Statistics for the Social Sciences

1. Statistics for the Social Sciences Psychology 340 Spring 2006 Factorial ANOVA

2. Outline • Basics of factorial ANOVA • Interpretations • Main effects • Interactions • Computations • Assumptions, effect sizes, and power • Other Factorial Designs • More than two factors • Within factorial ANOVAs • Factorial ANOVA in SPSS

3. Outline • Basics of factorial ANOVA • Interpretations • Main effects • Interactions • Computations • Assumptions, effect sizes, and power • Other Factorial Designs • Within factorial ANOVAs • Mixed factorial ANOVAs • Factorial ANOVA in SPSS

4. Assumptions in Two-Way ANOVA • Populations follow a normal curve • Populations have equal variances • Assumptions apply to the populations that go with each cell

5. Effect Size in Factorial ANOVA (completely between groups)

6. Approximate Sample Size Needed in Each Cell for 80% Power (.05 significance level) 10.16

7. Other ANOVA designs • Basics of repeated measures factorial ANOVA • Using SPSS • Basics of mixed factorial ANOVA • Using SPSS • Similar to the between groups factorial ANOVA • Main effects and interactions • Multiple sources for the error terms (different denominators for each main effect)

8. Example • Suppose that you are interested in how sleep deprivation impacts performance. You test 5 people on two tasks (motor and math) over the course of time without sleep (24 hrs, 36 hrs, and 48 hrs). Dependent variable is number of errors in the tasks. • Both factors are manipulated as within subject variables • Need to conduct a within groups factorial ANOVA

9. Example

10. Within factorial ANOVA in SPSS • Each condition goes in a separate column • It is to your benefit to systematically order those columns to reflect the factor structure • Make your column labels informative • Analyze -> General Linear Model -> Repeated measures • Enter your factor 1 & number of levels, then factor 2 & levels, etc. (remember the order of the columns) • Tell SPSS which columns correspond to which condition • As was the case before, lots of output • Focus on the within-subject effects • Note: each F has a different error term

11. Example

12. Example • It has been suggested that pupil size increases during emotional arousal. A researcher presents people with different types of stimuli (designed to elicit different emotions). The researcher examines whether similar effects are demonstrated by men and women. • Type of stimuli was manipulated within subjects • Sex is a between subjects variable • Need to conduct a mixed factorial ANOVA

13. Example

14. Mixed factorial ANOVA in SPSS • Each within condition goes in a separate column • It is to your benefit to systematically order those columns to reflect the factor structure • Make your column labels informative • Each between groups factor has a column that specifies group membership • Analyze -> General Linear Model -> Repeated measures • Enter your within groups factors: factor 1 & number of levels, then factor 2 & levels, etc. (remember the order of the columns) • Tell SPSS which columns correspond to which condition • Enter your between groups column that specifies group membership • As was the case before, lots of output • Need to look at the within-subject effects and the between groups effects

15. Example

16. Factorial ANOVA in Research Articles A two-factor ANOVA yielded a significant main effect of voice, F(2, 245) = 26.30, p < .001. As expected, participants responded less favorably in the low voice condition (M = 2.93) than in the high voice condition (M = 3.58). The mean rating in the control condition (M = 3.34) fell between these two extremes. Of greater importance, the interaction between culture and voice was also significant, F(2, 245) = 4.11, p < .02.

17. Recruiting • Looking for a teaching experience? • Enjoy (tolerate?) statistics • I am looking for Undergraduate Teaching Assistant(s) for PSY 138 next semester • If interested: • E-mail me about your interest: jccutti@ilstu.edu