1. Statistics for the Social Sciences Psychology 340 Spring 2005 Analysis of Variance (ANOVA)

2. Statistics for the Social Sciences Outline Brief review of last time ANOVA Post-hoc and planned comparisons Effect sizes in ANOVA ANOVA in SPSS

3. Statistics for the Social Sciences Example Effect of knowledge of prior behavior on jury decisions –Dependent variable: rate how innocent/guilty –Independent variable: 3 levels Criminal record Clean record No information (no mention of a record)

4. Statistics for the Social Sciences Analysis of Variance XBXB XAXA XCXC Criminal recordClean recordNo information 1054 716 539 73 843 –Need a measure that describes several difference scores –Variance Variance is essentially an average squared difference Test statistic Observed variance Variance from chance F-ratio = More than two groups

5. Statistics for the Social Sciences Testing Hypotheses with ANOVA –Step 2: Set your decision criteria –Step 3: Collect your data –Step 4: Compute your test statistics Compute your estimated variances Compute your F-ratio Compute your degrees of freedom (there are several) –Step 5: Make a decision about your null hypothesis Hypothesis testing: a five step program –Step 1: State your hypotheses –Additional tests: Planned comparisons & Post hoc tests Reconciling our multiple alternative hypotheses

6. Statistics for the Social Sciences Null hypothesis: H 0 : all the groups are equal XBXB XAXA XCXC –Step 1: State your hypotheses Hypothesis testing: a five step program Alternative hypotheses (H A ) –Not all of the populations all have same mean The ANOVA tests this one!! The ANOVA tests this one!! Testing Hypotheses with ANOVA Choosing between these requires additional test

7. Statistics for the Social Sciences 1 factor ANOVA XBXB XAXA XCXC Alternative hypotheses (H A ) –Not all of the populations all have same mean Planned contrasts and Post-hoc tests: –Further tests used to rule out the different alternative hypotheses –reject –fail to reject

8. Statistics for the Social Sciences Why do the ANOVA? What’s the big deal? Why not just run a bunch of t- tests instead of doing an ANOVA? –Experiment-wise error –The type I error rate of the family (the entire set) of comparisons  EW = 1 - (1 -  )c where c = # of comparisons »e.g., If you conduct two t-tests, each with an alpha level of 0.05, the combined chance of making a type I error is nearly 10 in 100 (rather than 5 in 100) –Planned comparisons and post hoc tests are procedures designed to reduce experiment-wise error

9. Statistics for the Social Sciences Which follow-up test? Planned comparisons –A set of specific comparisons that you “planned” to do in advance of conducting the overall ANOVA –General rule of thumb, don’t exceed the number of conditions that you have (or even stick with one fewer) Post-hoc tests –A set of comparisons that you decided to examine only after you find a significant (reject H 0 ) ANOVA

10. Statistics for the Social Sciences Planned Comparisons Different types –Simple comparisons - testing two groups –Complex comparisons - testing combined groups –Bonferroni procedure Use more stringent significance level for each comparison Basic procedure: –Within-groups population variance estimate (denominator) –Between-groups population variance estimate of the two groups of interest (numerator) –Figure F in usual way

11. Statistics for the Social Sciences Post-hoc tests Generally, you are testing all of the possible comparisons (rather than just a specific few) –Different types Tukey’s HSD test Scheffe test Others (Fisher’s LSD, Neuman-Keuls test, Duncan test) –Generally they differ with respect to how conservative they are.

12. Statistics for the Social Sciences Effect sizes in ANOVA The effect size for ANOVA is r 2 –Sometimes called  2 (“eta squared”) –The percent of the variance in the dependent variable that is accounted for by the independent variable –Size of effect depends, in part, on degrees of freedom See table 12-7 in textbook for what is considered “small” “medium” and “large”

13. Statistics for the Social Sciences ANOVA in SPSS Let’s see how to do a between groups 1-factor ANOVA in SPSS (and the other tests too)