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Part IV Significantly Different: Using Inferential Statistics

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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.

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Part IV Significantly Different: Using Inferential Statistics

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  1. Part IVSignificantly Different:Using Inferential Statistics Chapter 13  Two Groups Too Many? Try Analysis of Variance (ANOVA)

  2. 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

  3. Path to Wisdom & Knowledge • How do I know if ANOVA is the right test?

  4. 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)

  5. 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.

  6. Hypotheses • Null hypothesis • Research hypothesis

  7. Source Table Note: F value for two groups ANOVA is the same as t2

  8. 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)

  9. 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.

  10. 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

  11. Using the Computer • SPSS and the One-Way ANOVA

  12. SPSS Output • What does it all mean?

  13. Post Hoc Comparison

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