07 - ANOVA_Nonparametrics

07 - ANOVA_Nonparametrics - 1-Way ANOVA Significance n 1 2...

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1-Way ANOVA Significance 10% α n 4 4 3 A B C Equality of Variance ANOVA Table - ADA's (Normal Populations) 1 4 10 1 Source SS df MS F 2 5 11 2 Between 1.24 2 0.62 1.86 3.11 0.2166 3 7 12 3 Within 2.67 8 0.33 4 8 13 Total 3.91 10 Importance 13.57% Unimportant Estimates of Group ADA Means Group Confidence Interval 1-α A 1.5 ± 0.54 90% B 1 ± 0.54 90% C 0.67 ± 0.62 90% Tukey test for pairwise comparison of group ADA means A r 3 B B n - r 8 C C 3.38 T 1.13 Equality of Variance ANOVA Table - ADM's (Non-Normal Populations) Source SS df MS F Between 1.24 2 0.62 1.86 3.11 0.2166 Within 2.67 8 0.33 Total 3.91 10 Importance 13.57% Unimportant Estimates of Group ADM Means Group Confidence Interval 1-α A 1.5 ± 0.54 90% B 1 ± 0.54 90% C 0.67 ± 0.62 90% Post-Hoc Tukey test for pairwise comparison of group ADM means A r 3 B B n - r 8 C C 3.38 T 1.13 Means ANOVA Table Source SS df MS F Between 159.91 2 79.95 37.63 3.11 0.0001 Reject Within 17 8 2.13 Total 176.91 10 Importance 86.94% Very Important Estimates of Group Means Group Confidence Interval 1-α A 6 ± 1.36 90% B 11.5 ± 1.36 90% C 2 ± 1.57 90% Estimates of Group Variances Group PE n 90% Conf Int A 3.33 4 1.29 3.28 B 1.67 4 0.91 2.32 C 1 3 0.71 1.8 Post-Hoc Assuming Variances Equal Tukey test for pairwise comparison of group means A r 3 B Sig B n - r 8 C Sig Sig C 3.38 T 2.84 Assuming Variances Unequal Games Howell test for pairwise comparison of group means A r 3 B Sig B C Sig Sig C F critical p -value ϖ 2 q 0 F critical p -value ϖ 2 q 0 F critical p -value ϖ 2 q 0
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Randomized Complete Block Design α Mean 10.71 13 15.43 ANOVA Table 5% A B C Mean Source SS df MS F 1 12 16 15 14.33 Treatment 40.95 6 6.83 3.13 3 0.0439 Reject 2 11 10 14 11.67 Block 77.81 2 38.9 17.83 3.89 0.0003 Reject 3 10 11 17 12.67 Error 26.19 12 2.18 4 12 15 19 15.33 Total 144.95 20 F critical p -value
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2-Way ANOVA ^ Press the + button to see row means. Scroll down for column and cell means This template can be used only if there are an equal number of replicat C1 C2 C3 C4 R1 158 147 139 144 α 154 143 135 145 ANOVA Table 5% 146 140 142 139 Source SS df MS F 150 144 139 136 Row 128.63 2 64.31 3.59 3.26 0.0380 Reject Column 1295.42 3 431.81 24.08 2.87 0.0000 Reject Interaction 159.71 6 26.62 1.48 2.36 0.2112 Error 645.5 36 17.93 Total 2229.25 47 F critical p -value
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Kruskal-Wallis ANOVA - Independent Ordinal Data Group Data Rank 3 1 1 45 14 Group R n Test Statistic 2 1 38 10 1 90 6 15 H 12.36 3 1 56 16 2 56 6 9.33 4 1 60 17 3 25 6 4.17 Null Hypothesis 5 1 47 15 6 1 65 18 7 2 30 8 5% 8 2 40 11 0.0021 Reject 9 2 28 7 10 2 44 13 11 2 25 5 12 2 42 12 3 Total 18 13 3 22 4 14 3 19 3 Further Analysis 15 3 15 1 1 16 3 31 9 2 2 17 3 27 6 3 Sig 3 18 3 17 2 Avg. R H 0 : All the Groups have the same distribution At an α of p -value
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Mann-Whitney U Test The Learning Curve method Post-hoc for KW ANOVA Group Data Rank Counts Test Statistic Rank Sums 1 2 65 10 1 15 U 32.5 1 312.5 2 2 57 4 2 15 2 152.5 3 2 74 16 4 2 43 2 5 2 39 1 Test Statistic E[U] 112.5 6 2 88 23 z -3.32 24.11 7 2 62 8.5 8 2 69 11 9 2 70 12 Null Hypothesis 5% 10 2 72 13.5 0.0009 Reject 11 2 59 5 0.9995 12 2 60 6.5 0.0005 Reject 13 2 80 18 14 2 83 19 15 2 50 3 16 1 85 20 17 1 87 21 18 1 92 27 19 1 98 30 20 1 90 26 21 1 88 23 22 1 75 17 23 1 72 13.5 24 1 60 6.5 25 1 93 28 26 1 88 23 27 1 89 25 28 1 96 29 29 1 73 15 30 1 62 8.5 In case of large samples ( n 1 or n 2 > 10) σ (U) At an α of p -value H 0 : μ 1 = μ 2 H 0 : μ 1 >= μ 2 H 0 : μ 1 <= μ 2
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Friedman ANOVA - Ordinal Dependent Data Cruise Lines R 31 21 38 1 2 3 4 5 6 7 8 9 10 RowSum Results 1 1 2 3 6 n 15 2 2 1 3 6 k 3 3 1 3 2 6 4 2 1 3 6 9.73 5 3 1 2 6 6 3 1 2 6 0.0077 7
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