14a_Ch13_1-Factor_ANOVA_Indep_Outline

14a_Ch13_1-Factor_ANOVA_Indep_Outline - One-Factor Analysis...

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Unformatted text preview: One-Factor Analysis of Variance Independent Samples Topics . . . ANOVA instead of t test Variance instead of simple differences between means ANOVA: Hypotheses, F-ratio, Simple Formulas Total variance vs within variance vs between variance Definitional and computational formulas F-ratio Degrees of freedom; Distribution of F-ratios t Tests for Two Samples Let us look for significant differences between two groups of scores Treatment A Treatment B 0 4 1 3 3 6 1 3 0 4 What are the odds of finding the observed difference between the means if the treatment has no effect? t Tests for Two Samples Let us look for significant differences between two groups of scores Treatment A Treatment B 0 4 s 2 p = SS A + SS B 1 3 df A + df B 3 6 1 3 0 4 Part of this involves pooling the sample variances (with H 1 2 3 4 assumed true in our test, this is OK). Design with 3 samples How do we approach this? Treatment A Treatment B Treatment C 0 4 1 1 3 2 3 6 2 1 3 0 0 4 0 Compare 3 means? How? Variance Sample variance: 1 1 1 s 2 = 0 1 5 9 s 2 = 16 1 2 3 s 2 = 1 1 3 9 s 2 = 17.33 1 3 5 s 2 = 4 1 1 9 s 2 = 21.33 More dissimilar Greater s 2 Variance Unlike a simple difference (e.g., M 1 M 2 ) . . . Variance can tell us how different 2 or more scores (or groups of scores) are from each other ANOVA Analysis of Variance Inferential statistical test using variance Can be used to test for significant differences among two or more groups of scores 5 6 7 8 assumed true in our test, this is OK). Design with 3 samples How do we approach this? Treatment A Treatment B Treatment C 0 4 1 1 3 2 3 6 2 1 3 0 0 4 0 Compare 3 means? How? Variance Sample variance: 1 1 1 s 2 = 0 1 5 9 s 2 = 16 1 2 3 s 2 = 1 1 3 9 s 2 = 17.33 1 3 5 s 2 = 4 1 1 9 s 2 = 21.33 More dissimilar Greater s 2 Variance Unlike a simple difference (e.g., M 1 M 2 ) . . . Variance can tell us how different 2 or more scores (or groups of scores) are from each other ANOVA Analysis of Variance Inferential statistical test using variance Can be used to test for significant differences among two or more groups of scores 5 6 7 8 Can be applied to many different research designs e.g., independent samples, dependent samples, multiple independent variables, numerous combinations thereof...
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14a_Ch13_1-Factor_ANOVA_Indep_Outline - One-Factor Analysis...

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