14b_Ch13_One-Factor_ANOVA_Independent

14b_Ch13_One-Factor_ANOVA_Independent - One-Factor Analysis...

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One-Factor Analysis of Variance Assumptions, ANOVA Table, Effect Size, Post Hoc Tests, t and F for Two Independent Samples Independent Samples Assumptions ANOVA (Independent Samples) 1. Independent observations within each sample Assumptions ANOVA (Independent Samples) 1. Independent observations within each sample 2. The populations from which the sample were drawn must be normal
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Assumptions ANOVA (Independent Samples) 1. Independent observations within each sample 2. The populations from which the sample were drawn must be normal 3. Homogeneity of Variance — the populations from which the samples are drawn must have equal variances Group 1 Group 2 Group 3 Placebo Tranquilizer Hallucinogen Example . . . Example . . . – (1) alpha level use .05 – (2) numerator (between) df = 2 – (3) denominator (within) df = 15 F critical = 3.68 F observed = 15.42 Reject H 0 (observed is larger than critical) The treatments had significantly different effects
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Now let’s look at: – How the results are summarized in a table – How to measure effect size – How to pinpoint which means are different from each other when you have a significant ANOVA Example . . . ANOVA Summary Table Source SS df MS F Between Within Total ANOVA Summary Table Source SS df MS F Between 148 Within Total
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ANOVA Summary Table Source SS df MS F Between 148 Within 72 Total ANOVA Summary Table Source SS df MS F Between 148 Within 72 Total 220 ANOVA Summary Table Source SS df MS F Between 148 2 Within 72 Total 220 ANOVA Summary Table Source SS df MS F Between 148 2 Within 72 15 Total 220
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ANOVA Summary Table Source SS df MS F Between 148 2 Within 72 15 Total 220 17 ANOVA Summary Table Source SS df MS F Between 148 2 Within 72 15 Total 220 17 ÷ ANOVA Summary Table Source SS df MS F Between 148 2 74 Within 72 15 Total 220 17 = ÷ ANOVA Summary Table Source SS df MS F Between 148 2 74 Within 72 15 Total 220 17 ÷
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ANOVA Summary Table Source SS df MS F Between 148 2 74 Within 72 15 4.8 Total 220 17 = ÷ ANOVA Summary Table Source SS df MS F Between 148 2 74 Within 72 15 4.8 Total 220 17 ANOVA Summary Table Source SS df MS F Between 148 2 74 15.42 Within 72 15 4.8 Total 220 17 = ANOVA Summary Table Source SS df MS F Between 148 2 74 15.42 Within 72 15 4.8 Total 220 17
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Effect Size Proportion of variance accounted for = Variability due to treatment Total variability η 2 = SS between SS total Effect Size Proportion of variance accounted for = Variability due to treatment Total variability 2 = SS between SS total Eta Squared 2 = SS between SS total = 148 220 = .67
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Eta Squared η 2 = SS between SS total = 148 220 = .67 Eta Squared 2 = SS between SS total = 148 220 = .67 67% of the variability between groups is due to the drugs Post Hoc Tests Tukey’s HSD Scheffé
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Post Hoc Tests • If we reject H 0 , we know that not all of the means are the same 0 H : 1 μ = 2 = 3 • But we don’t know which means are different Post Hoc Tests Group 1 (Placebo) Group 2 (Tranquilizer) Group 3 (Hallucinogen)
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14b_Ch13_One-Factor_ANOVA_Independent - One-Factor Analysis...

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