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Part IV Significantly Different: Using Inferential Statistics Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Analysis of Variance (ANOVA) Used to test for differences between two or more group means. Group means differ from one another on a particular score / variable Example: Do GRE Scores differ by major? Test statistic = F test R.A. Fisher, creator Path to Wisdom & Knowledge How do I know if ANOVA is the right test? Different Flavors of ANOVA ANOVA examines the variance between groups and the variances within groups These variances are then compared against each other (Variance Between / Variance Within) Same function as the t Test…only in this case you have more than two groups One-way ANOVA Simple ANOVA Single factor (grouping variable) Computing the F Statistic Rationale…want the within group variance to be small and the between group variance to be large in order to find significance. Hypotheses Null hypothesis Research hypothesis Source Table Source Between SS 1,133.07 df 27 MS 566.54 Within 1,738.40 29 64.39 F 8.799 Note: F value for two groups ANOVA is the same as t2 Degrees of Freedom (df) Numerator Number of groups minus one k-1 3 groups --- 3 – 1 = 2 Denominator Total number of observations minus the number of groups N-1 10 participants per group x 3 groups = 30 – 3 = 27 Represented: F (2, 27) How to Interpret F (2,27) = 8.80, p < .05 F = test statistic 2,27 = df between groups & df within groups {Ah ha…3 groups and 30 total scores examined} 8.80 = obtained value Which we compared to the critical value p < .05 = probability less than 5% that the null hypothesis is true Meaning the obtained value is GREATER than the critical value There are significant differences in the means. Omnibus Test The F test is an “omnibus test” and only tells you that a difference exists Must conduct follow-up t tests to find out where the difference is… BUT…Type I error increases with every follow-up test / possible comparison made Cumulative Type 1 Error = 1 – (1 – alpha)k Where k = number of possible comparisons Using the Computer SPSS and the One-Way ANOVA SPSS Output What does it all mean? Post Hoc Comparison