALCULATING CRAMÉR'S V"]
[]
[null,"Cramér's V is calculated for crosstabulations with more than two rows or columns. Use the chi-square statistic in the yellow highlighted cell to calculate Cramér's V for this crosstabulation. \nKeep two decimal places throughout your calculations.\nTo check your answer, click on the 'Show Answer' button."]
[]
[]
[null,"OBSERVED FREQUENCIES",null,null,null,null,null,null,"Chi-Square statistic (χ2):",14.860000000000003]
[null,null,null,"Independent Variable",null,null,null,null,"Cramér's V:","hidden"]
[null,null,null,"Group 1","Group 2","Group 3","Total",null,"Need some help?"]
[null,"Dependent\n Variable","Attribute 1",1,13,7,21]
[null,null,"Attribute 2",13,18,5,36]
[null,null,"Attribute 3",20,13,16,49]
[null,null,"Total",34,44,28,106]
[]
[null,"CRAMÉR'S V CALCULATIONS"]
[null,"Cramér's V"]
[null,null,"= square root of {14.86 ÷ [106 x (3-1)]}"]
[null,null,"= square root of [? ÷ (? x ?)]"]
[null,null,"= square root of (? ÷ ?)"]
[null,null,"= square root of ?"]
[null,null,"= ?"]

{"sheet":"Gamma (2x2)-A","index":9,"n_rows":29,"n_cols":13,"rows_kept":29,"cut":false,"hidden":true,"merged":[[13,1,13,2],[15,1,15,2],[17,1,17,2],[0,1,0,10],[2,1,2,10],[5,1,5,5],[6,3,6,5],[8,1,10,1],[10,7,10,8]]}
[null,"PRACTICE CALCULATING GAMMA: 2x2 CROSSTABULATION"]
[]
[]
[]
[]
[null,"FREQUENCIES",null,null,null,null,null,"Gamma",{"$f":"G21","v":-0.5}]
[null,null,null,"Independent Variable"]
[null,null,null,"Low Group","High Group","Total",null,"Total # of Pairs",{"$f":"G26","v":2926}]
[null,"Dependent\n Variable","Low Attribute",13,29,42,null,"Number of Tied Pairs",{"$f":"G29","v":2151},null,{"$f":"RANDBETWEEN(1,20)","v":17},{"$f":"RANDBETWEEN(1,30)","v":12},{"$f":"SUM(K9:L9)","v":29}]
[null,null,"High Attribute",20,15,35,null,null,null,null,{"$f":"RANDBETWEEN(1,30)","v":15},{"$f":"RANDBETWEEN(1,20)","v":16},{"$f":"SUM(K10:L10)","v":31}]
[null,null,"Total",33,44,77,null,"Need some help?",null,null,{"$f":"SUM(K9:K10)","v":32},{"$f":"SUM(L9:L10)","v":28},{"$f":"SUM(K9:L10)","v":60}]
[]
[null,"GAMMA CALCULATIONS"]
[null,"Concordant pairs of cases",null,{"$f":"CONCATENATE(\"'= \",D9,\" x \",E10)","v":"'= 13 x 15"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G15)","v":"'= 195"},null,null,{"$f":"D9*E10","v":195}]
[null,"Discordant pairs of cases",null,{"$f":"CONCATENATE(\"'= \",E9,\" x \",D10)","v":"'= 29 x 20"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G17)","v":"'= 580"},null,null,{"$f":"E9*D10","v":580}]
[null,"Gamma"]
[null,null,null,{"$f":"CONCATENATE(\"'= (\",G15,\" - \",G17,\") ÷ (\",G15,\" + \",G17,\")\")","v":"'= (195 - 580) ÷ (195 + 580)"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G20,\" ÷ \",H20)","v":"'= -385 ÷ 775"},null,null,{"$f":"G15-G17","v":-385},{"$f":"G15+G17","v":775}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G21)","v":"'= -0.5"},null,null,{"$f":"ROUND(G20/H20,2)","v":-0.5}]
[null,"Total # of pairs of cases"]
[null,null,null,{"$f":"CONCATENATE(\"'= [\",F11,\" x (\",F11,\" - 1)] ÷ 2\")","v":"'= [77 x (77 - 1)] ÷ 2"}]
[null,null,null,{"$f":"CONCATENATE(\"'= (\",F11,\" x \",G24,\") ÷ 2\")","v":"'= (77 x 76) ÷ 2"},null,null,{"$f":"F11-1","v":76}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G25,\" ÷ 2\")","v":"'= 5852 ÷ 2"},null,null,{"$f":"F11*G24","v":5852}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G26)","v":"'= 2926"},null,null,{"$f":"G25/2","v":2926}]
[null,"Number of tied pairs of cases",null,"= total pairs - concordant pairs - discordant pairs"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G26,\" - \",G15,\" - \",G17)","v":"'= 2926 - 195 - 580"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G29)","v":"'= 2151"},null,null,{"$f":"G26-G15-G17","v":2151}]

{"sheet":"Gamma (3x3)-A","index":10,"n_rows":34,"n_cols":14,"rows_kept":34,"cut":false,"hidden":true,"merged":[[14,1,14,2],[18,1,18,2],[22,1,22,2],[0,1,0,11],[2,1,2,11],[5,1,5,6],[6,3,6,6],[8,1,11,1],[10,8,10,9]]}
[null,"PRACTICE CALCULATING GAMMA: 2x2 CROSSTABULATION"]
[]
[]
[]
[]
[null,"FREQUENCIES",null,null,null,null,null,null,"Gamma",{"$f":"G26","v":-0.47}]
[null,null,null,"Independent Variable"]
[null,null,null,"Low Group","Middle Group","High Group","Total",null,"Total # of Pairs",{"$f":"G31","v":5460}]
[null,"Dependent\n Variable","Low Attribute",1,13,18,32,null,"Number of Tied Pairs",{"$f":"G34","v":3424},{"$f":"RANDBETWEEN(1,20)","v":8},{"$f":"RANDBETWEEN(1,20)","v":2},{"$f":"RANDBETWEEN(1,30)","v":1},{"$f":"SUM(K9:M9)","v":11}]
[null,null,"Middle Attribute",2,19,14,35,null,null,null,{"$f":"RANDBETWEEN(1,30)","v":17},{"$f":"RANDBETWEEN(1,20)","v":3},{"$f":"RANDBETWEEN(1,20)","v":3},{"$f":"SUM(K10:M10)","v":23}]
[null,null,"High Attribute",3,28,7,38,null,"Need some help?",null,{"$f":"RANDBETWEEN(1,20)","v":17},{"$f":"RANDBETWEEN(1,30)","v":30},{"$f":"RANDBETWEEN(1,20)","v":18},65]
[null,null,"Total",6,60,39,105,null,null,null,{"$f":"SUM(K9:K11)","v":42},{"$f":"SUM(L9:L11)","v":35},22,{"$f":"SUM(K9:M11)","v":99}]
[]
[null,"GAMMA CALCULATIONS"]
[null,"Concordant pairs of cases",null,{"$f":"CONCATENATE(\"'= [\",D9,\" x (\",E10,\" + \",F10,\" + \",E11,\" + \",F11,\")] + [\",E9,\" x (\",F10,\" + \",F11,\")] + [\",D10,\" x (\",E11,\" + \",F11,\")] + [\",E10,\" x \",F11,\"]\")","v":"'= [1 x (19 + 14 + 28 + 7)] + [13 x (14 + 7)] + [2 x (28 + 7)] + [19 x 7]"}]
[null,null,null,{"$f":"CONCATENATE(\"'= (\",D9,\" x \",G16,\") + (\",E9,\" x \",H16,\") + (\",D10,\" x \",I16,\") + (\",E10,\" x \",F11,\")\")","v":"'= (1 x 68) + (13 x 21) + (2 x 35) + (19 x 7)"},null,null,{"$f":"SUM(E10:F11)","v":68},{"$f":"SUM(F10:F11)","v":21},{"$f":"SUM(E11:F11)","v":35}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G17,\" + \",H17,\" + \",I17,\" + \",J17)","v":"'= 68 + 273 + 70 + 133"},null,null,{"$f":"D9*G16","v":68},{"$f":"E9*H16","v":273},{"$f":"D10*I16","v":70},{"$f":"E10*F11","v":133}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G18)","v":"'= 544"},null,null,{"$f":"SUM(G17:J17)","v":544}]
[null,"Discordant pairs of cases",null,{"$f":"CONCATENATE(\"'= [\",F9,\" x (\",D10,\" + \",E10,\" + \",D11,\" + \",E11,\")] + [\",E9,\" x (\",D10,\" + \",D11,\")] + [\",F10,\" x (\",D11,\" + \",E11,\")] + [\",E10,\" x \",D11,\"]\")","v":"'= [18 x (2 + 19 + 3 + 28)] + [13 x (2 + 3)] + [14 x (3 + 28)] + [19 x 3]"}]
[null,null,null,{"$f":"CONCATENATE(\"'= (\",F9,\" x \",G20,\") + (\",E9,\" x \",H20,\") + (\",F10,\" x \",I20,\") + (\",E10,\" x \",D11,\")\")","v":"'= (18 x 52) + (13 x 5) + (14 x 31) + (19 x 3)"},null,null,{"$f":"SUM(D10:E11)","v":52},{"$f":"SUM(D10:D11)","v":5},{"$f":"SUM(D11:E11)","v":31}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G21,\" + \",H21,\" + \",I21,\" + \",J21)","v":"'= 936 + 65 + 434 + 57"},null,null,{"$f":"F9*G20","v":936},{"$f":"E9*H20","v":65},{"$f":"F10*I20","v":434},{"$f":"E10*D11","v":57}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G22)","v":"'= 1492"},null,null,{"$f":"SUM(G21:J21)","v":1492}]
[null,"Gamma"]
[null,null,null,{"$f":"CONCATENATE(\"'= (\",G18,\" - \",G22,\") ÷ (\",G18,\" + \",G22,\")\")","v":"'= (544 - 1492) ÷ (544 + 1492)"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G25,\" ÷ \",H25)","v":"'= -948 ÷ 2036"},null,null,{"$f":"G18-G22","v":-948},{"$f":"G18+G22","v":2036}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G26)","v":"'= -0.47"},null,null,{"$f":"ROUND(G25/H25,2)","v":-0.47}]
[null,"Total # of pairs of cases"]
[null,null,null,{"$f":"CONCATENATE(\"'= [\",G12,\" x (\",G12,\" - 1)] ÷ 2\")","v":"'= [105 x (105 - 1)] ÷ 2"}]
[null,null,null,{"$f":"CONCATENATE(\"'= (\",G12,\" x \",G29,\") ÷ 2\")","v":"'= (105 x 104) ÷ 2"},null,null,{"$f":"G12-1","v":104}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G30,\" ÷ 2\")","v":"'= 10920 ÷ 2"},null,null,{"$f":"G12*G29","v":10920}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G31)","v":"'= 5460"},null,null,{"$f":"G30/2","v":5460}]
[null,"Number of tied pairs of cases",null,"= total pairs - concordant pairs - discordant pairs"]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G31,\" - \",G18,\" - \",G22)","v":"'= 5460 - 544 - 1492"}]
[null,null,null,{"$f":"CONCATENATE(\"'= \",G34)","v":"'= 3424"},null,null,{"$f":"G31-G18-G22","v":3424}]

{"sheet":"Lambda (2x2)-A","index":11,"n_rows":24,"n_cols":13,"rows_kept":24,"cut":false,"hidden":true,"merged":[[0,1,0,10],[2,1,2,10],[5,1,5,5],[6,3,6,5],[8,1,10,1],[8,7,8,8],[9,7,9,8]]}
[null,"PRACTICE CALCULATING LAMBDA"]
[]
[]
[]
[]
[null,"OBSERVED FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,"Lambda",{"$f":"F24","v":0.06}]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1",13,3,16,null,"Need some help?",null,null,{"$f":"RANDBETWEEN(1,20)","v":15},{"$f":"RANDBETWEEN(1,30)","v":5},{"$f":"SUM(K9:L9)","v":20}]
[null,null,"Attribute 2",12,5,17,null,null,null,null,{"$f":"RANDBETWEEN(1,30)","v":16},{"$f":"RANDBETWEEN(1,20)","v":17},{"$f":"SUM(K10:L10)","v":33}]
[null,null,"Total",25,8,33,null,null,null,null,{"$f":"SUM(K9:K10)","v":31},{"$f":"SUM(L9:L10)","v":22},{"$f":"SUM(K9:L10)","v":53}]
[]
[null,"LAMBDA CALCULATIONS"]
[null,"E1"]
[null,null,{"$f":"CONCATENATE(\"'= \",F11,\" - \",F15)","v":"'= 33 - 17"},null,null,{"$f":"MAX(F9:F10)","v":17}]
[null,null,{"$f":"CONCATENATE(\"'= \",F16)","v":"'= 16"},null,null,{"$f":"F11-F15","v":16}]
[null,"E2"]
[null,null,{"$f":"CONCATENATE(\"'= (\",D11,\" - \",F18,\") + (\",E11,\" - \",G18,\")\")","v":"'= (25 - 13) + (8 - 5)"},null,null,{"$f":"MAX(D9:D10)","v":13},{"$f":"MAX(E9:E10)","v":5}]
[null,null,{"$f":"CONCATENATE(\"'= \",F19,\" + \",G19)","v":"'= 12 + 3"},null,null,{"$f":"D11-F18","v":12},{"$f":"E11-G18","v":3}]
[null,null,{"$f":"CONCATENATE(\"'= \",F20)","v":"'= 15"},null,null,{"$f":"F19+G19","v":15}]
[null,"Lambda"]
[null,null,{"$f":"CONCATENATE(\"'= (\",F16,\" - \",F20,\") ÷ \",F16)","v":"'= (16 - 15) ÷ 16"}]
[null,null,{"$f":"CONCATENATE(\"'= \",F23,\" ÷ \",F16)","v":"'= 1 ÷ 16"},null,null,{"$f":"F16-F20","v":1}]
[null,null,{"$f":"CONCATENATE(\"'= \",F24)","v":"'= 0.06"},null,null,{"$f":"ROUND(F23/F16,2)","v":0.06}]

{"sheet":"Lambda (3x3)-A","index":12,"n_rows":25,"n_cols":14,"rows_kept":25,"cut":false,"hidden":true,"merged":[[0,1,0,11],[2,1,2,11],[5,1,5,6],[6,3,6,6],[8,1,11,1],[8,8,8,9],[9,8,9,9]]}
[null,"PRACTICE CALCULATING LAMBDA"]
[]
[]
[]
[]
[null,"OBSERVED FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,null,"Lambda",{"$f":"F25","v":0.08}]
[null,null,null,"Group 1","Group 2",null,"Total"]
[null,"Dependent\n Variable","Attribute 1",9,13,8,30,null,"Need some help?",null,{"$f":"RANDBETWEEN(1,20)","v":15},{"$f":"RANDBETWEEN(1,20)","v":20},{"$f":"RANDBETWEEN(1,30)","v":29},{"$f":"SUM(K9:M9)","v":64}]
[null,null,"Attribute 2",16,11,7,34,null,null,null,{"$f":"RANDBETWEEN(1,30)","v":14},{"$f":"RANDBETWEEN(1,20)","v":15},{"$f":"RANDBETWEEN(1,20)","v":11},{"$f":"SUM(K10:M10)","v":40}]
[null,null,null,20,20,3,43,null,null,null,{"$f":"RANDBETWEEN(1,20)","v":2},{"$f":"RANDBETWEEN(1,30)","v":30},{"$f":"RANDBETWEEN(1,20)","v":3},35]
[null,null,"Total",45,44,18,107,null,null,null,{"$f":"SUM(K9:K11)","v":31},{"$f":"SUM(L9:L11)","v":65},43,{"$f":"SUM(K9:M11)","v":139}]
[]
[null,"LAMBDA CALCULATIONS"]
[null,"E1"]
[null,null,{"$f":"CONCATENATE(\"'= \",G12,\" - \",F16)","v":"'= 107 - 43"},null,null,{"$f":"MAX(G9:G11)","v":43}]
[null,null,{"$f":"CONCATENATE(\"'= \",F17)","v":"'= 64"},null,null,{"$f":"G12-F16","v":64}]
[null,"E2"]
[null,null,{"$f":"CONCATENATE(\"'= (\",D12,\" - \",F19,\") + (\",E12,\" - \",G19,\") + (\",F12,\" - \",H19,\")\")","v":"'= (45 - 20) + (44 - 20) + (18 - 8)"},null,null,{"$f":"MAX(D9:D11)","v":20},{"$f":"MAX(E9:E11)","v":20},{"$f":"MAX(F9:F11)","v":8}]
[null,null,{"$f":"CONCATENATE(\"'= \",F20,\" + \",G20,\" + \",H20)","v":"'= 25 + 24 + 10"},null,null,{"$f":"D12-F19","v":25},{"$f":"E12-G19","v":24},10]
[null,null,{"$f":"CONCATENATE(\"'= \",F21)","v":"'= 59"},null,null,{"$f":"F20+G20+H20","v":59}]
[null,"Lambda"]
[null,null,{"$f":"CONCATENATE(\"'= (\",F17,\" - \",F21,\") ÷ \",F17)","v":"'= (64 - 59) ÷ 64"}]
[null,null,{"$f":"CONCATENATE(\"'= \",F24,\" ÷ \",F17)","v":"'= 5 ÷ 64"},null,null,{"$f":"F17-F21","v":5}]
[null,null,{"$f":"CONCATENATE(\"'= \",F25)","v":"'= 0.08"},null,null,{"$f":"ROUND(F24/F17,2)","v":0.08}]

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[null,"PRACTICE CALCULATING EXPECTED FREQUENCIES AND THE CHI-SQUARE STATISTIC"]
[]
[]
[]
[]
[null,"OBSERVED FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,"Degrees of freedom",1]
[null,null,null,"Group 1","Group 2","Total",null,"Chi-square statistic",{"$f":"N33","v":3.63}]
[null,"Dependent\n Variable","Attribute 1",17,16,33,null,null,null,null,{"$f":"RANDBETWEEN(1,20)","v":16},{"$f":"RANDBETWEEN(1,20)","v":4},{"$f":"SUM(K9:L9)","v":20}]
[null,null,"Attribute 2",6,17,23,null,null,null,null,{"$f":"RANDBETWEEN(1,20)","v":8},{"$f":"RANDBETWEEN(1,20)","v":9},{"$f":"SUM(K10:L10)","v":17}]
[null,null,"Total",23,33,56,null,null,null,null,{"$f":"SUM(K9:K10)","v":24},{"$f":"SUM(L9:L10)","v":13},{"$f":"SUM(K9:L10)","v":37}]
[]
[null,"EXPECTED FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,"Need some help?"]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1",{"$f":"K23","v":13.55},{"$f":"L23","v":19.45},{"$f":"F9","v":33}]
[null,null,"Attribute 2",{"$f":"K24","v":9.4499999999999993},{"$f":"L24","v":13.55},{"$f":"F10","v":23}]
[null,null,"Total",23,33,56]
[]
[null,"EXPECTED FREQUENCY CALCULATIONS"]
[null,null,null,"Independent Variable"]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1",{"$f":"CONCATENATE(\"(\",F16,\" x \",D18,\") ÷ \",$F$11,\" = \",K23)","v":"(33 x 23) ÷ 56 = 13.55"},{"$f":"CONCATENATE(\"(\",F16,\" x \",E18,\") ÷ \",$F$11,\" = \",L23)","v":"(33 x 33) ÷ 56 = 19.45"},{"$f":"F16","v":33},null,{"$f":"CONCATENATE(\"(\",F16,\" x \",D18,\") ÷ \",$F$11,\" = ?\")","v":"(33 x 23) ÷ 56 = ?"},{"$f":"CONCATENATE(\"(\",F16,\" x \",E18,\") ÷ \",$F$11,\" = ?\")","v":"(33 x 33) ÷ 56 = ?"},null,{"$f":"ROUND((F16*D18)/$F$18,2)","v":13.55},{"$f":"ROUND((F16*E18)/$F$18,2)","v":19.45}]
[null,null,"Attribute 2",{"$f":"CONCATENATE(\"(\",F17,\" x \",D18,\") ÷ \",$F$11,\" = \",K24)","v":"(23 x 23) ÷ 56 = 9.45"},{"$f":"CONCATENATE(\"(\",F17,\" x \",E18,\") ÷ \",$F$11,\" = \",L24)","v":"(23 x 33) ÷ 56 = 13.55"},{"$f":"F17","v":23},null,{"$f":"CONCATENATE(\"(\",F17,\" x \",D18,\") ÷ \",$F$11,\" = ?\")","v":"(23 x 23) ÷ 56 = ?"},{"$f":"CONCATENATE(\"(\",F17,\" x \",E18,\") ÷ \",$F$11,\" = ?\")","v":"(23 x 33) ÷ 56 = ?"},null,{"$f":"ROUND((F17*D18)/$F$18,2)","v":9.4499999999999993},{"$f":"ROUND((F17*E18)/$F$18,2)","v":13.55}]
[null,null,"Total",{"$f":"D18","v":23},33,{"$f":"F18","v":56}]
[]
[null,"CHI-SQUARE STATISTIC CALCULATIONS"]
[null,"Cell",null,"Observed","Expected","Observed-Expected",null,"(Observed-Expected)2","(Observed-Expected)2 ÷ Expected"]
[null,"Group 1, Attribute 1",null,{"$f":"D9","v":17},{"$f":"K23","v":13.55},{"$f":"CONCATENATE(D29,\" - \",E29,\" = \",L29)","v":"17 - 13.55 = 3.45"},null,{"$f":"CONCATENATE(L29,\" x \",L29,\" = \", M29)","v":"3.45 x 3.45 = 11.9"},{"$f":"CONCATENATE(M29, \" ÷ \",E29,\" = \",N29)","v":"11.9 ÷ 13.55 = 0.88"},null,null,{"$f":"ROUND(D29-E29,2)","v":3.45},{"$f":"(ROUND(L29*L29,2))","v":11.9},{"$f":"ROUND(M29/E29,2)","v":0.88}]
[null,"Group 1, Attribute 2",null,{"$f":"D10","v":6},{"$f":"K24","v":9.4499999999999993},{"$f":"CONCATENATE(D30,\" - \",E30,\" = \",L30)","v":"6 - 9.45 = -3.45"},null,{"$f":"CONCATENATE(L30,\" x \",L30,\" = \", M30)","v":"-3.45 x -3.45 = 11.9"},{"$f":"CONCATENATE(M30, \" ÷ \",E30,\" = \",N30)","v":"11.9 ÷ 9.45 = 1.26"},null,null,{"$f":"ROUND(D30-E30,2)","v":-3.45},{"$f":"(ROUND(L30*L30,2))","v":11.9},{"$f":"ROUND(M30/E30,2)","v":1.26}]
[null,"Group 2, Attribute 1",null,{"$f":"E9","v":16},{"$f":"L23","v":19.45},"16 - 19.45 = -3.45",null,"-3.45 x -3.45 = 11.9","11.9 ÷ 19.45 = 0.61",null,null,-3.45,11.9,0.61]
[null,"Group 2, Attribute 2",null,{"$f":"E10","v":17},{"$f":"L24","v":13.55},"17 - 13.55 = 3.45",null,"3.45 x 3.45 = 11.9","11.9 ÷ 13.55 = 0.88",null,null,3.45,11.9,0.88]
[null,null,null,null,null,null,null,null,"Column Sum (χ2)",null,{"$f":"CONCATENATE(\"'= \",N33)","v":"'= 3.63"},null,null,{"$f":"SUM(N29:N32)","v":3.63}]
[]
[null,null,null,{"$f":"D29","v":17},{"$f":"E29","v":13.55},{"$f":"CONCATENATE(D29,\" - \",E29,\" = ?\")","v":"17 - 13.55 = ?"},null,{"$f":"CONCATENATE(L29,\" x \",L29,\" = ?\")","v":"3.45 x 3.45 = ?"},{"$f":"CONCATENATE(M29, \" ÷ \",E29,\" = ?\")","v":"11.9 ÷ 13.55 = ?"}]
[null,null,null,{"$f":"D30","v":6},9.4499999999999993,{"$f":"CONCATENATE(D30,\" - \",E30,\" = ?\")","v":"6 - 9.45 = ?"},null,{"$f":"CONCATENATE(L30,\" x \",L30,\" = ?\")","v":"-3.45 x -3.45 = ?"},{"$f":"CONCATENATE(M30, \" ÷ \",E30,\" = ?\")","v":"11.9 ÷ 9.45 = ?"}]
[null,null,null,{"$f":"D31","v":16},19.45,"16 - 19.45 = ?",null,"-3.45 x -3.45 = ?","11.9 ÷ 19.45 = ?"]
[null,null,null,{"$f":"D32","v":17},13.55,"17 - 13.55 = ?",null,"3.45 x 3.45 = ?","11.9 ÷ 13.55 = ?"]

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[null,"PRACTICE CALCULATING EXPECTED FREQUENCIES AND THE CHI-SQUARE STATISTIC"]
[]
[]
[]
[]
[null,"OBSERVED FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,null,"Degrees of freedom",1]
[null,null,null,"Group 1","Group 2","Group 3","Total",null,"Chi-square statistic",{"$f":"O41","v":39.019999999999996}]
[null,"Dependent\n Variable","Attribute 1",18,5,1,24,null,null,null,{"$f":"RANDBETWEEN(1,20)","v":8},{"$f":"RANDBETWEEN(1,20)","v":11},6,{"$f":"SUM(K9:M9)","v":25}]
[null,null,"Attribute 2",6,20,17,43,null,null,null,5,20,7,{"$f":"SUM(K10:M10)","v":32}]
[null,null,"Attribute 3",3,20,8,31,null,null,null,4,7,9,{"$f":"SUM(K11:M11)","v":20}]
[null,null,"Total",27,45,26,98,null,null,null,{"$f":"SUM(K9:K11)","v":17},{"$f":"SUM(L9:L11)","v":38},{"$f":"SUM(M9:M11)","v":22},{"$f":"SUM(K9:M11)","v":77}]
[]
[null,"EXPECTED FREQUENCIES"]
[null,null,null,"Independent Variable",null,null,null,null,"Need some help?"]
[null,null,null,"Group 1","Group 2","Group 3","Total"]
[null,"Dependent\n Variable","Attribute 1",{"$f":"L25","v":6.61},{"$f":"M25","v":11.02},{"$f":"N25","v":6.37},{"$f":"G9","v":24}]
[null,null,"Attribute 2",{"$f":"L26","v":11.85},{"$f":"M26","v":19.739999999999998},{"$f":"N26","v":11.41},{"$f":"G10","v":43}]
[null,null,"Attribute 3",{"$f":"L27","v":8.5399999999999991},{"$f":"M27","v":14.23},8.2200000000000006,{"$f":"G11","v":31}]
[null,null,"Total",{"$f":"D12","v":27},45,{"$f":"F12","v":26},98]
[]
[null,"EXPECTED FREQUENCY CALCULATIONS"]
[null,null,null,"Independent Variable"]
[null,null,null,"Group 1","Group 2","Group 3","Total"]
[null,"Dependent\n Variable","Attribute 1",{"$f":"CONCATENATE(\"(\",G17,\" x \",D20,\") ÷ \",$G$12,\" = \",L25)","v":"(24 x 27) ÷ 98 = 6.61"},{"$f":"CONCATENATE(\"(\",G17,\" x \",E20,\") ÷ \",$G$12,\" = \",M25)","v":"(24 x 45) ÷ 98 = 11.02"},{"$f":"CONCATENATE(\"(\",G17,\" x \",F20,\") ÷ \",$G$12,\" = \",N25)","v":"(24 x 26) ÷ 98 = 6.37"},{"$f":"G17","v":24},null,{"$f":"CONCATENATE(\"(\",G17,\" x \",D20,\") ÷ \",$G$12,\" = ?\")","v":"(24 x 27) ÷ 98 = ?"},{"$f":"CONCATENATE(\"(\",G17,\" x \",E20,\") ÷ \",$G$12,\" = ?\")","v":"(24 x 45) ÷ 98 = ?"},{"$f":"CONCATENATE(\"(\",G17,\" x \",F20,\") ÷ \",$G$12,\" = ?\")","v":"(24 x 26) ÷ 98 = ?"},{"$f":"ROUND((G17*D20)/$G$20,2)","v":6.61},{"$f":"ROUND((G17*E20)/$G$20,2)","v":11.02},{"$f":"ROUND((G17*F20)/$G$20,2)","v":6.37}]
[null,null,"Attribute 2",{"$f":"CONCATENATE(\"(\",G18,\" x \",D20,\") ÷ \",$G$12,\" = \",L26)","v":"(43 x 27) ÷ 98 = 11.85"},{"$f":"CONCATENATE(\"(\",G18,\" x \",E20,\") ÷ \",$G$12,\" = \",M26)","v":"(43 x 45) ÷ 98 = 19.74"},{"$f":"CONCATENATE(\"(\",G18,\" x \",F20,\") ÷ \",$G$12,\" = \",N26)","v":"(43 x 26) ÷ 98 = 11.41"},{"$f":"G18","v":43},null,{"$f":"CONCATENATE(\"(\",G18,\" x \",D20,\") ÷ \",$G$12,\" = ?\")","v":"(43 x 27) ÷ 98 = ?"},{"$f":"CONCATENATE(\"(\",G18,\" x \",E20,\") ÷ \",$G$12,\" = ?\")","v":"(43 x 45) ÷ 98 = ?"},{"$f":"CONCATENATE(\"(\",G18,\" x \",F20,\") ÷ \",$G$12,\" = ?\")","v":"(43 x 26) ÷ 98 = ?"},{"$f":"ROUND((G18*D20)/$G$20,2)","v":11.85},{"$f":"ROUND((G18*E20)/$G$20,2)","v":19.739999999999998},{"$f":"ROUND((G18*F20)/$G$20,2)","v":11.41}]
[null,null,"Attribute 3",{"$f":"CONCATENATE(\"(\",G19,\" x \",D20,\") ÷ \",$G$12,\" = \",L27)","v":"(31 x 27) ÷ 98 = 8.54"},{"$f":"CONCATENATE(\"(\",G19,\" x \",E20,\") ÷ \",$G$12,\" = \",M27)","v":"(31 x 45) ÷ 98 = 14.23"},{"$f":"CONCATENATE(\"(\",G19,\" x \",F20,\") ÷ \",$G$12,\" = \",N27)","v":"(31 x 26) ÷ 98 = 8.22"},{"$f":"G19","v":31},null,{"$f":"CONCATENATE(\"(\",G19,\" x \",D20,\") ÷ \",$G$12,\" = ?\")","v":"(31 x 27) ÷ 98 = ?"},{"$f":"CONCATENATE(\"(\",G19,\" x \",E20,\") ÷ \",$G$12,\" = ?\")","v":"(31 x 45) ÷ 98 = ?"},{"$f":"CONCATENATE(\"(\",G19,\" x \",F20,\") ÷ \",$G$12,\" = ?\")","v":"(31 x 26) ÷ 98 = ?"},{"$f":"ROUND((G19*D20)/$G$20,2)","v":8.5399999999999991},{"$f":"ROUND((G19*E20)/$G$20,2)","v":14.23},{"$f":"ROUND((G19*F20)/$G$20,2)","v":8.2200000000000006}]
[null,null,"Total",{"$f":"D20","v":27},45,{"$f":"F20","v":26},{"$f":"G20","v":98}]
[]
[null,"CHI-SQUARE STATISTIC CALCULATIONS"]
[null,"Cell",null,"Observed","Expected","Observed-Expected",null,"(Observed-Expected)2",null,"(Observed-Expected)2 ÷ Expected"]
[null,"Group 1, Attribute 1",null,{"$f":"D9","v":18},{"$f":"L25","v":6.61},{"$f":"CONCATENATE(D32,\" - \",E32,\" = \",M32)","v":"18 - 6.61 = 11.39"},null,{"$f":"CONCATENATE(M32,\" x \",M32,\" = \", N32)","v":"11.39 x 11.39 = 129.73"},null,{"$f":"CONCATENATE(N32, \" ÷ \",E32,\" = \",O32)","v":"129.73 ÷ 6.61 = 19.63"},null,null,{"$f":"ROUND(D32-E32,2)","v":11.39},{"$f":"(ROUND(M32*M32,2))","v":129.72999999999999},{"$f":"ROUND(N32/E32,2)","v":19.63}]
[null,"Group 1, Attribute 2",null,{"$f":"D10","v":6},{"$f":"L26","v":11.85},{"$f":"CONCATENATE(D33,\" - \",E33,\" = \",M33)","v":"6 - 11.85 = -5.85"},null,{"$f":"CONCATENATE(M33,\" x \",M33,\" = \", N33)","v":"-5.85 x -5.85 = 34.22"},null,{"$f":"CONCATENATE(N33, \" ÷ \",E33,\" = \",O33)","v":"34.22 ÷ 11.85 = 2.89"},null,null,{"$f":"ROUND(D33-E33,2)","v":-5.85},{"$f":"(ROUND(M33*M33,2))","v":34.22},{"$f":"ROUND(N33/E33,2)","v":2.89}]
[null,"Group 1, Attribute 3",null,3,8.5399999999999991,"3 - 8.54 = -5.54",null,"-5.54 x -5.54 = 30.69",null,"30.69 ÷ 8.54 = 3.59",null,null,-5.54,30.69,3.59]
[null,"Group 2, Attribute 1",null,{"$f":"E9","v":5},{"$f":"M25","v":11.02},"5 - 11.02 = -6.02",null,"-6.02 x -6.02 = 36.24",null,"36.24 ÷ 11.02 = 3.29",null,null,-6.02,36.24,3.29]
[null,"Group 2, Attribute 2",null,{"$f":"E10","v":20},{"$f":"M26","v":19.739999999999998},"20 - 19.74 = 0.26",null,"0.26 x 0.26 = 0.07",null,"0.07 ÷ 19.74 = 0",null,null,0.26,7.0000000000000007E-2,0]
[null,"Group 2, Attribute 3",null,{"$f":"E11","v":20},{"$f":"M27","v":14.23},"20 - 14.23 = 5.77",null,"5.77 x 5.77 = 33.29",null,"33.29 ÷ 14.23 = 2.34",null,null,5.77,33.29,2.34]
[null,"Group 3, Attribute 1",null,{"$f":"F9","v":1},{"$f":"N25","v":6.37},"1 - 6.37 = -5.37",null,"-5.37 x -5.37 = 28.84",null,"28.84 ÷ 6.37 = 4.53",null,null,-5.37,28.84,4.53]
[null,"Group 3, Attribute 2",null,{"$f":"F10","v":17},{"$f":"N26","v":11.41},"17 - 11.41 = 5.59",null,"5.59 x 5.59 = 31.25",null,"31.25 ÷ 11.41 = 2.74",null,null,5.59,31.25,2.74]
[null,"Group 3, Attribute 3",null,8,8.2200000000000006,"8 - 8.22 = -0.22",null,"-0.22 x -0.22 = 0.05",null,"0.05 ÷ 8.22 = 0.01",null,null,-0.22,0.05,0.01]
[null,null,null,null,null,null,null,null,null,"Column Sum (χ2)",null,{"$f":"CONCATENATE(\"'= \",O41)","v":"'= 39.02"},null,null,{"$f":"SUM(O32:O40)","v":39.019999999999996}]
[]
[null,null,null,{"$f":"D32","v":18},{"$f":"E32","v":6.61},{"$f":"CONCATENATE(D32,\" - \",E32,\" = ?\")","v":"18 - 6.61 = ?"},null,{"$f":"CONCATENATE(M32,\" x \",M32,\" = ?\")","v":"11.39 x 11.39 = ?"},null,{"$f":"CONCATENATE(N32, \" ÷ \",E32,\" = ?\")","v":"129.73 ÷ 6.61 = ?"}]
[null,null,null,{"$f":"D33","v":6},11.85,{"$f":"CONCATENATE(D33,\" - \",E33,\" = ?\")","v":"6 - 11.85 = ?"},null,{"$f":"CONCATENATE(M33,\" x \",M33,\" = ?\")","v":"-5.85 x -5.85 = ?"},null,{"$f":"CONCATENATE(N33, \" ÷ \",E33,\" = ?\")","v":"34.22 ÷ 11.85 = ?"}]
[null,null,null,3,8.5399999999999991,"3 - 8.54 = ?",null,"-5.54 x -5.54 = ?",null,"30.69 ÷ 8.54 = ?"]
[null,null,null,5,11.02,"5 - 11.02 = ?",null,"-6.02 x -6.02 = ?",null,"36.24 ÷ 11.02 = ?"]
[null,null,null,20,19.739999999999998,"20 - 19.74 = ?",null,"0.26 x 0.26 = ?",null,"0.07 ÷ 19.74 = ?"]
[null,null,null,20,14.23,"20 - 14.23 = ?",null,"5.77 x 5.77 = ?",null,"33.29 ÷ 14.23 = ?"]
[null,null,null,1,6.37,"1 - 6.37 = ?",null,"-5.37 x -5.37 = ?",null,"28.84 ÷ 6.37 = ?"]
[null,null,null,17,11.41,"17 - 11.41 = ?",null,"5.59 x 5.59 = ?",null,"31.25 ÷ 11.41 = ?"]
[null,null,null,8,8.2200000000000006,"8 - 8.22 = ?",null,"-0.22 x -0.22 = ?",null,"0.05 ÷ 8.22 = ?"]

{"sheet":"Phi-A","index":15,"n_rows":25,"n_cols":13,"rows_kept":25,"cut":false,"hidden":true,"merged":[[0,1,0,10],[2,1,2,10],[5,1,5,5],[6,3,6,5],[8,1,10,1],[8,7,8,8],[9,7,9,8]]}
[null,"PRACTICE CALCULATING PHI"]
[]
[]
[]
[]
[null,"OBSERVED FREQUENCIES",null,null,null,null,null,"Chi-square statistic",{"$f":"F25","v":1.8}]
[null,null,null,"Independent Variable",null,null,null,"Phi",{"$f":"E17","v":0.22}]
[null,null,null,"Group 1","Group 2","Total"]
[null,"Dependent\n Variable","Attribute 1",10,12,22,null,"Need some help?",null,null,{"$f":"RANDBETWEEN(1,20)","v":15},{"$f":"RANDBETWEEN(1,20)","v":16},{"$f":"SUM(K9:L9)","v":31}]
[null,null,"Attribute 2",12,6,18,null,null,null,null,{"$f":"RANDBETWEEN(1,20)","v":2},{"$f":"RANDBETWEEN(1,20)","v":15},{"$f":"SUM(K10:L10)","v":17}]
[null,null,"Total",22,18,40,null,null,null,null,{"$f":"SUM(K9:K10)","v":17},{"$f":"SUM(L9:L10)","v":31},{"$f":"SUM(K9:L10)","v":48}]
[]
[null,"PHI CALCULATIONS"]
[null,"Phi"]
[null,null,{"$f":"CONCATENATE(\"'= square root of (\",F25,\" ÷ \",F11,\")\")","v":"'= square root of (1.8 ÷ 40)"}]
[null,null,{"$f":"CONCATENATE(\"'= square root of \",E16)","v":"'= square root of 0.05"},null,{"$f":"ROUND(F25/F11,2)","v":0.05}]
[null,null,{"$f":"CONCATENATE(\"'= \",E17)","v":"'= 0.22"},null,{"$f":"ROUND(SQRT(E16),2)","v":0.22}]
[]
[]
[]
[null,{"$f":"D9","v":10},{"$f":"ROUND((F9*D11)/F11,2)","v":12.1},{"$f":"ROUND(B21-C21,2)","v":-2.1},{"$f":"ROUND(D21*D21,2)","v":4.41},{"$f":"ROUND(E21/C21,2)","v":0.36}]
[null,{"$f":"D10","v":12},{"$f":"ROUND((F10*D11)/F11,2)","v":9.9},{"$f":"ROUND(B22-C22,2)","v":2.1},{"$f":"ROUND(D22*D22,2)","v":4.41},{"$f":"ROUND(E22/C22,2)","v":0.45}]
[null,{"$f":"E9","v":12},{"$f":"ROUND((F9*E11)/F11,2)","v":9.9},2.1,4.41,0.45]
[null,{"$f":"E10","v":6},{"$f":"ROUND((F10*E11)/F11,2)","v":8.1},-2.1,4.41,0.54]
[null,null,null,null,null,{"$f":"SUM(F21:F24)","v":1.8}]

{"sheet":"Cramér's V-A","index":16,"n_rows":32,"n_cols":14,"rows_kept":32,"cut":false,"hidden":true,"merged":[[0,1,0,11],[2,1,2,11],[5,1,5,6],[6,3,6,6],[8,1,11,1],[8,8,8,9],[9,8,9,9]]}
[null,"PRACTICE CALCULATING CRAMÉR'S V"]
[]
[]
[]
[]
[null,"OBSERVED FREQUENCIES",null,null,null,null,null,null,"Chi-square statistic",{"$f":"F32","v":14.860000000000003}]
[null,null,null,"Independent Variable",null,null,null,null,"Cramér's V ",{"$f":"E20","v":0.26}]
[null,null,null,"Group 1","Group 2","Group 3","Total"]
[null,"Dependent\n Variable","Attribute 1",1,13,7,21,null,"Need some help?",null,{"$f":"RANDBETWEEN(1,20)","v":1},{"$f":"RANDBETWEEN(1,20)","v":11},{"$f":"RANDBETWEEN(1,20)","v":3},{"$f":"SUM(K9:M9)","v":15}]
[null,null,"Attribute 2",13,18,5,36,null,null,null,{"$f":"RANDBETWEEN(1,20)","v":10},{"$f":"RANDBETWEEN(1,20)","v":2},1,{"$f":"SUM(K10:M10)","v":13}]
[null,null,"Attribute 3",20,13,16,49,null,null,null,19,10,20,{"$f":"SUM(K11:M11)","v":49}]
[null,null,"Total",34,44,28,106,null,null,null,{"$f":"SUM(K9:K11)","v":30},{"$f":"SUM(L9:L11)","v":23},{"$f":"SUM(M9:M11)","v":24},{"$f":"SUM(K9:M11)","v":77}]
[]
[null,"CRAMÉR'S V CALCULATIONS"]
[null,"Cramér's V"]
[null,null,{"$f":"CONCATENATE(\"'= square root of {\",F32,\" ÷ [\",G12,\" x (3-1)]}\")","v":"'= square root of {14.86 ÷ [106 x (3-1)]}"}]
[null,null,{"$f":"CONCATENATE(\"'= square root of [\",F32,\" ÷ (\",G12,\" x 2)]\")","v":"'= square root of [14.86 ÷ (106 x 2)]"}]
[null,null,{"$f":"CONCATENATE(\"'= square root of (\",F32,\" ÷ \",E18,\")\")","v":"'= square root of (14.86 ÷ 212)"},null,{"$f":"G12*2","v":212}]
[null,null,{"$f":"CONCATENATE(\"'= square root of \",E19)","v":"'= square root of 0.07"},null,{"$f":"ROUND(F32/E18,2)","v":7.0000000000000007E-2}]
[null,null,{"$f":"CONCATENATE(\"'= \",E20)","v":"'= 0.26"},null,{"$f":"ROUND(SQRT(E19),2)","v":0.26}]
[]
[]
[null,{"$f":"D9","v":1},{"$f":"ROUND((G9*$D$12)/$G$12,2)","v":6.74},{"$f":"ROUND(B23-C23,2)","v":-5.74},{"$f":"ROUND(D23*D23,2)","v":32.950000000000003},{"$f":"ROUND(E23/C23,2)","v":4.8899999999999997}]
[null,{"$f":"D10","v":13},{"$f":"ROUND((G10*$D$12)/$G$12,2)","v":11.55},{"$f":"ROUND(B24-C24,2)","v":1.45},{"$f":"ROUND(D24*D24,2)","v":2.1},{"$f":"ROUND(E24/C24,2)","v":0.18}]
[null,{"$f":"D11","v":20},{"$f":"ROUND((G11*$D$12)/$G$12,2)","v":15.72},4.28,18.32,1.17]
[null,{"$f":"E9","v":13},{"$f":"ROUND((G9*$E$12)/$G$12,2)","v":8.7200000000000006},4.28,18.32,2.1]
[null,{"$f":"E10","v":18},{"$f":"ROUND((G10*$E$12)/$G$12,2)","v":14.94},3.06,9.36,0.63]
[null,13,20.34,-7.34,53.88,2.65]
[null,{"$f":"F9","v":7},{"$f":"ROUND((G9*$F$12)/$G$12,2)","v":5.55},1.45,2.1,0.38]
[null,{"$f":"F10","v":5},{"$f":"ROUND((G10*$F$12)/$G$12,2)","v":9.51},-4.51,20.34,2.14]
[null,16,12.94,3.06,9.36,0.72]
[null,null,null,null,null,{"$f":"SUM(F23:F31)","v":14.860000000000003}]