{"text_format":"1","workbook":"xlsx","n_sheets":9,"sheets":["Data","ANOVA1","XLSTAT_20240813_135708_1_HID","ANOVA2","XLSTAT_20240813_134557_1_HID","XLSTAT_20220616_181340_1_HID","XLSTAT_20220616_181333_1_HID","ANOVA_HID","ANOVA1_HID"],"not_rendered":{"charts":14,"images":5,"macros":1,"external_links":0,"defined_names":48,"comments":2,"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":"Data","index":0,"n_rows":25,"n_cols":12,"rows_kept":25,"cut":false,"hidden":false,"merged":[]}
[null,"Toothpaste","Whiteness",null,null,null,null,"ToothPaste","T1","T2","T3","T4"]
[null,"T1",16,null,null,null,null,null,16,18,19,20]
[null,"T1",17,null,null,null,null,null,17,20,27,23]
[null,"T1",17,null,null,null,null,null,17,20,28,24]
[null,"T1",19,null,null,null,null,null,19,21,29,25]
[null,"T1",21,null,null,null,null,null,21,22,32,26]
[null,"T1",24,null,null,null,null,null,24,23,34,29]
[null,"T2",18]
[null,"T2",20]
[null,"T2",20]
[null,"T2",21]
[null,"T2",22]
[null,"T2",23]
[null,"T3",19]
[null,"T3",27]
[null,"T3",28]
[null,"T3",29]
[null,"T3",32]
[null,"T3",34]
[null,"T4",20]
[null,"T4",23]
[null,"T4",24]
[null,"T4",25]
[null,"T4",26]
[null,"T4",29]

{"sheet":"ANOVA1","index":1,"n_rows":310,"n_cols":13,"rows_kept":310,"cut":false,"hidden":false,"merged":[[220,4,220,5],[238,4,238,6],[255,3,255,4],[264,3,264,5]]}
[null,"XLSTAT 2024.2.2.1422 - ANOVA - Start time: 08/13/2024 at 13:57:09 / End time: 08/13/2024 at 13:57:14 / Microsoft Excel 16.017830"]
[null,"Y / Dependent variables: Workbook = demoANO (3).xlsm / Sheet = Data / Range = 'Data'!$C:$C / 24 rows and 1 column"]
[null,"X / Qualitative: Workbook = demoANO (3).xlsm / Sheet = Data / Range = 'Data'!$B:$B / 24 rows and 1 column"]
[null,"Constraints: a1=0"]
[null,"Confidence interval (%): 95"]
[null,"Tolerance: 0.0001"]
[null,"Use least squares means: Yes"]
[]
[]
[]
[]
[null,"Summary statistics (Quantitative data):"]
[]
[null,"Variable","Observations","Obs. with missing data","Obs. without missing data","Minimum","Maximum","Mean","Std. deviation"]
[null,"Whiteness",24,0,24,16,34,23.083333333333336,4.8626050154451042]
[]
[]
[null,"Summary statistics (Qualitative data):"]
[]
[null,"Variable","Categories","Counts","Frequencies","%"]
[null,"Toothpaste","T1",6,6,25]
[null,"","T2",6,6,25]
[null,"","T3",6,6,25]
[null,"","T4",6,6,25]
[]
[]
[null,"Correlation matrix:"]
[]
[null,null,"Toothpaste-T1","Toothpaste-T2","Toothpaste-T3","Toothpaste-T4","Whiteness"]
[null,"Toothpaste-T1",1,-0.33333333333333331,-0.33333333333333331,-0.33333333333333331,-0.49525277285476044]
[null,"Toothpaste-T2",-0.33333333333333331,1,-0.33333333333333331,-0.33333333333333331,-0.29310878393445011]
[null,"Toothpaste-T3",-0.33333333333333331,-0.33333333333333331,1,-0.33333333333333331,0.61653916620694671]
[null,"Toothpaste-T4",-0.33333333333333331,-0.33333333333333331,-0.33333333333333331,1,0.17182239058226384]
[null,"Whiteness",-0.49525277285476044,-0.29310878393445011,0.61653916620694671,0.17182239058226384,1]
[]
[]
[null,"Regression of variable Whiteness:"]
[]
[null,"Goodness of fit statistics (Whiteness):"]
[]
[null,"Observations",24]
[null,"Sum of weights",24]
[null,"DF",20]
[null,"R²",0.55562365920931656]
[null,"Adjusted R²",0.48896720809071403]
[null,"MSE",12.083333333333332]
[null,"RMSE",3.4761089357690347]
[null,"MAPE",10.478077013107558]
[null,"DW",1.7495402298850578]
[null,"Cp",4]
[null,"AIC",63.428132860126865]
[null,"AICC",65.533396018021605]
[null,"SBC",68.140348181518647]
[null,"PC",0.6221268771069568]
[]
[]
[null,"Analysis of variance (Whiteness):"]
[]
[null,"Source","DF","Sum of squares","Mean squares","F","Pr > F","p-values signification codes"]
[null,"Model",3,302.16666666666663,100.72222222222221,8.3356321839080465,8.5735129101731269E-4,"***"]
[null,"Error",20,241.66666666666666,12.083333333333332,null,null,""]
[null,"Corrected Total",23,543.83333333333326,null,null,null,""]
[null,"Computed against model Y=Mean(Y)"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[null,"Model parameters (Whiteness):"]
[]
[null,"Source","Value","Standard error","t","Pr > |t|","Lower bound (95%)","Upper bound (95%)","p-values signification codes"]
[null,"Intercept",19.000000000000004,1.4191155304938667,13.388621004935242,1.9186405245104359E-11,16.039776876288446,21.960223123711561,"***"]
[null,"Toothpaste-T1",0,0,null,null,null,null,""]
[null,"Toothpaste-T2",1.6666666666666656,2.0069324297987157,0.83045479853739923,0.41608547943285479,-2.5197210225366677,5.8530543558699986,"°"]
[null,"Toothpaste-T3",9.1666666666666643,2.0069324297987157,4.5675013919556973,1.869554931959172E-4,4.9802789774633309,13.353054355869997,"***"]
[null,"Toothpaste-T4",5.4999999999999991,2.0069324297987157,2.7405008351734188,1.2606952819436579E-2,1.3136123107966657,9.6863876892033325,"*"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[null,"Equation of the model (Whiteness):"]
[]
[null,"Whiteness = 19+1.66666666666667*Toothpaste-T2+9.16666666666666*Toothpaste-T3+5.5*Toothpaste-T4"]
[]
[]
[null,"Standardized coefficients (Whiteness):"]
[]
[null,"Source","Value","Standard error","t","Pr > |t|","Lower bound (95%)","Upper bound (95%)","p-values signification codes"]
[null,"Toothpaste-T1",0,0,null,null,null,null,""]
[null,"Toothpaste-T2",0.1516079916902327,0.18256019708386945,0.83045479853739923,0.41608547943285479,-0.22920590630786641,0.53242188968833182,"°"]
[null,"Toothpaste-T3",0.83384395429628011,0.18256019708386945,4.5675013919556973,1.869554931959172E-4,0.45303005629818099,1.2146578522943792,"***"]
[null,"Toothpaste-T4",0.50030637257776811,0.18256019708386945,2.7405008351734184,1.2606952819436801E-2,0.11949247457966899,0.88112027057586717,"*"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Predictions and residuals (Whiteness):"]
[]
[null,"Observation","Weight","Whiteness","Pred(Whiteness)","Residual","Std. residual","Std. dev. on pred. (Mean)","Lower bound 95% (Mean)","Upper bound 95% (Mean)","Std. dev. on pred. (Observation)","Lower bound 95% (Observation)","Upper bound 95% (Observation)"]
[null,"Obs1",1,16,19.000000000000004,-3.0000000000000036,-0.8630339426736926,1.4191155304938665,16.039776876288446,21.960223123711561,3.7546267753562699,11.167985789396431,26.832014210603575]
[null,"Obs2",1,17,19.000000000000004,-2.0000000000000036,-0.57535596178246207,1.4191155304938665,16.039776876288446,21.960223123711561,3.7546267753562699,11.167985789396431,26.832014210603575]
[null,"Obs3",1,17,19.000000000000004,-2.0000000000000036,-0.57535596178246207,1.4191155304938665,16.039776876288446,21.960223123711561,3.7546267753562699,11.167985789396431,26.832014210603575]
[null,"Obs4",1,19,19.000000000000004,-3.5527136788005009E-15,-1.0220374978019838E-15,1.4191155304938665,16.039776876288446,21.960223123711561,3.7546267753562699,11.167985789396431,26.832014210603575]
[null,"Obs5",1,21,19.000000000000004,1.9999999999999964,0.57535596178245996,1.4191155304938665,16.039776876288446,21.960223123711561,3.7546267753562699,11.167985789396431,26.832014210603575]
[null,"Obs6",1,24,19.000000000000004,4.9999999999999964,1.4383899044561514,1.4191155304938665,16.039776876288446,21.960223123711561,3.7546267753562699,11.167985789396431,26.832014210603575]
[null,"Obs7",1,18,20.666666666666668,-2.6666666666666679,-0.76714128237661505,1.4191155304938667,17.70644354295511,23.626889790378225,3.7546267753562699,12.834652456063095,28.498680877270239]
[null,"Obs8",1,20,20.666666666666668,-0.66666666666666785,-0.19178532059415401,1.4191155304938667,17.70644354295511,23.626889790378225,3.7546267753562699,12.834652456063095,28.498680877270239]
[null,"Obs9",1,20,20.666666666666668,-0.66666666666666785,-0.19178532059415401,1.4191155304938667,17.70644354295511,23.626889790378225,3.7546267753562699,12.834652456063095,28.498680877270239]
[null,"Obs10",1,21,20.666666666666668,0.33333333333333215,9.5892660297076493E-2,1.4191155304938667,17.70644354295511,23.626889790378225,3.7546267753562699,12.834652456063095,28.498680877270239]
[null,"Obs11",1,22,20.666666666666668,1.3333333333333321,0.38357064118830703,1.4191155304938667,17.70644354295511,23.626889790378225,3.7546267753562699,12.834652456063095,28.498680877270239]
[null,"Obs12",1,23,20.666666666666668,2.3333333333333321,0.6712486220795375,1.4191155304938667,17.70644354295511,23.626889790378225,3.7546267753562699,12.834652456063095,28.498680877270239]
[null,"Obs13",1,19,28.166666666666668,-9.1666666666666679,-2.6370481581696135,1.4191155304938667,25.20644354295511,31.126889790378225,3.7546267753562699,20.334652456063097,35.998680877270239]
[null,"Obs14",1,27,28.166666666666668,-1.1666666666666679,-0.33562431103976925,1.4191155304938667,25.20644354295511,31.126889790378225,3.7546267753562699,20.334652456063097,35.998680877270239]
[null,"Obs15",1,28,28.166666666666668,-0.16666666666666785,-4.794633014853876E-2,1.4191155304938667,25.20644354295511,31.126889790378225,3.7546267753562699,20.334652456063097,35.998680877270239]
[null,"Obs16",1,29,28.166666666666668,0.83333333333333215,0.23973165074269176,1.4191155304938667,25.20644354295511,31.126889790378225,3.7546267753562699,20.334652456063097,35.998680877270239]
[null,"Obs17",1,32,28.166666666666668,3.8333333333333321,1.1027655934163834,1.4191155304938667,25.20644354295511,31.126889790378225,3.7546267753562699,20.334652456063097,35.998680877270239]
[null,"Obs18",1,34,28.166666666666668,5.8333333333333321,1.6781215551988444,1.4191155304938667,25.20644354295511,31.126889790378225,3.7546267753562699,20.334652456063097,35.998680877270239]
[null,"Obs19",1,20,24.500000000000004,-4.5000000000000036,-1.2945509140105382,1.4191155304938667,21.539776876288446,27.460223123711561,3.7546267753562699,16.667985789396432,32.332014210603575]
[null,"Obs20",1,23,24.500000000000004,-1.5000000000000036,-0.4315169713368468,1.4191155304938667,21.539776876288446,27.460223123711561,3.7546267753562699,16.667985789396432,32.332014210603575]
[null,"Obs21",1,24,24.500000000000004,-0.50000000000000355,-0.14383899044561627,1.4191155304938667,21.539776876288446,27.460223123711561,3.7546267753562699,16.667985789396432,32.332014210603575]
[null,"Obs22",1,25,24.500000000000004,0.49999999999999645,0.14383899044561424,1.4191155304938667,21.539776876288446,27.460223123711561,3.7546267753562699,16.667985789396432,32.332014210603575]
[null,"Obs23",1,26,24.500000000000004,1.4999999999999964,0.43151697133684475,1.4191155304938667,21.539776876288446,27.460223123711561,3.7546267753562699,16.667985789396432,32.332014210603575]
[null,"Obs24",1,29,24.500000000000004,4.4999999999999964,1.2945509140105362,1.4191155304938667,21.539776876288446,27.460223123711561,3.7546267753562699,16.667985789396432,32.332014210603575]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Means charts:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Toothpaste / Tukey (HSD) / Analysis of the differences between the categories with a confidence interval of 95% (Whiteness):"]
[]
[null,"Contrast","Difference","Standardized difference","Critical value","Pr > Diff","Significant","Lower bound (95%)","Upper bound (95%)","Lower bound (95%)","Upper bound (95%)"]
[null,"T3 vs T1",9.1666666666666643,4.5675013919556973,2.7989362191789064,9.9119543489090134E-4,"Yes",3.5493907994583109,14.783942533875017,null,"|||||||||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T2",7.4999999999999982,3.7370465934182975,2.7989362191789064,6.5533653827084537E-3,"Yes",1.882724132791644,13.117275867208352,null,"||||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T4",3.6666666666666652,1.8270005567822785,2.7989362191789064,0.29042683955906179,"No",-1.95060920054169,9.2839425338750203,"||||||","||||||||||||||||||||||||||||"]
[null,"T4 vs T1",5.4999999999999991,2.7405008351734188,2.7989362191789064,5.6306070289758092E-2,"No",-0.11727586720835426,11.117275867208352,"|","||||||||||||||||||||||||||||||||||"]
[null,"T4 vs T2",3.8333333333333335,1.9100460366360192,2.7989362191789064,0.25550781517432419,"No",-1.7839425338750208,9.4506092005416882,"|||||","|||||||||||||||||||||||||||||"]
[null,"T2 vs T1",1.6666666666666656,0.83045479853739923,2.7989362191789064,0.83939452963446226,"No",-3.9506092005416877,7.2839425338750186,"||||||||||||","||||||||||||||||||||||"]
[null,"q studentized range statistic:",null,null,3.9582935613800836]
[null,"Minimum significant difference:",null,null,5.6172758672083543]
[]
[]
[null,"Category","LS means","Standard error","Groups"]
[null,"T3",28.166666666666668,1.4191155304938667,"A"]
[null,"T4",24.500000000000004,1.4191155304938667,"A","B"]
[null,"T2",20.666666666666668,1.4191155304938667,null,"B"]
[null,"T1",19.000000000000004,1.4191155304938667,null,"B"]
[]
[]
[null,"Toothpaste / REGWQ / Analysis of the differences between the categories with a confidence interval of 95% (Whiteness):"]
[]
[null,"Contrast","Difference","Standardized difference","Critical value","Pr > Diff","alpha (Modified)","Significant","Lower bound (95%)","Upper bound (95%)","Lower bound (95%)","Upper bound (95%)"]
[null,"T3 vs T1",9.1666666666666643,4.5675013919556973,2.7989362191789064,9.9119543489090134E-4,0.05,"Yes",3.5493907994583109,14.783942533875017,null,"|||||||||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T2",7.4999999999999982,3.7370465934182975,2.5299819071269876,3.5578188677446443E-3,0.05,"Yes",2.4224972637828435,12.577502736217152,null,"||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T4",3.6666666666666652,1.8270005567822785,2.5299819071269876,8.2662540767321269E-2,0.05,"No",-1.4108360695504896,8.7441694028838199,"||||","||||||||||||||||||||||||||"]
[null,"T4 vs T1",5.4999999999999991,2.7405008351734188,2.5299819071269876,3.2344958105723687E-2,0.05,"Yes",0.42249726378284524,10.577502736217152,null,"||||||||||||||||||||||||||||||||"]
[null,"T4 vs T2",3.8333333333333335,1.9100460366360192,2.4170821224191492,7.0573973625122188E-2,2.5320565519103666E-2,"No",-1.0175871636363669,8.6842538303030334,"|||","||||||||||||||||||||||||||"]
[null,"T2 vs T1",1.6666666666666656,0.83045479853739923,2.4170821224191492,0.41608547943287755,2.5320565519103666E-2,"No",-3.1842538303030339,6.5175871636363656,"||||||||||","||||||||||||||||||||"]
[]
[]
[null,"Category","LS means","Standard error","Groups"]
[null,"T3",28.166666666666668,1.4191155304938667,"A"]
[null,"T4",24.500000000000004,1.4191155304938667,"A","B"]
[null,"T2",20.666666666666668,1.4191155304938667,null,"B","C"]
[null,"T1",19.000000000000004,1.4191155304938667,null,null,"C"]
[]
[]
[null,"Toothpaste / Dunnett (two sided) / Analysis of the differences between the control category Toothpaste-T1 and the other categories with a confidence interval of 95%:"]
[]
[null,"Contrast","Difference","Standardized difference","Critical value","Critical difference","Pr > Diff","Significant"]
[null,"T1 vs T3",-9.1666666666666643,-4.5675013919556973,2.5404156731478773,5.0984425996094096,5.3704328855097572E-4,1]
[null,"T1 vs T4",-5.4999999999999991,-2.7405008351734188,2.5404156731478773,5.0984425996094096,3.2925142196790214E-2,1]
[null,"T1 vs T2",-1.6666666666666656,-0.83045479853739923,2.5404156731478773,5.0984425996094096,0.74518866462860256,0]
[]
[]
[null,"Summary of all pairwise comparisons for Toothpaste (Tukey (HSD)):"]
[]
[null,"Category","LS means(Whiteness)","Groups"]
[null,"T3",28.166666666666668,"A"]
[null,"T4",24.500000000000004,"A","B"]
[null,"T2",20.666666666666668,null,"B"]
[null,"T1",19.000000000000004,null,"B"]
[]
[]
[null,"Summary of all pairwise comparisons for Toothpaste (REGWQ):"]
[]
[null,"Category","LS means(Whiteness)","Groups"]
[null,"T3",28.166666666666668,"A"]
[null,"T4",24.500000000000004,"A","B"]
[null,"T2",20.666666666666668,null,"B","C"]
[null,"T1",19.000000000000004,null,null,"C"]
[]
[]
[null,"Summary (LS means) - Toothpaste:"]
[]
[null,"Category","Whiteness"]
[null,"T3",28.166666666666668]
[null,"T4",24.500000000000004]
[null,"T2",20.666666666666668]
[null,"T1",19.000000000000004]
[null,"Pr > F(Model)",8.5735129101731269E-4]
[null,"Significant","Yes"]
[null,"The grouping letters displayed here are those of the last test. If you wish to see the grouping letters of the other tests, please refer to the comments in each of the cells or restart the analysis with the only test that interests you."]
[]
[]
[null,"Summary (LS means) - Toothpaste (Color):"]
[]
[null,"Category","Whiteness"]
[null,"T3",28.166666666666668]
[null,"T4",24.500000000000004]
[null,"T2",20.666666666666668]
[null,"T1",19.000000000000004]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[null,"You have activated the option 'Filter Ys' in the charts tab. Only the dependent variables for which the Fisher's F of the model is significant are displayed in the summary chart."]

{"sheet":"XLSTAT_20240813_135708_1_HID","index":2,"n_rows":70,"n_cols":11,"rows_kept":70,"cut":false,"hidden":true,"merged":[]}
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{"sheet":"ANOVA2","index":3,"n_rows":309,"n_cols":13,"rows_kept":309,"cut":false,"hidden":false,"merged":[[219,4,219,5],[237,4,237,6],[254,3,254,4],[263,3,263,5]]}
[null,"XLSTAT 2024.2.2.1422 - ANOVA - Start time: 08/13/2024 at 13:46:49 / End time: 08/13/2024 at 13:46:54 / Microsoft Excel 16.017830"]
[null,"Data table: Workbook = demoANO (3).xlsm / Sheet = Data / Range = 'Data'!$H$1:$L$7 / 7 rows and 4 columns"]
[null,"Constraints: a1=0"]
[null,"Confidence interval (%): 95"]
[null,"Tolerance: 0.0001"]
[null,"Use least squares means: Yes"]
[]
[]
[]
[]
[null,"Summary statistics (Quantitative data):"]
[]
[null,"Variable","Observations","Obs. with missing data","Obs. without missing data","Minimum","Maximum","Mean","Std. deviation"]
[null,"Y",24,0,24,16,34,23.083333333333336,4.8626050154451033]
[]
[]
[null,"Summary statistics (Qualitative data):"]
[]
[null,"Variable","Categories","Counts","Frequencies","%"]
[null,"ToothPaste","T1",6,6,25]
[null,"","T2",6,6,25]
[null,"","T3",6,6,25]
[null,"","T4",6,6,25]
[]
[]
[null,"Correlation matrix:"]
[]
[null,null,"ToothPaste-T1","ToothPaste-T2","ToothPaste-T3","ToothPaste-T4","Y"]
[null,"ToothPaste-T1",1,-0.33333333333333331,-0.33333333333333331,-0.33333333333333331,-0.49525277285476066]
[null,"ToothPaste-T2",-0.33333333333333331,1,-0.33333333333333331,-0.33333333333333331,-0.29310878393445011]
[null,"ToothPaste-T3",-0.33333333333333331,-0.33333333333333331,1,-0.33333333333333331,0.61653916620694682]
[null,"ToothPaste-T4",-0.33333333333333331,-0.33333333333333331,-0.33333333333333331,1,0.17182239058226387]
[null,"Y",-0.49525277285476066,-0.29310878393445011,0.61653916620694682,0.17182239058226387,1]
[]
[]
[null,"Regression of variable Y:"]
[]
[null,"Goodness of fit statistics (Y):"]
[]
[null,"Observations",24]
[null,"Sum of weights",24]
[null,"DF",20]
[null,"R²",0.55562365920931689]
[null,"Adjusted R²",0.48896720809071442]
[null,"MSE",12.083333333333321]
[null,"RMSE",3.4761089357690333]
[null,"MAPE",10.478077013107558]
[null,"DW",0.51068965517241371]
[null,"Cp",4]
[null,"AIC",63.428132860126844]
[null,"AICC",65.533396018021577]
[null,"SBC",68.140348181518632]
[null,"PC",0.62212687710695636]
[]
[]
[null,"Analysis of variance (Y):"]
[]
[null,"Source","DF","Sum of squares","Mean squares","F","Pr > F","p-values signification codes"]
[null,"Model",3,302.16666666666663,100.72222222222221,8.3356321839080536,8.5735129101730976E-4,"***"]
[null,"Error",20,241.66666666666643,12.083333333333321,null,null,""]
[null,"Corrected Total",23,543.83333333333303,null,null,null,""]
[null,"Computed against model Y=Mean(Y)"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[null,"Model parameters (Y):"]
[]
[null,"Source","Value","Standard error","t","Pr > |t|","Lower bound (95%)","Upper bound (95%)","p-values signification codes"]
[null,"Intercept",19.000000000000004,1.4191155304938661,13.388621004935249,1.9186405245104155E-11,16.039776876288446,21.960223123711561,"***"]
[null,"ToothPaste-T1",0,0,null,null,null,null,""]
[null,"ToothPaste-T2",1.6666666666666665,2.0069324297987148,0.83045479853740012,0.41608547943285479,-2.5197210225366651,5.8530543558699986,"°"]
[null,"ToothPaste-T3",9.1666666666666679,2.0069324297987148,4.5675013919557017,1.869554931959172E-4,4.9802789774633363,13.35305435587,"***"]
[null,"ToothPaste-T4",5.5,2.0069324297987148,2.7405008351734206,1.2606952819436579E-2,1.3136123107966684,9.6863876892033325,"*"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[null,"Equation of the model (Y):"]
[]
[null,"Y = 19+1.66666666666667*ToothPaste-T2+9.16666666666667*ToothPaste-T3+5.5*ToothPaste-T4"]
[]
[]
[null,"Standardized coefficients (Y):"]
[]
[null,"Source","Value","Standard error","t","Pr > |t|","Lower bound (95%)","Upper bound (95%)","p-values signification codes"]
[null,"ToothPaste-T1",0,0,null,null,null,null,""]
[null,"ToothPaste-T2",0.15160799169023281,0.18256019708386939,0.83045479853740012,0.41608547943285479,-0.22920590630786619,0.53242188968833182,"°"]
[null,"ToothPaste-T3",0.83384395429628055,0.18256019708386939,4.5675013919557008,1.869554931959172E-4,0.45303005629818155,1.2146578522943796,"***"]
[null,"ToothPaste-T4",0.50030637257776833,0.18256019708386939,2.7405008351734206,1.2606952819436579E-2,0.11949247457966933,0.88112027057586739,"*"]
[null,"Signification codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Predictions and residuals (Y):"]
[]
[null,"Observation","Weight","Y","Pred(Y)","Residual","Std. residual","Std. dev. on pred. (Mean)","Lower bound 95% (Mean)","Upper bound 95% (Mean)","Std. dev. on pred. (Observation)","Lower bound 95% (Observation)","Upper bound 95% (Observation)"]
[null,"Obs1",1,16,19.000000000000004,-3.0000000000000036,-0.86303394267369293,1.4191155304938661,16.039776876288446,21.960223123711561,3.7546267753562681,11.167985789396436,26.832014210603571]
[null,"Obs2",1,18,20.666666666666671,-2.6666666666666714,-0.76714128237661638,1.4191155304938661,17.706443542955114,23.626889790378229,3.7546267753562681,12.834652456063104,28.498680877270239]
[null,"Obs3",1,19,28.166666666666671,-9.1666666666666714,-2.6370481581696152,1.4191155304938661,25.206443542955114,31.126889790378229,3.7546267753562681,20.334652456063104,35.998680877270239]
[null,"Obs4",1,20,24.500000000000004,-4.5000000000000036,-1.2945509140105389,1.4191155304938661,21.539776876288446,27.460223123711561,3.7546267753562681,16.667985789396436,32.332014210603575]
[null,"Obs5",1,17,19.000000000000004,-2.0000000000000036,-0.57535596178246229,1.4191155304938661,16.039776876288446,21.960223123711561,3.7546267753562681,11.167985789396436,26.832014210603571]
[null,"Obs6",1,20,20.666666666666671,-0.6666666666666714,-0.19178532059415512,1.4191155304938661,17.706443542955114,23.626889790378229,3.7546267753562681,12.834652456063104,28.498680877270239]
[null,"Obs7",1,27,28.166666666666671,-1.1666666666666714,-0.33562431103977042,1.4191155304938661,25.206443542955114,31.126889790378229,3.7546267753562681,20.334652456063104,35.998680877270239]
[null,"Obs8",1,23,24.500000000000004,-1.5000000000000036,-0.43151697133684697,1.4191155304938661,21.539776876288446,27.460223123711561,3.7546267753562681,16.667985789396436,32.332014210603575]
[null,"Obs9",1,17,19.000000000000004,-2.0000000000000036,-0.57535596178246229,1.4191155304938661,16.039776876288446,21.960223123711561,3.7546267753562681,11.167985789396436,26.832014210603571]
[null,"Obs10",1,20,20.666666666666671,-0.6666666666666714,-0.19178532059415512,1.4191155304938661,17.706443542955114,23.626889790378229,3.7546267753562681,12.834652456063104,28.498680877270239]
[null,"Obs11",1,28,28.166666666666671,-0.1666666666666714,-4.7946330148539801E-2,1.4191155304938661,25.206443542955114,31.126889790378229,3.7546267753562681,20.334652456063104,35.998680877270239]
[null,"Obs12",1,24,24.500000000000004,-0.50000000000000355,-0.14383899044561632,1.4191155304938661,21.539776876288446,27.460223123711561,3.7546267753562681,16.667985789396436,32.332014210603575]
[null,"Obs13",1,19,19.000000000000004,-3.5527136788005009E-15,-1.0220374978019842E-15,1.4191155304938661,16.039776876288446,21.960223123711561,3.7546267753562681,11.167985789396436,26.832014210603571]
[null,"Obs14",1,21,20.666666666666671,0.3333333333333286,9.5892660297075508E-2,1.4191155304938661,17.706443542955114,23.626889790378229,3.7546267753562681,12.834652456063104,28.498680877270239]
[null,"Obs15",1,29,28.166666666666671,0.8333333333333286,0.23973165074269082,1.4191155304938661,25.206443542955114,31.126889790378229,3.7546267753562681,20.334652456063104,35.998680877270239]
[null,"Obs16",1,25,24.500000000000004,0.49999999999999645,0.1438389904456143,1.4191155304938661,21.539776876288446,27.460223123711561,3.7546267753562681,16.667985789396436,32.332014210603575]
[null,"Obs17",1,21,19.000000000000004,1.9999999999999964,0.57535596178246018,1.4191155304938661,16.039776876288446,21.960223123711561,3.7546267753562681,11.167985789396436,26.832014210603571]
[null,"Obs18",1,22,20.666666666666671,1.3333333333333286,0.38357064118830614,1.4191155304938661,17.706443542955114,23.626889790378229,3.7546267753562681,12.834652456063104,28.498680877270239]
[null,"Obs19",1,32,28.166666666666671,3.8333333333333286,1.1027655934163827,1.4191155304938661,25.206443542955114,31.126889790378229,3.7546267753562681,20.334652456063104,35.998680877270239]
[null,"Obs20",1,26,24.500000000000004,1.4999999999999964,0.43151697133684491,1.4191155304938661,21.539776876288446,27.460223123711561,3.7546267753562681,16.667985789396436,32.332014210603575]
[null,"Obs21",1,24,19.000000000000004,4.9999999999999964,1.4383899044561521,1.4191155304938661,16.039776876288446,21.960223123711561,3.7546267753562681,11.167985789396436,26.832014210603571]
[null,"Obs22",1,23,20.666666666666671,2.3333333333333286,0.67124862207953673,1.4191155304938661,17.706443542955114,23.626889790378229,3.7546267753562681,12.834652456063104,28.498680877270239]
[null,"Obs23",1,34,28.166666666666671,5.8333333333333286,1.678121555198844,1.4191155304938661,25.206443542955114,31.126889790378229,3.7546267753562681,20.334652456063104,35.998680877270239]
[null,"Obs24",1,29,24.500000000000004,4.4999999999999964,1.2945509140105369,1.4191155304938661,21.539776876288446,27.460223123711561,3.7546267753562681,16.667985789396436,32.332014210603575]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"Means charts:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[]
[]
[null,"ToothPaste / Tukey (HSD) / Analysis of the differences between the categories with a confidence interval of 95% (Y):"]
[]
[null,"Contrast","Difference","Standardized difference","Critical value","Pr > Diff","Significant","Lower bound (95%)","Upper bound (95%)","Lower bound (95%)","Upper bound (95%)"]
[null,"T3 vs T1",9.1666666666666679,4.5675013919557017,2.7989362191789064,9.9119543489090134E-4,"Yes",3.5493907994583171,14.783942533875019,null,"|||||||||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T2",7.5000000000000018,3.7370465934183006,2.7989362191789064,6.5533653827082317E-3,"Yes",1.8827241327916493,13.117275867208354,null,"||||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T4",3.6666666666666679,1.8270005567822805,2.7989362191789064,0.29042683955906112,"No",-1.9506092005416846,9.2839425338750203,"||||||","||||||||||||||||||||||||||||"]
[null,"T4 vs T1",5.5,2.7405008351734206,2.7989362191789064,5.630607028975787E-2,"No",-0.1172758672083507,11.117275867208351,"|","||||||||||||||||||||||||||||||||||"]
[null,"T4 vs T2",3.8333333333333335,1.9100460366360199,2.7989362191789064,0.25550781517432397,"No",-1.783942533875019,9.4506092005416864,"|||||","|||||||||||||||||||||||||||||"]
[null,"T2 vs T1",1.6666666666666665,0.83045479853740012,2.7989362191789064,0.83939452963446182,"No",-3.9506092005416842,7.2839425338750168,"||||||||||||","||||||||||||||||||||||"]
[null,"q studentized range statistic:",null,null,3.9582935613800836]
[null,"Minimum significant difference:",null,null,5.6172758672083516]
[]
[]
[null,"Category","LS means","Standard error","Groups"]
[null,"T3",28.166666666666671,1.4191155304938661,"A"]
[null,"T4",24.500000000000004,1.4191155304938661,"A","B"]
[null,"T2",20.666666666666671,1.4191155304938661,null,"B"]
[null,"T1",19.000000000000004,1.4191155304938661,null,"B"]
[]
[]
[null,"ToothPaste / REGWQ / Analysis of the differences between the categories with a confidence interval of 95% (Y):"]
[]
[null,"Contrast","Difference","Standardized difference","Critical value","Pr > Diff","alpha (Modified)","Significant","Lower bound (95%)","Upper bound (95%)","Lower bound (95%)","Upper bound (95%)"]
[null,"T3 vs T1",9.1666666666666679,4.5675013919557017,2.7989362191789064,9.9119543489090134E-4,0.05,"Yes",3.5493907994583171,14.783942533875019,null,"|||||||||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T2",7.5000000000000018,3.7370465934183006,2.5299819071269876,3.5578188677444222E-3,0.05,"Yes",2.4224972637828488,12.577502736217156,null,"||||||||||||||||||||||||||||||||||||||"]
[null,"T3 vs T4",3.6666666666666679,1.8270005567822805,2.5299819071269876,8.2662540767320936E-2,0.05,"No",-1.4108360695504851,8.7441694028838199,"||||","||||||||||||||||||||||||||"]
[null,"T4 vs T1",5.5,2.7405008351734206,2.5299819071269876,3.2344958105723576E-2,0.05,"Yes",0.4224972637828488,10.577502736217152,null,"||||||||||||||||||||||||||||||||"]
[null,"T4 vs T2",3.8333333333333335,1.9100460366360199,2.4170821224191492,7.0573973625121855E-2,2.5320565519103666E-2,"No",-1.0175871636363651,8.6842538303030317,"|||","||||||||||||||||||||||||||"]
[null,"T2 vs T1",1.6666666666666665,0.83045479853740012,2.4170821224191492,0.4160854794328771,2.5320565519103666E-2,"No",-3.1842538303030312,6.5175871636363638,"||||||||||","||||||||||||||||||||"]
[]
[]
[null,"Category","LS means","Standard error","Groups"]
[null,"T3",28.166666666666671,1.4191155304938661,"A"]
[null,"T4",24.500000000000004,1.4191155304938661,"A","B"]
[null,"T2",20.666666666666671,1.4191155304938661,null,"B","C"]
[null,"T1",19.000000000000004,1.4191155304938661,null,null,"C"]
[]
[]
[null,"ToothPaste / Dunnett (two sided) / Analysis of the differences between the control category ToothPaste-T1 and the other categories with a confidence interval of 95%:"]
[]
[null,"Contrast","Difference","Standardized difference","Critical value","Critical difference","Pr > Diff","Significant"]
[null,"T1 vs T3",-9.1666666666666679,-4.5675013919557017,2.5404156731478773,5.0984425996094069,5.3704328855097572E-4,1]
[null,"T1 vs T4",-5.5,-2.7405008351734206,2.5404156731478773,5.0984425996094069,3.2925142196790214E-2,1]
[null,"T1 vs T2",-1.6666666666666665,-0.83045479853740012,2.5404156731478773,5.0984425996094069,0.74518866462860189,0]
[]
[]
[null,"Summary of all pairwise comparisons for ToothPaste (Tukey (HSD)):"]
[]
[null,"Category","LS means(Y)","Groups"]
[null,"T3",28.166666666666671,"A"]
[null,"T4",24.500000000000004,"A","B"]
[null,"T2",20.666666666666671,null,"B"]
[null,"T1",19.000000000000004,null,"B"]
[]
[]
[null,"Summary of all pairwise comparisons for ToothPaste (REGWQ):"]
[]
[null,"Category","LS means(Y)","Groups"]
[null,"T3",28.166666666666671,"A"]
[null,"T4",24.500000000000004,"A","B"]
[null,"T2",20.666666666666671,null,"B","C"]
[null,"T1",19.000000000000004,null,null,"C"]
[]
[]
[null,"Summary (LS means) - ToothPaste:"]
[]
[null,"Category","Y"]
[null,"T3",28.166666666666671]
[null,"T4",24.500000000000004]
[null,"T2",20.666666666666671]
[null,"T1",19.000000000000004]
[null,"Pr > F(Model)",8.5735129101730976E-4]
[null,"Significant","Yes"]
[null,"The grouping letters displayed here are those of the last test. If you wish to see the grouping letters of the other tests, please refer to the comments in each of the cells or restart the analysis with the only test that interests you."]
[]
[]
[null,"Summary (LS means) - ToothPaste (Color):"]
[]
[null,"Category","Y"]
[null,"T3",28.166666666666671]
[null,"T4",24.500000000000004]
[null,"T2",20.666666666666671]
[null,"T1",19.000000000000004]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null," "]
[null,"You have activated the option 'Filter Ys' in the charts tab. Only the dependent variables for which the Fisher's F of the model is significant are displayed in the summary chart."]

{"sheet":"XLSTAT_20240813_134557_1_HID","index":4,"n_rows":70,"n_cols":11,"rows_kept":70,"cut":false,"hidden":true,"merged":[]}
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