{"text_format":"1","workbook":"xlsx","n_sheets":5,"sheets":["Title","ANOVA (2 groups)","ANOVA (3 groups)","ANOVA (2 groups)-A","ANOVA (3 groups)-A"],"not_rendered":{"charts":0,"images":19,"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":"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 8"]
[]
[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":"ANOVA (2 groups)","index":1,"n_rows":93,"n_cols":13,"rows_kept":93,"cut":false,"hidden":false,"merged":[[63,5,63,6],[62,5,62,6],[61,5,61,6],[60,5,60,6],[59,5,59,6],[58,5,58,6],[57,5,57,6],[56,5,56,6],[62,3,62,4],[63,3,63,4],[35,3,35,4],[36,3,36,4],[37,3,37,4],[38,3,38,4],[39,3,39,4],[30,3,30,4],[31,3,31,4],[32,3,32,4],[45,3,45,4],[40,3,40,4],[41,3,41,4],[42,3,42,4],[33,3,33,4],[34,3,34,4],[55,5,55,6],[54,5,54,6],[53,5,53,6],[50,5,50,6],[49,5,49,6],[48,5,48,6],[47,5,47,6],[46,5,46,6],[45,5,45,6],[72,5,72,6],[71,5,71,6],[70,5,70,6],[69,5,69,6],[68,5,68,6],[67,5,67,6],[66,5,66,6],[65,5,65,6],[64,5,64,6],[74,5,74,6],[5,7,5,9],[23,8,23,10],[23,11,23,12],[24,8,24,10],[25,8,25,10],[24,11,24,12],[25,11,25,12],[40,5,40,6],[41,5,41,6],[42,5,42,6],[43,5,43,6],[44,5,44,6],[35,5,35,6],[36,5,36,6],[37,5,37,6],[38,5,38,6],[39,5,39,6],[30,5,30,6],[31,5,31,6],[32,5,32,6],[33,5,33,6],[34,5,34,6],[73,5,73,6],[71,3,71,4],[72,3,72,4],[73,3,73,4],[68,3,68,4],[69,3,69,4],[70,3,70,4],[65,3,65,4],[66,3,66,4],[67,3,67,4],[64,3,64,4],[59,3,59,4],[60,3,60,4],[61,3,61,4],[56,3,56,4],[57,3,57,4],[58,3,58,4],[43,3,43,4],[44,3,44,4],[53,3,53,4],[54,3,54,4],[55,3,55,4],[46,3,46,4],[47,3,47,4],[48,3,48,4],[49,3,49,4],[29,3,29,4],[2,1,2,13],[0,1,0,13],[24,3,24,4],[25,3,25,4],[23,5,23,6],[24,5,24,6],[25,5,25,6],[29,5,29,6],[23,3,23,4],[20,7,20,9],[10,7,10,9],[15,7,15,9],[5,1,5,2],[5,4,5,5],[6,1,7,1],[6,2,7,2],[6,4,7,4],[6,5,7,5],[18,1,19,2]]}
[null,"PRACTICE CALCULATING ONE-WAY ANOVA (2 GROUPS)"]
[]
[null,"Using the values in the yellow highlighed cells, calculate the between group sum of squares, the within group sum of squares, \nthe total sum of squares, the degrees of freedom and the F-statistic. \nKeep two decimal places throughout your calculations. \nTo check your answers, click on the 'Show Sum of Squares' and/or 'Show F-Statistic' buttons."]
[]
[]
[null,"GROUP 1",null,null,"GROUP 2",null,null,"Means"]
[null,"Case #","Value on \nVariable X",null,"Case #","Value on \nVariable X",null,"Group 1 Mean (x-bargroup):",null,26.9]
[null,null,null,null,null,null,null,"Group 2 Mean (x-bargroup):",null,18.899999999999999]
[null,1,32,null,11,24,null,"Overall Mean (x-bartotal):",null,22.9]
[null,2,38,null,12,25]
[null,3,17,null,13,26,null,"Sum of Squares"]
[null,4,24,null,14,21,null,"Between group sum of squares:",null,"hidden"]
[null,5,10,null,15,19,null,"Within group sum of squares:",null,"hidden"]
[null,6,24,null,16,5,null,"Total sum of squares:",null,"hidden"]
[null,7,29,null,17,23]
[null,8,40,null,18,16,null,"F-statistic"]
[null,9,20,null,19,10,null,"Between group degrees of freedom:",null,"hidden"]
[null,10,35,null,20,20,null,"Within group degrees of freedom:",null,"hidden"]
[null,"Need some help?",null,null,null,null,null,"F-statistic:",null,"hidden"]
[]
[null,null,null,null,null,null,null,"If the F-statistic is higher than 4.41, then p<0.05."]
[]
[null,"BETWEEN GROUP SUM OF SQUARES CALCULATION"]
[null,"Group # ","Group Mean\n","Overall Mean\n",null,"Cases in Group\n",null,"Group Mean-Overall Mean\n","(Group Mean-Overall Mean)2\n",null,null,"Number of Cases in Group x \n(Group Mean-Overall Mean)2\n"]
[null,1,26.9,22.9,null,10,null,"26.9 - 22.9 = ?","4 x 4 = ?",null,null,"10 x 16 = ?"]
[null,2,18.899999999999999,22.9,null,10,null,"18.9 - 22.9 = ?","-4 x -4 = ?",null,null,"10 x 16 = ?"]
[null,null,null,null,null,null,null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"WITHIN GROUP SUM OF SQUARES CALCULATION"]
[null,"Case #","Value\n","Group Mean\n",null,"Value-Group Mean\n",null,"(Value - Group Mean)2\n"]
[null,1,32,26.9,null,"32 - 26.9 = ?",null,"5.1 x 5.1 = ?"]
[null,2,38,26.9,null,"38 - 26.9 = ?",null,"11.1 x 11.1 = ?"]
[null,3,17,26.9,null,"17 - 26.9 = ?",null,"-9.9 x -9.9 = ?"]
[null,4,24,26.9,null,"24 - 26.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,5,10,26.9,null,"10 - 26.9 = ?",null,"-16.9 x -16.9 = ?"]
[null,6,24,26.9,null,"24 - 26.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,7,29,26.9,null,"29 - 26.9 = ?",null,"2.1 x 2.1 = ?"]
[null,8,40,26.9,null,"40 - 26.9 = ?",null,"13.1 x 13.1 = ?"]
[null,9,20,26.9,null,"20 - 26.9 = ?",null,"-6.9 x -6.9 = ?"]
[null,10,35,26.9,null,"35 - 26.9 = ?",null,"8.1 x 8.1 = ?"]
[null,11,24,18.899999999999999,null,"24 - 18.9 = ?",null,"5.1 x 5.1 = ?"]
[null,12,25,18.899999999999999,null,"25 - 18.9 = ?",null,"6.1 x 6.1 = ?"]
[null,13,26,18.899999999999999,null,"26 - 18.9 = ?",null,"7.1 x 7.1 = ?"]
[null,14,21,18.899999999999999,null,"21 - 18.9 = ?",null,"2.1 x 2.1 = ?"]
[null,15,19,18.899999999999999,null,"19 - 18.9 = ?",null,"0.1 x 0.1 = ?"]
[null,16,5,18.899999999999999,null,"5 - 18.9 = ?",null,"-13.9 x -13.9 = ?"]
[null,17,23,18.899999999999999,null,"23 - 18.9 = ?",null,"4.1 x 4.1 = ?"]
[null,18,16,18.899999999999999,null,"16 - 18.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,19,10,18.899999999999999,null,"10 - 18.9 = ?",null,"-8.9 x -8.9 = ?"]
[null,20,20,18.899999999999999,null,"20 - 18.9 = ?",null,"1.1 x 1.1 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",null,"= ?"]
[]
[null,"TOTAL SUM OF SQUARES CALCULATION"]
[null,"Case #","Value\n","Overall Mean\n",null,"Value-Overall Mean\n",null,"(Value - Overall Mean)2\n"]
[null,1,32,22.9,null,"32 - 22.9 = ?",null,"9.1 x 9.1 = ?"]
[null,2,38,22.9,null,"38 - 22.9 = ?",null,"15.1 x 15.1 = ?"]
[null,3,17,22.9,null,"17 - 22.9 = ?",null,"-5.9 x -5.9 = ?"]
[null,4,24,22.9,null,"24 - 22.9 = ?",null,"1.1 x 1.1 = ?"]
[null,5,10,22.9,null,"10 - 22.9 = ?",null,"-12.9 x -12.9 = ?"]
[null,6,24,22.9,null,"24 - 22.9 = ?",null,"1.1 x 1.1 = ?"]
[null,7,29,22.9,null,"29 - 22.9 = ?",null,"6.1 x 6.1 = ?"]
[null,8,40,22.9,null,"40 - 22.9 = ?",null,"17.1 x 17.1 = ?"]
[null,9,20,22.9,null,"20 - 22.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,10,35,22.9,null,"35 - 22.9 = ?",null,"12.1 x 12.1 = ?"]
[null,11,24,22.9,null,"24 - 22.9 = ?",null,"1.1 x 1.1 = ?"]
[null,12,25,22.9,null,"25 - 22.9 = ?",null,"2.1 x 2.1 = ?"]
[null,13,26,22.9,null,"26 - 22.9 = ?",null,"3.1 x 3.1 = ?"]
[null,14,21,22.9,null,"21 - 22.9 = ?",null,"-1.9 x -1.9 = ?"]
[null,15,19,22.9,null,"19 - 22.9 = ?",null,"-3.9 x -3.9 = ?"]
[null,16,5,22.9,null,"5 - 22.9 = ?",null,"-17.9 x -17.9 = ?"]
[null,17,23,22.9,null,"23 - 22.9 = ?",null,"0.1 x 0.1 = ?"]
[null,18,16,22.9,null,"16 - 22.9 = ?",null,"-6.9 x -6.9 = ?"]
[null,19,10,22.9,null,"10 - 22.9 = ?",null,"-12.9 x -12.9 = ?"]
[null,20,20,22.9,null,"20 - 22.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",null,"= ?"]
[]
[null,"F-STATISTIC CALCULATION"]
[null,"Between group degrees of freedom"]
[null,null,null,null,null,"= 2 - 1"]
[null,null,null,null,null,"= ?"]
[null,"Within group degrees of freedom"]
[null,null,null,null,null,"= (10 - 1) + (10 - 1)"]
[null,null,null,null,null,"= ? + ?"]
[null,null,null,null,null,"= ?"]
[null,"F-Statistic Numerator"]
[null,null,null,null,null,"= 320 ÷ 1"]
[null,null,null,null,null,"= ?"]
[null,"F-Statistic Denominator"]
[null,null,null,null,null,"= 1255.8 ÷ 18"]
[null,null,null,null,null,"= ?"]
[null,"F-Statistic"]
[null,null,null,null,null,"= 320 ÷ 69.77"]
[null,null,null,null,null,"= ?"]

{"sheet":"ANOVA (3 groups)","index":2,"n_rows":103,"n_cols":13,"rows_kept":103,"cut":false,"hidden":false,"merged":[[0,1,0,14],[25,3,25,4],[25,5,25,6],[26,3,26,4],[26,5,26,6],[24,3,24,4],[24,5,24,6],[5,1,5,2],[5,4,5,5],[5,10,5,12],[6,1,7,1],[6,2,7,2],[6,4,7,4],[6,5,7,5],[6,7,7,7],[6,8,7,8],[34,3,34,4],[34,5,34,6],[35,3,35,4],[35,5,35,6],[36,3,36,4],[36,5,36,6],[31,3,31,4],[31,5,31,6],[32,3,32,4],[32,5,32,6],[33,3,33,4],[33,5,33,6],[40,3,40,4],[40,5,40,6],[41,3,41,4],[41,5,41,6],[42,3,42,4],[42,5,42,6],[37,3,37,4],[37,5,37,6],[38,3,38,4],[38,5,38,6],[39,3,39,4],[39,5,39,6],[46,3,46,4],[46,5,46,6],[47,3,47,4],[47,5,47,6],[48,3,48,4],[48,5,48,6],[43,3,43,4],[43,5,43,6],[44,3,44,4],[44,5,44,6],[45,3,45,4],[45,5,45,6],[56,5,56,6],[59,3,59,4],[59,5,59,6],[60,3,60,4],[60,5,60,6],[61,3,61,4],[61,5,61,6],[49,3,49,4],[49,5,49,6],[50,3,50,4],[50,5,50,6],[51,3,51,4],[51,5,51,6],[65,3,65,4],[65,5,65,6],[66,3,66,4],[66,5,66,6],[67,3,67,4],[67,5,67,6],[62,3,62,4],[62,5,62,6],[63,3,63,4],[63,5,63,6],[64,3,64,4],[64,5,64,6],[71,5,71,6],[72,3,72,4],[72,5,72,6],[73,3,73,4],[73,5,73,6],[68,3,68,4],[68,5,68,6],[69,3,69,4],[69,5,69,6],[70,3,70,4],[70,5,70,6],[42,7,42,8],[84,5,84,6],[5,7,5,8],[27,3,27,4],[27,5,27,6],[31,7,31,8],[32,7,32,8],[33,7,33,8],[34,7,34,8],[35,7,35,8],[36,7,36,8],[77,3,77,4],[77,5,77,6],[78,3,78,4],[78,5,78,6],[79,3,79,4],[79,5,79,6],[74,3,74,4],[74,5,74,6],[75,3,75,4],[75,5,75,6],[76,3,76,4],[76,5,76,6],[71,3,71,4],[63,7,63,8],[27,7,27,9],[24,11,24,13],[25,11,25,13],[26,11,26,13],[27,11,27,13],[28,12,28,13],[49,7,49,8],[50,7,50,8],[51,7,51,8],[24,7,24,9],[25,7,25,9],[26,7,26,9],[43,7,43,8],[44,7,44,8],[45,7,45,8],[46,7,46,8],[47,7,47,8],[48,7,48,8],[37,7,37,8],[38,7,38,8],[39,7,39,8],[40,7,40,8],[41,7,41,8],[79,7,79,8],[84,7,84,8],[2,1,2,14],[52,3,52,4],[53,3,53,4],[54,3,54,4],[55,3,55,4],[70,7,70,8],[71,7,71,8],[72,7,72,8],[73,7,73,8],[74,7,74,8],[75,7,75,8],[64,7,64,8],[65,7,65,8],[66,7,66,8],[67,7,67,8],[68,7,68,8],[69,7,69,8],[56,7,56,8],[59,7,59,8],[60,7,60,8],[61,7,61,8],[62,7,62,8],[80,7,80,8],[81,7,81,8],[82,7,82,8],[83,7,83,8],[21,10,21,12],[80,3,80,4],[81,3,81,4],[82,3,82,4],[83,3,83,4],[80,5,80,6],[81,5,81,6],[82,5,82,6],[83,5,83,6],[52,5,52,6],[53,5,53,6],[54,5,54,6],[55,5,55,6],[52,7,52,8],[53,7,53,8],[54,7,54,8],[55,7,55,8],[76,7,76,8],[77,7,77,8],[78,7,78,8]]}
[null,"PRACTICE CALCULATING ONE-WAY ANOVA (3 GROUPS)"]
[]
[null,"Using the values in the yellow highlighed cells, calculate the between group sum of squares, the within group sum of squares, \nthe total sum of squares, the degrees of freedom and the F-statistic.  Keep two decimal places throughout your calculations.\nBecause of rounding, the total sum of squares may not be exactly equal to the sum of the between group sum of squares and the within group sum of squares.\nTo check your answers, click on the 'Show Sum of Squares' and/or 'Show F-Statistic' buttons."]
[]
[]
[null,"GROUP 1",null,null,"GROUP 2",null,null,"GROUP 3",null,null,"Means"]
[null,"Case #","Value on \nVariable X",null,"Case #","Value on \nVariable X",null,"Case #","Value on \nVariable X",null,"Group 1 Mean (x-bargroup):",null,10.14]
[null,null,null,null,null,null,null,null,null,null,"Group 2 Mean (x-bargroup):",null,15.78]
[null,1,13,null,8,19,null,17,16,null,"Group 3 Mean (x-bargroup):",null,14.38]
[null,2,11,null,9,18,null,18,10,null,"Overall Mean (x-bartotal):",null,13.67]
[null,3,11,null,10,15,null,19,11]
[null,4,3,null,11,9,null,20,11,null,"Sum of Squares"]
[null,5,16,null,12,12,null,21,23,null,"Between group sum of squares:",null,"hidden"]
[null,6,15,null,13,20,null,22,7,null,"Within group sum of squares:",null,"hidden"]
[null,7,2,null,14,24,null,23,11,null,"Total sum of squares:",null,"hidden"]
[null,null,null,null,15,14,null,24,26]
[null,null,null,null,16,11,null,null,null,null,"F-statistic"]
[null,null,null,null,null,null,null,null,null,null,"Between group degrees of freedom:",null,"hidden"]
[null,null,null,null,null,null,null,null,null,null,"Within group degrees of freedom:",null,"hidden"]
[null,"Need some help?",null,null,null,null,null,null,null,null,"F-statistic:",null,"hidden"]
[]
[null,null,null,null,null,null,null,null,null,null,"If the F-statistic is higher than 3.44, then p<0.05."]
[]
[null,"BETWEEN GROUP SUM OF SQUARES CALCULATION"]
[null,"Group # ","Group Mean\n","Overall Mean\n",null,"Cases in Group\n",null,"Group Mean-Overall Mean\n",null,null,"(Group Mean-Overall Mean)2\n","Number of Cases in Group x \n(Group Mean-Overall Mean)2\n"]
[null,1,10.14,13.67,null,7,null,"10.14 - 13.67 = ?",null,null,"-3.53 x -3.53 = ?","7 x 12.46 = ?"]
[null,2,15.78,13.67,null,9,null,"15.78 - 13.67 = ?",null,null,"2.11 x 2.11 = ?","9 x 4.45 = ?"]
[null,3,14.38,13.67,null,8,null,"14.38 - 13.67 = ?",null,null,"0.71 x 0.71 = ?","8 x 0.5 = ?"]
[null,null,null,null,null,null,null,null,null,null,null,"Column Sum (Σ)","= ?"]
[]
[null,"WITHIN GROUP SUM OF SQUARES CALCULATION"]
[null,"Case #","Value\n","Group Mean\n",null,"Value-Group Mean\n",null,"(Value - Group Mean)2\n"]
[null,1,13,10.14,null,"13 - 10.14 = ?",null,"2.86 x 2.86 = ?"]
[null,2,11,10.14,null,"11 - 10.14 = ?",null,"0.86 x 0.86 = ?"]
[null,3,11,10.14,null,"11 - 10.14 = ?",null,"0.86 x 0.86 = ?"]
[null,4,3,10.14,null,"3 - 10.14 = ?",null,"-7.14 x -7.14 = ?"]
[null,5,16,10.14,null,"16 - 10.14 = ?",null,"5.86 x 5.86 = ?"]
[null,6,15,10.14,null,"15 - 10.14 = ?",null,"4.86 x 4.86 = ?"]
[null,7,2,10.14,null,"2 - 10.14 = ?",null,"-8.14 x -8.14 = ?"]
[null,8,19,15.78,null,"19 - 15.78 = ?",null,"3.22 x 3.22 = ?"]
[null,9,18,15.78,null,"18 - 15.78 = ?",null,"2.22 x 2.22 = ?"]
[null,10,15,15.78,null,"15 - 15.78 = ?",null,"-0.78 x -0.78 = ?"]
[null,11,9,15.78,null,"9 - 15.78 = ?",null,"-6.78 x -6.78 = ?"]
[null,12,12,15.78,null,"12 - 15.78 = ?",null,"-3.78 x -3.78 = ?"]
[null,13,20,15.78,null,"20 - 15.78 = ?",null,"4.22 x 4.22 = ?"]
[null,14,24,15.78,null,"24 - 15.78 = ?",null,"8.22 x 8.22 = ?"]
[null,15,14,15.78,null,"14 - 15.78 = ?",null,"-1.78 x -1.78 = ?"]
[null,16,11,15.78,null,"11 - 15.78 = ?",null,"-4.78 x -4.78 = ?"]
[null,17,16,14.38,null,"16 - 14.38 = ?",null,"1.62 x 1.62 = ?"]
[null,18,10,14.38,null,"10 - 14.38 = ?",null,"-4.38 x -4.38 = ?"]
[null,19,11,14.38,null,"11 - 14.38 = ?",null,"-3.38 x -3.38 = ?"]
[null,20,11,14.38,null,"11 - 14.38 = ?",null,"-3.38 x -3.38 = ?"]
[null,21,23,14.38,null,"23 - 14.38 = ?",null,"8.62 x 8.62 = ?"]
[null,22,7,14.38,null,"7 - 14.38 = ?",null,"-7.38 x -7.38 = ?"]
[null,23,11,14.38,null,"11 - 14.38 = ?",null,"-3.38 x -3.38 = ?"]
[null,24,26,14.38,null,"26 - 14.38 = ?",null,"11.62 x 11.62 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",null,"= ?"]
[]
[null,"TOTAL SUM OF SQUARES CALCULATION"]
[null,"Case #","Value\n","Overall Mean\n",null,"Value-Overall Mean\n",null,"(Value - Overall Mean)2\n"]
[null,1,13,13.67,null,"13 - 13.67 = ?",null,"-0.67 x -0.67 = ?"]
[null,2,11,13.67,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,3,11,13.67,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,4,3,13.67,null,"3 - 13.67 = ?",null,"-10.67 x -10.67 = ?"]
[null,5,16,13.67,null,"16 - 13.67 = ?",null,"2.33 x 2.33 = ?"]
[null,6,15,13.67,null,"15 - 13.67 = ?",null,"1.33 x 1.33 = ?"]
[null,7,2,13.67,null,"2 - 13.67 = ?",null,"-11.67 x -11.67 = ?"]
[null,8,19,13.67,null,"19 - 13.67 = ?",null,"5.33 x 5.33 = ?"]
[null,9,18,13.67,null,"18 - 13.67 = ?",null,"4.33 x 4.33 = ?"]
[null,10,15,13.67,null,"15 - 13.67 = ?",null,"1.33 x 1.33 = ?"]
[null,11,9,13.67,null,"9 - 13.67 = ?",null,"-4.67 x -4.67 = ?"]
[null,12,12,13.67,null,"12 - 13.67 = ?",null,"-1.67 x -1.67 = ?"]
[null,13,20,13.67,null,"20 - 13.67 = ?",null,"6.33 x 6.33 = ?"]
[null,14,24,13.67,null,"24 - 13.67 = ?",null,"10.33 x 10.33 = ?"]
[null,15,14,13.67,null,"14 - 13.67 = ?",null,"0.33 x 0.33 = ?"]
[null,16,11,13.67,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,17,16,13.67,null,"16 - 13.67 = ?",null,"2.33 x 2.33 = ?"]
[null,18,10,13.67,null,"10 - 13.67 = ?",null,"-3.67 x -3.67 = ?"]
[null,19,11,13.67,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,20,11,13.67,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,21,23,13.67,null,"23 - 13.67 = ?",null,"9.33 x 9.33 = ?"]
[null,22,7,13.67,null,"7 - 13.67 = ?",null,"-6.67 x -6.67 = ?"]
[null,23,11,13.67,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,24,26,13.67,null,"26 - 13.67 = ?",null,"12.33 x 12.33 = ?"]
[null,null,null,null,null,"Column Sum (Σ)",null,"= ?"]
[]
[null,"F-STATISTIC CALCULATION"]
[null,"Between group degrees of freedom"]
[null,null,null,null,null,"= 3 - 1"]
[null,null,null,null,null,"= ?"]
[null,"Within group degrees of freedom"]
[null,null,null,null,null,"= (7 - 1) + (9 - 1) + (8 - 1)"]
[null,null,null,null,null,"= ? + ? + ?"]
[null,null,null,null,null,"= ?"]
[null,"F-Statistic Numerator"]
[null,null,null,null,null,"= 131.27 ÷ 2"]
[null,null,null,null,null,"= ?"]
[null,"F-Statistic Denominator"]
[null,null,null,null,null,"= 692.27 ÷ 21"]
[null,null,null,null,null,"= ?"]
[null,"F-Statistic"]
[null,null,null,null,null,"= 65.64 ÷ 32.97"]
[null,null,null,null,null,"= ?"]

{"sheet":"ANOVA (2 groups)-A","index":3,"n_rows":93,"n_cols":22,"rows_kept":93,"cut":false,"hidden":true,"merged":[[73,3,73,4],[73,5,73,6],[74,5,74,6],[23,11,23,12],[70,3,70,4],[70,5,70,6],[71,3,71,4],[71,5,71,6],[72,3,72,4],[72,5,72,6],[67,3,67,4],[67,5,67,6],[68,3,68,4],[68,5,68,6],[69,3,69,4],[69,5,69,6],[64,3,64,4],[64,5,64,6],[65,3,65,4],[65,5,65,6],[66,3,66,4],[66,5,66,6],[61,3,61,4],[61,5,61,6],[62,3,62,4],[62,5,62,6],[63,3,63,4],[63,5,63,6],[58,3,58,4],[58,5,58,6],[59,3,59,4],[59,5,59,6],[60,3,60,4],[60,5,60,6],[55,3,55,4],[55,5,55,6],[56,3,56,4],[56,5,56,6],[57,3,57,4],[57,5,57,6],[49,3,49,4],[49,5,49,6],[50,5,50,6],[53,3,53,4],[53,5,53,6],[54,3,54,4],[54,5,54,6],[46,3,46,4],[46,5,46,6],[47,3,47,4],[47,5,47,6],[48,3,48,4],[48,5,48,6],[43,3,43,4],[43,5,43,6],[44,3,44,4],[44,5,44,6],[45,3,45,4],[45,5,45,6],[40,3,40,4],[40,5,40,6],[41,3,41,4],[41,5,41,6],[42,3,42,4],[42,5,42,6],[37,3,37,4],[37,5,37,6],[38,3,38,4],[38,5,38,6],[39,3,39,4],[39,5,39,6],[34,3,34,4],[34,5,34,6],[35,3,35,4],[35,5,35,6],[36,3,36,4],[36,5,36,6],[31,3,31,4],[31,5,31,6],[32,3,32,4],[32,5,32,6],[33,3,33,4],[33,5,33,6],[29,3,29,4],[29,5,29,6],[30,3,30,4],[30,5,30,6],[15,7,15,9],[20,7,20,9],[23,3,23,4],[23,5,23,6],[24,3,24,4],[24,5,24,6],[25,8,25,10],[0,1,0,13],[2,1,2,13],[5,1,5,2],[5,4,5,5],[5,7,5,9],[10,7,10,9],[23,8,23,10],[24,8,24,10],[25,3,25,4],[25,5,25,6],[24,11,24,12],[25,11,25,12],[30,11,30,12],[30,13,30,14],[30,17,30,18],[31,17,31,18],[32,17,32,18],[33,17,33,18],[34,17,34,18],[35,17,35,18],[36,17,36,18],[37,17,37,18],[38,17,38,18],[39,17,39,18],[40,17,40,18],[41,17,41,18],[42,17,42,18],[43,17,43,18],[44,17,44,18],[45,17,45,18],[46,17,46,18],[47,17,47,18],[48,17,48,18],[49,17,49,18],[54,17,54,18],[55,17,55,18],[56,17,56,18],[57,17,57,18],[58,17,58,18],[68,17,68,18],[69,17,69,18],[70,17,70,18],[71,17,71,18],[72,17,72,18],[73,17,73,18],[59,17,59,18],[60,17,60,18],[61,17,61,18],[62,17,62,18],[63,17,63,18],[64,17,64,18],[65,17,65,18],[66,17,66,18],[67,17,67,18]]}
[null,"PRACTICE CALCULATING ANOVA (2 GROUPS)"]
[]
[]
[]
[]
[null,"GROUP 1",null,null,"GROUP 2",null,null,"Means"]
[null,"Case #","Value",null,"Case #","Value",null,"Group 1 Mean",null,{"$f":"ROUND(AVERAGE(C8:C17),2)","v":26.9}]
[{"$f":"RANDBETWEEN(10,40)","v":11},1,32,{"$f":"RANDBETWEEN(1,30)","v":15},11,24,null,"Group 2 Mean",null,{"$f":"ROUND(AVERAGE(F8:F17),2)","v":18.899999999999999}]
[{"$f":"RANDBETWEEN(10,40)","v":32},2,38,{"$f":"RANDBETWEEN(1,30)","v":3},12,25,null,"Overall Mean",null,{"$f":"ROUND(AVERAGE(C8:C17,F8:F17),2)","v":22.9}]
[39,3,17,2,13,26]
[13,4,24,4,14,21,null,"Sum of Squares"]
[30,5,10,8,15,19,null,"Between group sum of squares",null,{"$f":"P27","v":320}]
[10,6,24,6,16,5,null,"Within group sum of squares",null,{"$f":"J51","v":1255.8}]
[18,7,29,15,17,23,null,"Total sum of squares",null,{"$f":"J75","v":1575.8}]
[23,8,40,18,18,16]
[27,9,20,26,19,10,null,"F-statistic"]
[28,10,35,4,20,20,null,"Between group degrees of freedom",null,{"$f":"1","v":1}]
[null,null,null,null,null,null,null,"Within group degrees of freedom",null,{"$f":"18","v":18}]
[null,"Need some help?",null,null,null,null,null,"F-statistic",null,{"$f":"H92","v":4.59}]
[]
[null,null,null,null,null,null,null,"If the F-statistic is greater than 4.41 then p<0.05."]
[]
[null,"BETWEEN GROUP SUM OF SQUARES CALCULATION"]
[null,"Group # ","Group Mean","Overall Mean",null,"Cases in Group",null,"Group Mean-Overall Mean","(Group Mean-Overall Mean)2",null,null,"Number of Cases*(Group Mean-Overall Mean)2"]
[null,1,{"$f":"J7","v":26.9},{"$f":"J9","v":22.9},null,10,null,{"$f":"CONCATENATE(C25,\" - \",D25,\" = \",N25)","v":"26.9 - 22.9 = 4"},{"$f":"CONCATENATE(N25,\" x \",N25,\" = \",O25)","v":"4 x 4 = 16"},null,null,{"$f":"CONCATENATE(F25,\" x \",O25,\" = \",P25)","v":"10 x 16 = 160"},null,{"$f":"ROUND(J7-J9,2)","v":4},{"$f":"ROUND(N25*N25,2)","v":16},{"$f":"ROUND(O25*F25,2)","v":160},null,{"$f":"CONCATENATE(C25,\" - \",D25,\" = ?\")","v":"26.9 - 22.9 = ?"},{"$f":"CONCATENATE(N25,\" x \",N25,\" = ?\")","v":"4 x 4 = ?"},null,null,{"$f":"CONCATENATE(F25,\" x \",O25,\" = ?\")","v":"10 x 16 = ?"}]
[null,2,{"$f":"J8","v":18.899999999999999},{"$f":"J9","v":22.9},null,10,null,{"$f":"CONCATENATE(C26,\" - \",D26,\" = \",N26)","v":"18.9 - 22.9 = -4"},{"$f":"CONCATENATE(N26,\" x \",N26,\" = \",O26)","v":"-4 x -4 = 16"},null,null,{"$f":"CONCATENATE(F26,\" x \",O26,\" = \",P26)","v":"10 x 16 = 160"},null,{"$f":"ROUND(J8-J9,2)","v":-4},{"$f":"ROUND(N26*N26,2)","v":16},{"$f":"ROUND(O26*F26,2)","v":160},null,{"$f":"CONCATENATE(C26,\" - \",D26,\" = ?\")","v":"18.9 - 22.9 = ?"},{"$f":"CONCATENATE(N26,\" x \",N26,\" = ?\")","v":"-4 x -4 = ?"},null,null,{"$f":"CONCATENATE(F26,\" x \",O26,\" = ?\")","v":"10 x 16 = ?"}]
[null,null,null,null,null,null,null,null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",P27)","v":"'= 320"},null,null,{"$f":"ROUND(SUM(P25:P26),2)","v":320}]
[]
[null,"WITHIN GROUP SUM OF SQUARES CALCULATION"]
[null,"Case #","Value","Group Mean",null,"Value-Group Mean",null,"(Value - Group Mean)2"]
[null,1,{"$f":"C8","v":32},{"$f":"$J$7","v":26.9},null,{"$f":"CONCATENATE(C31,\" - \",D31,\" = \",I31)","v":"32 - 26.9 = 5.1"},null,{"$f":"CONCATENATE(I31,\" x \",I31,\" = \",J31)","v":"5.1 x 5.1 = 26.01"},{"$f":"ROUND(C31-D31,2)","v":5.0999999999999996},{"$f":"ROUND(I31*I31,2)","v":26.01},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C31,\" - \",D31,\" = ?\")","v":"32 - 26.9 = ?"},null,{"$f":"CONCATENATE(I31,\" x \",I31,\" = ?\")","v":"5.1 x 5.1 = ?"}]
[null,2,38,{"$f":"$J$7","v":26.9},null,{"$f":"CONCATENATE(C32,\" - \",D32,\" = \",I32)","v":"38 - 26.9 = 11.1"},null,{"$f":"CONCATENATE(I32,\" x \",I32,\" = \",J32)","v":"11.1 x 11.1 = 123.21"},{"$f":"ROUND(C32-D32,2)","v":11.1},{"$f":"ROUND(I32*I32,2)","v":123.21},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C32,\" - \",D32,\" = ?\")","v":"38 - 26.9 = ?"},null,{"$f":"CONCATENATE(I32,\" x \",I32,\" = ?\")","v":"11.1 x 11.1 = ?"}]
[null,3,17,26.9,null,"17 - 26.9 = -9.9",null,"-9.9 x -9.9 = 98.01",-9.9,98.01,null,null,null,null,null,null,null,"17 - 26.9 = ?",null,"-9.9 x -9.9 = ?"]
[null,4,24,26.9,null,"24 - 26.9 = -2.9",null,"-2.9 x -2.9 = 8.41",-2.9,8.41,null,null,null,null,null,null,null,"24 - 26.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,5,10,26.9,null,"10 - 26.9 = -16.9",null,"-16.9 x -16.9 = 285.61",-16.899999999999999,285.61,null,null,null,null,null,null,null,"10 - 26.9 = ?",null,"-16.9 x -16.9 = ?"]
[null,6,24,26.9,null,"24 - 26.9 = -2.9",null,"-2.9 x -2.9 = 8.41",-2.9,8.41,null,null,null,null,null,null,null,"24 - 26.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,7,29,26.9,null,"29 - 26.9 = 2.1",null,"2.1 x 2.1 = 4.41",2.1,4.41,null,null,null,null,null,null,null,"29 - 26.9 = ?",null,"2.1 x 2.1 = ?"]
[null,8,40,26.9,null,"40 - 26.9 = 13.1",null,"13.1 x 13.1 = 171.61",13.1,171.61,null,null,null,null,null,null,null,"40 - 26.9 = ?",null,"13.1 x 13.1 = ?"]
[null,9,20,26.9,null,"20 - 26.9 = -6.9",null,"-6.9 x -6.9 = 47.61",-6.9,47.61,null,null,null,null,null,null,null,"20 - 26.9 = ?",null,"-6.9 x -6.9 = ?"]
[null,10,35,26.9,null,"35 - 26.9 = 8.1",null,"8.1 x 8.1 = 65.61",8.1,65.61,null,null,null,null,null,null,null,"35 - 26.9 = ?",null,"8.1 x 8.1 = ?"]
[null,11,{"$f":"F8","v":24},{"$f":"$J$8","v":18.899999999999999},null,"24 - 18.9 = 5.1",null,"5.1 x 5.1 = 26.01",5.0999999999999996,26.01,null,null,null,null,null,null,null,"24 - 18.9 = ?",null,"5.1 x 5.1 = ?"]
[null,12,25,{"$f":"$J$8","v":18.899999999999999},null,{"$f":"CONCATENATE(C42,\" - \",D42,\" = \",I42)","v":"25 - 18.9 = 6.1"},null,"6.1 x 6.1 = 37.21",6.1,37.21,null,null,null,null,null,null,null,"25 - 18.9 = ?",null,"6.1 x 6.1 = ?"]
[null,13,26,18.899999999999999,null,{"$f":"CONCATENATE(C43,\" - \",D43,\" = \",I43)","v":"26 - 18.9 = 7.1"},null,"7.1 x 7.1 = 50.41",7.1,50.41,null,null,null,null,null,null,null,"26 - 18.9 = ?",null,"7.1 x 7.1 = ?"]
[null,14,21,18.899999999999999,null,"21 - 18.9 = 2.1",null,{"$f":"CONCATENATE(I44,\" x \",I44,\" = \",J44)","v":"2.1 x 2.1 = 4.41"},2.1,4.41,null,null,null,null,null,null,null,"21 - 18.9 = ?",null,"2.1 x 2.1 = ?"]
[null,15,19,18.899999999999999,null,"19 - 18.9 = 0.1",null,"0.1 x 0.1 = 0.01",0.1,0.01,null,null,null,null,null,null,null,"19 - 18.9 = ?",null,"0.1 x 0.1 = ?"]
[null,16,5,18.899999999999999,null,"5 - 18.9 = -13.9",null,"-13.9 x -13.9 = 193.21",-13.9,193.21,null,null,null,null,null,null,null,"5 - 18.9 = ?",null,"-13.9 x -13.9 = ?"]
[null,17,23,18.899999999999999,null,"23 - 18.9 = 4.1",null,"4.1 x 4.1 = 16.81",4.0999999999999996,16.809999999999999,null,null,null,null,null,null,null,"23 - 18.9 = ?",null,"4.1 x 4.1 = ?"]
[null,18,16,18.899999999999999,null,"16 - 18.9 = -2.9",null,"-2.9 x -2.9 = 8.41",-2.9,8.41,null,null,null,null,null,null,null,"16 - 18.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,19,10,18.899999999999999,null,"10 - 18.9 = -8.9",null,"-8.9 x -8.9 = 79.21",-8.9,79.209999999999994,null,null,null,null,null,null,null,"10 - 18.9 = ?",null,"-8.9 x -8.9 = ?"]
[null,20,20,18.899999999999999,null,"20 - 18.9 = 1.1",null,"1.1 x 1.1 = 1.21",1.1000000000000001,1.21,null,null,null,null,null,null,null,"20 - 18.9 = ?",null,"1.1 x 1.1 = ?"]
[null,null,null,null,null,"Column Sum:",null,{"$f":"CONCATENATE(\"'= \",J51)","v":"'= 1255.8"},null,{"$f":"SUM(J31:J50)","v":1255.8}]
[]
[null,"TOTAL SUM OF SQUARES CALCULATION"]
[null,"Case #","Value","Overall Mean",null,"Value-Group Mean",null,"(Value - Group Mean)2"]
[null,1,{"$f":"C31","v":32},{"$f":"$J$9","v":22.9},null,{"$f":"CONCATENATE(C55,\" - \",D55,\" = \",I55)","v":"32 - 22.9 = 9.1"},null,{"$f":"CONCATENATE(I55,\" x \",I55,\" = \",J55)","v":"9.1 x 9.1 = 82.81"},{"$f":"ROUND(C55-D55,2)","v":9.1},{"$f":"ROUND(I55*I55,2)","v":82.81},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C55,\" - \",D55,\" = ?\")","v":"32 - 22.9 = ?"},null,{"$f":"CONCATENATE(I55,\" x \",I55,\" = ?\")","v":"9.1 x 9.1 = ?"}]
[null,2,{"$f":"C32","v":38},{"$f":"$J$9","v":22.9},null,{"$f":"CONCATENATE(C56,\" - \",D56,\" = \",I56)","v":"38 - 22.9 = 15.1"},null,{"$f":"CONCATENATE(I56,\" x \",I56,\" = \",J56)","v":"15.1 x 15.1 = 228.01"},{"$f":"ROUND(C56-D56,2)","v":15.1},{"$f":"ROUND(I56*I56,2)","v":228.01},null,null,null,null,null,null,null,{"$f":"CONCATENATE(C56,\" - \",D56,\" = ?\")","v":"38 - 22.9 = ?"},null,{"$f":"CONCATENATE(I56,\" x \",I56,\" = ?\")","v":"15.1 x 15.1 = ?"}]
[null,3,17,22.9,null,"17 - 22.9 = -5.9",null,"-5.9 x -5.9 = 34.81",-5.9,34.81,null,null,null,null,null,null,null,"17 - 22.9 = ?",null,"-5.9 x -5.9 = ?"]
[null,4,24,22.9,null,"24 - 22.9 = 1.1",null,"1.1 x 1.1 = 1.21",1.1000000000000001,1.21,null,null,null,null,null,null,null,"24 - 22.9 = ?",null,"1.1 x 1.1 = ?"]
[null,5,10,22.9,null,"10 - 22.9 = -12.9",null,"-12.9 x -12.9 = 166.41",-12.9,166.41,null,null,null,null,null,null,null,"10 - 22.9 = ?",null,"-12.9 x -12.9 = ?"]
[null,6,24,22.9,null,"24 - 22.9 = 1.1",null,"1.1 x 1.1 = 1.21",1.1000000000000001,1.21,null,null,null,null,null,null,null,"24 - 22.9 = ?",null,"1.1 x 1.1 = ?"]
[null,7,29,22.9,null,"29 - 22.9 = 6.1",null,"6.1 x 6.1 = 37.21",6.1,37.21,null,null,null,null,null,null,null,"29 - 22.9 = ?",null,"6.1 x 6.1 = ?"]
[null,8,40,22.9,null,"40 - 22.9 = 17.1",null,"17.1 x 17.1 = 292.41",17.100000000000001,292.41000000000003,null,null,null,null,null,null,null,"40 - 22.9 = ?",null,"17.1 x 17.1 = ?"]
[null,9,20,22.9,null,"20 - 22.9 = -2.9",null,"-2.9 x -2.9 = 8.41",-2.9,8.41,null,null,null,null,null,null,null,"20 - 22.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,10,35,22.9,null,"35 - 22.9 = 12.1",null,"12.1 x 12.1 = 146.41",12.1,146.41,null,null,null,null,null,null,null,"35 - 22.9 = ?",null,"12.1 x 12.1 = ?"]
[null,11,24,22.9,null,"24 - 22.9 = 1.1",null,"1.1 x 1.1 = 1.21",1.1000000000000001,1.21,null,null,null,null,null,null,null,"24 - 22.9 = ?",null,"1.1 x 1.1 = ?"]
[null,12,25,22.9,null,"25 - 22.9 = 2.1",null,"2.1 x 2.1 = 4.41",2.1,4.41,null,null,null,null,null,null,null,"25 - 22.9 = ?",null,"2.1 x 2.1 = ?"]
[null,13,26,22.9,null,"26 - 22.9 = 3.1",null,"3.1 x 3.1 = 9.61",3.1,9.61,null,null,null,null,null,null,null,"26 - 22.9 = ?",null,"3.1 x 3.1 = ?"]
[null,14,21,22.9,null,"21 - 22.9 = -1.9",null,"-1.9 x -1.9 = 3.61",-1.9,3.61,null,null,null,null,null,null,null,"21 - 22.9 = ?",null,"-1.9 x -1.9 = ?"]
[null,15,19,22.9,null,"19 - 22.9 = -3.9",null,"-3.9 x -3.9 = 15.21",-3.9,15.21,null,null,null,null,null,null,null,"19 - 22.9 = ?",null,"-3.9 x -3.9 = ?"]
[null,16,5,22.9,null,"5 - 22.9 = -17.9",null,"-17.9 x -17.9 = 320.41",-17.899999999999999,320.41000000000003,null,null,null,null,null,null,null,"5 - 22.9 = ?",null,"-17.9 x -17.9 = ?"]
[null,17,23,22.9,null,"23 - 22.9 = 0.1",null,"0.1 x 0.1 = 0.01",0.1,0.01,null,null,null,null,null,null,null,"23 - 22.9 = ?",null,"0.1 x 0.1 = ?"]
[null,18,16,22.9,null,"16 - 22.9 = -6.9",null,"-6.9 x -6.9 = 47.61",-6.9,47.61,null,null,null,null,null,null,null,"16 - 22.9 = ?",null,"-6.9 x -6.9 = ?"]
[null,19,10,22.9,null,"10 - 22.9 = -12.9",null,"-12.9 x -12.9 = 166.41",-12.9,166.41,null,null,null,null,null,null,null,"10 - 22.9 = ?",null,"-12.9 x -12.9 = ?"]
[null,20,20,22.9,null,"20 - 22.9 = -2.9",null,"-2.9 x -2.9 = 8.41",-2.9,8.41,null,null,null,null,null,null,null,"20 - 22.9 = ?",null,"-2.9 x -2.9 = ?"]
[null,null,null,null,null,"Column Sum:",null,{"$f":"CONCATENATE(\"'= \",J75)","v":"'= 1575.8"},null,{"$f":"ROUND(SUM(J55:J74),2)","v":1575.8}]
[]
[null,"F-RATIO CALCULATION"]
[null,"Between group degrees of freedom"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 2 - 1\")","v":"'= 2 - 1"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 1\")","v":"'= 1"}]
[null,"Within group degrees of freedom"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= (10 - 1) + (10 - 1)\")","v":"'= (10 - 1) + (10 - 1)"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 9 + 9\")","v":"'= 9 + 9"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 18\")","v":"'= 18"}]
[null,"F-Statistic Numerator"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",P27,\" ÷ 1\")","v":"'= 320 ÷ 1"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",P27)","v":"'= 320"}]
[null,"F-Statistic Denominator"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",J51,\" ÷ 18\")","v":"'= 1255.8 ÷ 18"},null,{"$f":"ROUND(J51/18,2)","v":69.77}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",H89)","v":"'= 69.77"}]
[null,"F-Statistic"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",P27,\" ÷ \",H89)","v":"'= 320 ÷ 69.77"},null,{"$f":"ROUND(P27/H89,2)","v":4.59}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",H92)","v":"'= 4.59"}]

{"sheet":"ANOVA (3 groups)-A","index":4,"n_rows":103,"n_cols":22,"rows_kept":103,"cut":false,"hidden":true,"merged":[[0,1,0,14],[2,1,2,14],[5,1,5,2],[5,4,5,5],[5,7,5,8],[5,10,5,12],[21,10,21,12],[24,3,24,4],[24,5,24,6],[24,7,24,9],[24,11,24,13],[25,3,25,4],[25,5,25,6],[25,7,25,9],[25,11,25,13],[28,12,28,13],[31,3,31,4],[31,5,31,6],[31,7,31,8],[32,3,32,4],[32,5,32,6],[32,7,32,8],[26,3,26,4],[26,5,26,6],[26,7,26,9],[26,11,26,13],[27,3,27,4],[27,5,27,6],[27,7,27,9],[27,11,27,13],[35,3,35,4],[35,5,35,6],[35,7,35,8],[36,3,36,4],[36,5,36,6],[36,7,36,8],[33,3,33,4],[33,5,33,6],[33,7,33,8],[34,3,34,4],[34,5,34,6],[34,7,34,8],[39,3,39,4],[39,5,39,6],[39,7,39,8],[40,3,40,4],[40,5,40,6],[40,7,40,8],[37,3,37,4],[37,5,37,6],[37,7,37,8],[38,3,38,4],[38,5,38,6],[38,7,38,8],[43,3,43,4],[43,5,43,6],[43,7,43,8],[44,3,44,4],[44,5,44,6],[44,7,44,8],[41,3,41,4],[41,5,41,6],[41,7,41,8],[42,3,42,4],[42,5,42,6],[42,7,42,8],[47,3,47,4],[47,5,47,6],[47,7,47,8],[48,3,48,4],[48,5,48,6],[48,7,48,8],[45,3,45,4],[45,5,45,6],[45,7,45,8],[46,3,46,4],[46,5,46,6],[46,7,46,8],[51,3,51,4],[51,5,51,6],[51,7,51,8],[52,3,52,4],[52,5,52,6],[52,7,52,8],[49,3,49,4],[49,5,49,6],[49,7,49,8],[50,3,50,4],[50,5,50,6],[50,7,50,8],[55,3,55,4],[55,5,55,6],[55,7,55,8],[56,5,56,6],[56,7,56,8],[59,3,59,4],[59,5,59,6],[59,7,59,8],[53,3,53,4],[53,5,53,6],[53,7,53,8],[54,3,54,4],[54,5,54,6],[54,7,54,8],[62,3,62,4],[62,5,62,6],[62,7,62,8],[63,3,63,4],[63,5,63,6],[63,7,63,8],[60,3,60,4],[60,5,60,6],[60,7,60,8],[61,3,61,4],[61,5,61,6],[61,7,61,8],[66,3,66,4],[66,5,66,6],[66,7,66,8],[67,3,67,4],[67,5,67,6],[67,7,67,8],[64,3,64,4],[64,5,64,6],[64,7,64,8],[65,3,65,4],[65,5,65,6],[65,7,65,8],[70,3,70,4],[70,5,70,6],[70,7,70,8],[71,3,71,4],[71,5,71,6],[71,7,71,8],[68,3,68,4],[68,5,68,6],[68,7,68,8],[69,3,69,4],[69,5,69,6],[69,7,69,8],[74,3,74,4],[74,5,74,6],[74,7,74,8],[75,3,75,4],[75,5,75,6],[75,7,75,8],[72,3,72,4],[72,5,72,6],[72,7,72,8],[73,3,73,4],[73,5,73,6],[73,7,73,8],[78,3,78,4],[78,5,78,6],[78,7,78,8],[79,3,79,4],[79,5,79,6],[79,7,79,8],[76,3,76,4],[76,5,76,6],[76,7,76,8],[77,3,77,4],[77,5,77,6],[77,7,77,8],[84,5,84,6],[84,7,84,8],[82,3,82,4],[82,5,82,6],[82,7,82,8],[83,3,83,4],[83,5,83,6],[83,7,83,8],[80,3,80,4],[80,5,80,6],[80,7,80,8],[81,3,81,4],[81,5,81,6],[81,7,81,8],[25,17,25,19],[25,21,25,23],[26,17,26,19],[26,21,26,23],[27,17,27,19],[27,21,27,23],[32,17,32,18],[32,19,32,20],[33,17,33,18],[33,19,33,20],[34,17,34,18],[34,19,34,20],[35,17,35,18],[35,19,35,20],[36,17,36,18],[36,19,36,20],[37,17,37,18],[37,19,37,20],[38,17,38,18],[38,19,38,20],[39,17,39,18],[39,19,39,20],[40,17,40,18],[40,19,40,20],[41,17,41,18],[41,19,41,20],[42,17,42,18],[42,19,42,20],[43,17,43,18],[43,19,43,20],[44,17,44,18],[44,19,44,20],[45,17,45,18],[45,19,45,20],[46,17,46,18],[46,19,46,20],[47,17,47,18],[47,19,47,20],[48,17,48,18],[48,19,48,20],[49,17,49,18],[49,19,49,20],[50,17,50,18],[50,19,50,20],[51,17,51,18],[51,19,51,20],[52,17,52,18],[52,19,52,20],[53,17,53,18],[53,19,53,20],[54,17,54,18],[54,19,54,20],[55,17,55,18],[55,19,55,20],[56,17,56,18],[56,19,56,20],[60,17,60,18],[60,19,60,20],[61,17,61,18],[61,19,61,20],[62,17,62,18],[62,19,62,20],[63,17,63,18],[63,19,63,20],[64,17,64,18],[64,19,64,20],[65,17,65,18],[65,19,65,20],[66,17,66,18],[66,19,66,20],[67,17,67,18],[67,19,67,20],[68,17,68,18],[68,19,68,20],[69,17,69,18],[69,19,69,20],[70,17,70,18],[70,19,70,20],[71,17,71,18],[71,19,71,20],[72,17,72,18],[72,19,72,20],[73,17,73,18],[73,19,73,20],[74,17,74,18],[74,19,74,20],[75,17,75,18],[75,19,75,20],[76,17,76,18],[76,19,76,20],[82,17,82,18],[82,19,82,20],[83,17,83,18],[83,19,83,20],[84,17,84,18],[84,19,84,20],[77,17,77,18],[77,19,77,20],[78,17,78,18],[78,19,78,20],[79,17,79,18],[79,19,79,20],[80,17,80,18],[80,19,80,20],[81,17,81,18],[81,19,81,20]]}
[null,"PRACTICE CALCULATING ANOVA (3 GROUPS)"]
[]
[]
[]
[]
[null,"GROUP 1",null,null,"GROUP 2",null,null,"GROUP 3",null,null,"Means"]
[null,"Case #","Value",null,"Case #","Value",null,"Case #","Value",null,"Group 1 Mean",null,{"$f":"ROUND(AVERAGE(C8:C14),2)","v":10.14}]
[{"$f":"RANDBETWEEN(1,20)","v":14},1,13,{"$f":"RANDBETWEEN(4,24)","v":24},8,19,{"$f":"RANDBETWEEN(6,26)","v":24},17,16,null,"Group 2 Mean",null,{"$f":"ROUND(AVERAGE(F8:F16),2)","v":15.78}]
[{"$f":"RANDBETWEEN(1,20)","v":7},2,11,{"$f":"RANDBETWEEN(4,24)","v":7},9,18,{"$f":"RANDBETWEEN(6,26)","v":21},18,10,null,"Group 3 Mean",null,{"$f":"ROUND(AVERAGE(I8:I15),2)","v":14.38}]
[15,3,11,8,10,15,24,19,11,null,"Overall Mean",null,{"$f":"ROUND(AVERAGE(C8:C14,F8:F16,I8:I15),2)","v":13.67}]
[10,4,3,5,11,9,10,20,11]
[1,5,16,8,12,12,12,21,23,null,"Sum of Squares"]
[5,6,15,19,13,20,14,22,7,null,"Between group sum of squares",null,{"$f":"Q29","v":131.26999999999998}]
[17,7,2,12,14,24,19,23,11,null,"Within group sum of squares",null,{"$f":"K57","v":692.27}]
[null,null,null,18,15,14,24,24,26,null,"Total sum of squares",null,{"$f":"K85","v":823.36}]
[null,null,null,13,16,11]
[null,null,null,null,null,null,null,null,null,null,"F-statistic"]
[null,null,null,null,null,null,null,null,null,null,"Between group degrees of freedom",null,2]
[null,"Need some help?",null,null,null,null,null,null,null,null,"Within group degrees of freedom",null,21]
[null,null,null,null,null,null,null,null,null,null,"F-statistic",null,{"$f":"I103","v":1.99}]
[]
[null,null,null,null,null,null,null,null,null,null,"If the F-statistic is greater than 3.44 then p<0.05."]
[]
[null,"BETWEEN GROUP SUM OF SQUARES CALCULATION"]
[null,"Group # ","Group Mean","Overall Mean",null,"Cases in Group",null,"Group Mean-Overall Mean",null,null,"(Group Mean-Overall Mean)2","Cases in Group*(Group Mean-Overall Mean)2"]
[null,1,{"$f":"M7","v":10.14},{"$f":"$M$10","v":13.67},null,7,null,{"$f":"CONCATENATE(C26,\" - \",D26,\" = \",O26)","v":"10.14 - 13.67 = -3.53"},null,null,{"$f":"CONCATENATE(O26,\" x \",O26,\" = \",P26)","v":"-3.53 x -3.53 = 12.46"},{"$f":"CONCATENATE(F26,\" x \",P26,\" = \",Q26)","v":"7 x 12.46 = 87.22"},null,null,{"$f":"ROUND(C26-D26,2)","v":-3.53},{"$f":"ROUND(O26*O26,2)","v":12.46},{"$f":"ROUND(P26*F26,2)","v":87.22},{"$f":"CONCATENATE(C26,\" - \",D26,\" = ?\")","v":"10.14 - 13.67 = ?"},null,null,{"$f":"CONCATENATE(O26,\" x \",O26,\" = ?\")","v":"-3.53 x -3.53 = ?"},{"$f":"CONCATENATE(F26,\" x \",P26,\" = ?\")","v":"7 x 12.46 = ?"}]
[null,2,{"$f":"M8","v":15.78},{"$f":"$M$10","v":13.67},null,9,null,{"$f":"CONCATENATE(C27,\" - \",D27,\" = \",O27)","v":"15.78 - 13.67 = 2.11"},null,null,{"$f":"CONCATENATE(O27,\" x \",O27,\" = \",P27)","v":"2.11 x 2.11 = 4.45"},{"$f":"CONCATENATE(F27,\" x \",P27,\" = \",Q27)","v":"9 x 4.45 = 40.05"},null,null,{"$f":"ROUND(C27-D27,2)","v":2.11},{"$f":"ROUND(O27*O27,2)","v":4.45},{"$f":"ROUND(P27*F27,2)","v":40.049999999999997},{"$f":"CONCATENATE(C27,\" - \",D27,\" = ?\")","v":"15.78 - 13.67 = ?"},null,null,{"$f":"CONCATENATE(O27,\" x \",O27,\" = ?\")","v":"2.11 x 2.11 = ?"},{"$f":"CONCATENATE(F27,\" x \",P27,\" = ?\")","v":"9 x 4.45 = ?"}]
[null,3,{"$f":"M9","v":14.38},13.67,null,8,null,"14.38 - 13.67 = 0.71",null,null,"0.71 x 0.71 = 0.5","8 x 0.5 = 4",null,null,{"$f":"ROUND(C28-D28,2)","v":0.71},0.5,4,"14.38 - 13.67 = ?",null,null,"0.71 x 0.71 = ?","8 x 0.5 = ?"]
[null,null,null,null,null,null,null,null,null,null,null,"Column Sum:",{"$f":"CONCATENATE(\"'= \",Q29)","v":"'= 131.27"},null,null,null,{"$f":"SUM(Q26:Q28)","v":131.26999999999998}]
[]
[null,"WITHIN GROUP SUM OF SQUARES CALCULATION"]
[null,"Case #","Value","Group Mean",null,"Value-Group Mean",null,"(Value - Group Mean)2"]
[null,1,{"$f":"C8","v":13},{"$f":"$M$7","v":10.14},null,{"$f":"CONCATENATE(C33,\" - \",D33,\" = \",J33)","v":"13 - 10.14 = 2.86"},null,{"$f":"CONCATENATE(J33,\" x \",J33,\" = \",K33)","v":"2.86 x 2.86 = 8.18"},null,{"$f":"ROUND(C33-D33,2)","v":2.86},{"$f":"ROUND(J33*J33,2)","v":8.18},null,null,null,null,null,null,{"$f":"CONCATENATE(C33,\" - \",D33,\" = ?\")","v":"13 - 10.14 = ?"},null,{"$f":"CONCATENATE(J33,\" x \",J33,\" = ?\")","v":"2.86 x 2.86 = ?"}]
[null,2,{"$f":"C9","v":11},{"$f":"$M$7","v":10.14},null,{"$f":"CONCATENATE(C34,\" - \",D34,\" = \",J34)","v":"11 - 10.14 = 0.86"},null,{"$f":"CONCATENATE(J34,\" x \",J34,\" = \",K34)","v":"0.86 x 0.86 = 0.74"},null,{"$f":"ROUND(C34-D34,2)","v":0.86},{"$f":"ROUND(J34*J34,2)","v":0.74},null,null,null,null,null,null,{"$f":"CONCATENATE(C34,\" - \",D34,\" = ?\")","v":"11 - 10.14 = ?"},null,{"$f":"CONCATENATE(J34,\" x \",J34,\" = ?\")","v":"0.86 x 0.86 = ?"}]
[null,3,11,10.14,null,"11 - 10.14 = 0.86",null,"0.86 x 0.86 = 0.74",null,0.86,0.74,null,null,null,null,null,null,"11 - 10.14 = ?",null,"0.86 x 0.86 = ?"]
[null,4,3,10.14,null,"3 - 10.14 = -7.14",null,"-7.14 x -7.14 = 50.98",null,-7.14,50.98,null,null,null,null,null,null,"3 - 10.14 = ?",null,"-7.14 x -7.14 = ?"]
[null,5,16,10.14,null,"16 - 10.14 = 5.86",null,"5.86 x 5.86 = 34.34",null,5.86,34.340000000000003,null,null,null,null,null,null,"16 - 10.14 = ?",null,"5.86 x 5.86 = ?"]
[null,6,15,10.14,null,"15 - 10.14 = 4.86",null,"4.86 x 4.86 = 23.62",null,4.8600000000000003,23.62,null,null,null,null,null,null,"15 - 10.14 = ?",null,"4.86 x 4.86 = ?"]
[null,7,{"$f":"C14","v":2},10.14,null,"2 - 10.14 = -8.14",null,"-8.14 x -8.14 = 66.26",null,-8.14,66.260000000000005,null,null,null,null,null,null,"2 - 10.14 = ?",null,"-8.14 x -8.14 = ?"]
[null,8,{"$f":"F8","v":19},{"$f":"$M$8","v":15.78},null,"19 - 15.78 = 3.22",null,"3.22 x 3.22 = 10.37",null,3.22,10.37,null,null,null,null,null,null,"19 - 15.78 = ?",null,"3.22 x 3.22 = ?"]
[null,9,{"$f":"F9","v":18},{"$f":"$M$8","v":15.78},null,"18 - 15.78 = 2.22",null,"2.22 x 2.22 = 4.93",null,2.2200000000000002,4.93,null,null,null,null,null,null,"18 - 15.78 = ?",null,"2.22 x 2.22 = ?"]
[null,10,15,15.78,null,"15 - 15.78 = -0.78",null,"-0.78 x -0.78 = 0.61",null,-0.78,0.61,null,null,null,null,null,null,"15 - 15.78 = ?",null,"-0.78 x -0.78 = ?"]
[null,11,9,15.78,null,"9 - 15.78 = -6.78",null,"-6.78 x -6.78 = 45.97",null,-6.78,45.97,null,null,null,null,null,null,"9 - 15.78 = ?",null,"-6.78 x -6.78 = ?"]
[null,12,12,15.78,null,"12 - 15.78 = -3.78",null,"-3.78 x -3.78 = 14.29",null,-3.78,14.29,null,null,null,null,null,null,"12 - 15.78 = ?",null,"-3.78 x -3.78 = ?"]
[null,13,20,15.78,null,"20 - 15.78 = 4.22",null,"4.22 x 4.22 = 17.81",null,4.22,17.809999999999999,null,null,null,null,null,null,"20 - 15.78 = ?",null,"4.22 x 4.22 = ?"]
[null,14,24,15.78,null,"24 - 15.78 = 8.22",null,"8.22 x 8.22 = 67.57",null,8.2200000000000006,67.569999999999993,null,null,null,null,null,null,"24 - 15.78 = ?",null,"8.22 x 8.22 = ?"]
[null,15,14,15.78,null,"14 - 15.78 = -1.78",null,"-1.78 x -1.78 = 3.17",null,-1.78,3.17,null,null,null,null,null,null,"14 - 15.78 = ?",null,"-1.78 x -1.78 = ?"]
[null,16,11,15.78,null,"11 - 15.78 = -4.78",null,"-4.78 x -4.78 = 22.85",null,-4.78,22.85,null,null,null,null,null,null,"11 - 15.78 = ?",null,"-4.78 x -4.78 = ?"]
[null,17,{"$f":"I8","v":16},{"$f":"$M$9","v":14.38},null,"16 - 14.38 = 1.62",null,"1.62 x 1.62 = 2.62",null,1.62,2.62,null,null,null,null,null,null,"16 - 14.38 = ?",null,"1.62 x 1.62 = ?"]
[null,18,{"$f":"I9","v":10},{"$f":"$M$9","v":14.38},null,"10 - 14.38 = -4.38",null,"-4.38 x -4.38 = 19.18",null,-4.38,19.18,null,null,null,null,null,null,"10 - 14.38 = ?",null,"-4.38 x -4.38 = ?"]
[null,19,11,14.38,null,"11 - 14.38 = -3.38",null,"-3.38 x -3.38 = 11.42",null,-3.38,11.42,null,null,null,null,null,null,"11 - 14.38 = ?",null,"-3.38 x -3.38 = ?"]
[null,20,11,14.38,null,"11 - 14.38 = -3.38",null,"-3.38 x -3.38 = 11.42",null,-3.38,11.42,null,null,null,null,null,null,"11 - 14.38 = ?",null,"-3.38 x -3.38 = ?"]
[null,21,23,14.38,null,"23 - 14.38 = 8.62",null,"8.62 x 8.62 = 74.3",null,8.6199999999999992,74.3,null,null,null,null,null,null,"23 - 14.38 = ?",null,"8.62 x 8.62 = ?"]
[null,22,7,14.38,null,"7 - 14.38 = -7.38",null,"-7.38 x -7.38 = 54.46",null,-7.38,54.46,null,null,null,null,null,null,"7 - 14.38 = ?",null,"-7.38 x -7.38 = ?"]
[null,23,11,14.38,null,"11 - 14.38 = -3.38",null,"-3.38 x -3.38 = 11.42",null,-3.38,11.42,null,null,null,null,null,null,"11 - 14.38 = ?",null,"-3.38 x -3.38 = ?"]
[null,24,26,14.38,null,"26 - 14.38 = 11.62",null,"11.62 x 11.62 = 135.02",null,11.62,135.02000000000001,null,null,null,null,null,null,"26 - 14.38 = ?",null,"11.62 x 11.62 = ?"]
[null,null,null,null,null,"Column Sum:",null,{"$f":"CONCATENATE(\"'= \",K57)","v":"'= 692.27"},null,null,{"$f":"ROUND(SUM(K33:K56),2)","v":692.27}]
[]
[null,"TOTAL SUM OF SQUARES CALCULATION"]
[null,"Case #","Value","Overall Mean",null,"Value-Group Mean",null,"(Value - Group Mean)2"]
[null,1,{"$f":"C8","v":13},{"$f":"$M$10","v":13.67},null,{"$f":"CONCATENATE(C61,\" - \",D61,\" = \",J61)","v":"13 - 13.67 = -0.67"},null,{"$f":"CONCATENATE(J61,\" x \",J61,\" = \",K61)","v":"-0.67 x -0.67 = 0.45"},null,{"$f":"ROUND(C61-D61,2)","v":-0.67},{"$f":"ROUND(J61*J61,2)","v":0.45},null,null,null,null,null,null,{"$f":"CONCATENATE(C61,\" - \",D61,\" = ?\")","v":"13 - 13.67 = ?"},null,{"$f":"CONCATENATE(J61,\" x \",J61,\" = ?\")","v":"-0.67 x -0.67 = ?"}]
[null,2,{"$f":"C9","v":11},{"$f":"$M$10","v":13.67},null,{"$f":"CONCATENATE(C62,\" - \",D62,\" = \",J62)","v":"11 - 13.67 = -2.67"},null,{"$f":"CONCATENATE(J62,\" x \",J62,\" = \",K62)","v":"-2.67 x -2.67 = 7.13"},null,{"$f":"ROUND(C62-D62,2)","v":-2.67},{"$f":"ROUND(J62*J62,2)","v":7.13},null,null,null,null,null,null,{"$f":"CONCATENATE(C62,\" - \",D62,\" = ?\")","v":"11 - 13.67 = ?"},null,{"$f":"CONCATENATE(J62,\" x \",J62,\" = ?\")","v":"-2.67 x -2.67 = ?"}]
[null,3,11,13.67,null,"11 - 13.67 = -2.67",null,"-2.67 x -2.67 = 7.13",null,-2.67,7.13,null,null,null,null,null,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,4,3,13.67,null,"3 - 13.67 = -10.67",null,"-10.67 x -10.67 = 113.85",null,-10.67,113.85,null,null,null,null,null,null,"3 - 13.67 = ?",null,"-10.67 x -10.67 = ?"]
[null,5,16,13.67,null,"16 - 13.67 = 2.33",null,"2.33 x 2.33 = 5.43",null,2.33,5.43,null,null,null,null,null,null,"16 - 13.67 = ?",null,"2.33 x 2.33 = ?"]
[null,6,15,13.67,null,"15 - 13.67 = 1.33",null,"1.33 x 1.33 = 1.77",null,1.33,1.77,null,null,null,null,null,null,"15 - 13.67 = ?",null,"1.33 x 1.33 = ?"]
[null,7,2,13.67,null,"2 - 13.67 = -11.67",null,"-11.67 x -11.67 = 136.19",null,-11.67,136.19,null,null,null,null,null,null,"2 - 13.67 = ?",null,"-11.67 x -11.67 = ?"]
[null,8,{"$f":"F8","v":19},13.67,null,"19 - 13.67 = 5.33",null,"5.33 x 5.33 = 28.41",null,5.33,28.41,null,null,null,null,null,null,"19 - 13.67 = ?",null,"5.33 x 5.33 = ?"]
[null,9,{"$f":"F9","v":18},13.67,null,"18 - 13.67 = 4.33",null,"4.33 x 4.33 = 18.75",null,4.33,18.75,null,null,null,null,null,null,"18 - 13.67 = ?",null,"4.33 x 4.33 = ?"]
[null,10,15,13.67,null,"15 - 13.67 = 1.33",null,"1.33 x 1.33 = 1.77",null,1.33,1.77,null,null,null,null,null,null,"15 - 13.67 = ?",null,"1.33 x 1.33 = ?"]
[null,11,9,13.67,null,"9 - 13.67 = -4.67",null,"-4.67 x -4.67 = 21.81",null,-4.67,21.81,null,null,null,null,null,null,"9 - 13.67 = ?",null,"-4.67 x -4.67 = ?"]
[null,12,12,13.67,null,"12 - 13.67 = -1.67",null,"-1.67 x -1.67 = 2.79",null,-1.67,2.79,null,null,null,null,null,null,"12 - 13.67 = ?",null,"-1.67 x -1.67 = ?"]
[null,13,20,13.67,null,"20 - 13.67 = 6.33",null,"6.33 x 6.33 = 40.07",null,6.33,40.07,null,null,null,null,null,null,"20 - 13.67 = ?",null,"6.33 x 6.33 = ?"]
[null,14,24,13.67,null,"24 - 13.67 = 10.33",null,"10.33 x 10.33 = 106.71",null,10.33,106.71,null,null,null,null,null,null,"24 - 13.67 = ?",null,"10.33 x 10.33 = ?"]
[null,15,14,13.67,null,"14 - 13.67 = 0.33",null,"0.33 x 0.33 = 0.11",null,0.33,0.11,null,null,null,null,null,null,"14 - 13.67 = ?",null,"0.33 x 0.33 = ?"]
[null,16,11,13.67,null,"11 - 13.67 = -2.67",null,"-2.67 x -2.67 = 7.13",null,-2.67,7.13,null,null,null,null,null,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,17,{"$f":"I8","v":16},13.67,null,"16 - 13.67 = 2.33",null,"2.33 x 2.33 = 5.43",null,2.33,5.43,null,null,null,null,null,null,"16 - 13.67 = ?",null,"2.33 x 2.33 = ?"]
[null,18,{"$f":"I9","v":10},13.67,null,"10 - 13.67 = -3.67",null,"-3.67 x -3.67 = 13.47",null,-3.67,13.47,null,null,null,null,null,null,"10 - 13.67 = ?",null,"-3.67 x -3.67 = ?"]
[null,19,11,13.67,null,"11 - 13.67 = -2.67",null,"-2.67 x -2.67 = 7.13",null,-2.67,7.13,null,null,null,null,null,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,20,11,13.67,null,"11 - 13.67 = -2.67",null,"-2.67 x -2.67 = 7.13",null,-2.67,7.13,null,null,null,null,null,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,21,23,13.67,null,"23 - 13.67 = 9.33",null,"9.33 x 9.33 = 87.05",null,9.33,87.05,null,null,null,null,null,null,"23 - 13.67 = ?",null,"9.33 x 9.33 = ?"]
[null,22,7,13.67,null,"7 - 13.67 = -6.67",null,"-6.67 x -6.67 = 44.49",null,-6.67,44.49,null,null,null,null,null,null,"7 - 13.67 = ?",null,"-6.67 x -6.67 = ?"]
[null,23,11,13.67,null,"11 - 13.67 = -2.67",null,"-2.67 x -2.67 = 7.13",null,-2.67,7.13,null,null,null,null,null,null,"11 - 13.67 = ?",null,"-2.67 x -2.67 = ?"]
[null,24,26,13.67,null,"26 - 13.67 = 12.33",null,"12.33 x 12.33 = 152.03",null,12.33,152.03,null,null,null,null,null,null,"26 - 13.67 = ?",null,"12.33 x 12.33 = ?"]
[null,null,null,null,null,"Column Sum:",null,{"$f":"CONCATENATE(\"'= \",K85)","v":"'= 823.36"},null,null,{"$f":"ROUND(SUM(K61:K84),2)","v":823.36}]
[]
[null,"F-RATIO CALCULATION"]
[null,"Between group degrees of freedom"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 3 - 1\")","v":"'= 3 - 1"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 2\")","v":"'= 2"}]
[null,"Within group degrees of freedom"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= (7 - 1) + (9 - 1) + (8 - 1)\")","v":"'= (7 - 1) + (9 - 1) + (8 - 1)"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 6 + 8 + 7\")","v":"'= 6 + 8 + 7"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= 21\")","v":"'= 21"}]
[null,"F-Statistic Numerator"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",Q29,\" ÷ 2\")","v":"'= 131.27 ÷ 2"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",I97)","v":"'= 65.64"},null,null,{"$f":"ROUND(Q29/2,2)","v":65.64}]
[null,"F-Statistic Denominator"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",K57,\" ÷ 21\")","v":"'= 692.27 ÷ 21"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",I100)","v":"'= 32.97"},null,null,{"$f":"ROUND(K57/21,2)","v":32.97}]
[null,"F-Statistic"]
[null,null,null,null,null,{"$f":"CONCATENATE(\"'= \",I97,\" ÷ \",I100)","v":"'= 65.64 ÷ 32.97"}]
[null,null,null,null,null,{"$f":"CONCATENATE(\"' = \",I103)","v":"' = 1.99"},null,null,{"$f":"ROUND(I97/I100,2)","v":1.99}]