Statistics for the Social Sciences Psychology 340 Spring 2006 Factorial ANOVA

Statistics for the Social Sciences 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

Statistics for the Social Sciences 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

Statistics for the Social Sciences Assumptions in Two-Way ANOVA Populations follow a normal curve Populations have equal variances Assumptions apply to the populations that go with each cell

Statistics for the Social Sciences Effect Size in Factorial ANOVA (completely between groups)

Statistics for the Social Sciences Approximate Sample Size Needed in Each Cell for 80% Power (.05 significance level) 10.16

Statistics for the Social Sciences 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)

Statistics for the Social Sciences 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

Statistics for the Social Sciences Example Factor B: Hours awake 24 B 1 36 B 2 48 B 3 Factor A: Task A 1 Motor A 2 Math

Statistics for the Social Sciences 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

Statistics for the Social Sciences Example SourceSSdfMSF p A Error (A) B Error (B) AB Error (AB) <

Statistics for the Social Sciences 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

Statistics for the Social Sciences Example Factor B: Stimulus Neutral B 1 Pleasant B 2 Aversive B 3 FactorA: Sex A 1 Men A 2 Women

Statistics for the Social Sciences 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

Statistics for the Social Sciences Example SourceSSdfMS F p Between Sex (A) Error (A) Within Stimulus (B) Sex * Stimulus Error (B)

Statistics for the Social Sciences 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.

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