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ANOVA

ANOVA. Used to test difference of means between 3 or more groups. Assumptions: Independent samples Normal distribution Equal Variance. Hypothesis. Hr: At least one group mean is not equal to at least one other group mean. Ho: μ 1 = μ 2 = μ 3. Conceptualizing ANOVA.

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ANOVA

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  1. ANOVA • Used to test difference of means between 3 or more groups. Assumptions: Independent samples Normal distribution Equal Variance

  2. Hypothesis • Hr: At least one group mean is not equal to at least one other group mean. • Ho: μ1 = μ2 = μ3

  3. Conceptualizing ANOVA • Does the IV (i.e., belonging to a group (religion, social class, race) explain variation (differences) in the DV. Example: Research Question: Does the average IQ differ among working, middle, and lower class individuals? Hr: The average IQ for at least one social class is different from one or more of the other social classes.

  4. Anova uses an F test to test the relationship between the IV and DV when we have three or more groups. • A significant F value: • Reject Ho • At least one group mean is significantly different from the other group means.

  5. A Closer Look at the F Test Compares variation within groups to variation between groups . Variation between groups is the deviation of each group mean from every other group mean. Variation within groups is the deviation of the raw scores from each group mean.

  6. Calculating ANOVA F = MS (mean square) Between/ MS Within MS is derived from SS (Sum of Squares) (3 components SS total, SS within, SS between) • See Social Class & IQ example on overhead

  7. ANOVA in SPSS • Hr: The average age for first kid born for at least one group is different from one or more of the other group means. • See SPSS overhead • Remember F = MS between / MS within

  8. SPSS output MS between = SS between / df between df between = k (# of groups –1) = 4-1=3 MS between = 1382.697/3= 460.90 MS within = SS within / df within df within = N (total N) – K (# of groups) df = 1960- 4 = 1956 MS within = 53296.40/1956 = 27.25 F = 460.90/27.25 = 16.91

  9. Decision • What is the significance level of for a calculated F of 16.91? • Do we reject the Ho • How would you write up this result? • How often would we make a type I error?

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