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Unformatted text preview: OneFactor Analysis of Variance Independent Samples Topics . . . • ANOVA instead of t test – Variance instead of simple differences between means • ANOVA: Hypotheses, Fratio, Simple Formulas • Total variance vs within variance vs between variance • Definitional and computational formulas • Fratio –Degrees of freedom; Distribution of Fratios 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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This note was uploaded on 08/22/2011 for the course PSY 207 taught by Professor Pfordesher during the Fall '07 term at SUNY Buffalo.
 Fall '07
 Pfordesher

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