1. Lecture 16: Factorial ANOVA Interactions Practice Laura McAvinue School of Psychology Trinity College Dublin

2. Recall Eysenck’s Study Eysenck was interested in the effects of Age & Depth of Processing on Recall. He obtained a sample of 60 old & young participants and randomly assigned them to three groups. All three groups were given a list of words to study. The first group was asked to count the number of letters in each word, the second group was asked to think of an adjective that could be used with the word and a third group was asked to form an image associated with the word.

3. The Data CountAdjImageTotal Old 71113.410.47 Young 6.514.817.612.97 Total 6.7512.915.5

4. This factorial ANOVA will allow us to investigate three kinds of effects. What are these? –Main effect due to Age –Main effect due to Learning Condition –Interaction between Age & Learning Condition Factorial ANOVA

5. Dependent variable = Recall Independent variables = Age & Learning Condition Ask for descriptive statistics Ask for homogeneity of variance test Ask for profile plot of the means Run the Factorial ANOVA

6. Check the Assumptions Is Levene’s statistic significant? –Yes! What can we conclude from this? –We cannot assume equality of variance among the groups –Results of ANOVA may not be valid

7. Is there a main effect of age? –Report this Is there a main effect of Condition? –Report this Is there an interaction between Age & Condition? –Report this Examine the Output

8. What does the ANOVA tell us? Main effect of age –F (1, 54) = 11.08, p =.002 Main effect of Condition –F (2, 54) = 47.726, p <.001 Interaction between Age & Condition –F (2, 54) = 4.012, p =.024

9. What is a main effect? –The effect of one independent variable averaged across the levels of the other independent variable –The effect of one independent variable ignoring the other variable What is a simple effect? –The effect of one variable at one level of another variable Should we do an analysis of simple effects here? –Yes! Why? –Because there is a significant interaction between Age & Condition –In order to tease apart the interaction Simple Effects

10. What are the Simple Effects we can analyse? The effects of Age at each level of Learning Condition –The effect of age under counting condition –The effect of age under adjective condition –The effect of age under imagery condition The effects of Learning Condition at each level of Age –The effect of learning condition for young participants –The effect of learning condition for old participants

11. Split File Organise output according to Learning Condition One Way ANOVA with Recall as the dependent variable & Age as the independent variable Split File Organise output according to Age One Way ANOVA with Recall as the dependent variable and Learning Condition as the Independent variable Simple Effects of Age at each Level of Learning Condition Simple Effects of Learning Condition at each Level of Age

12. Simple Effects ANOVA Table Source of Variation SSDfMSF Age Age at Counting Age at Adjective Age at Imagery Learning Cond. Learning at Old Learning at Young Error

13. Simple Effects ANOVA Table Source of Variation SSDfMSF Age Age at Counting1.251.148 Age at Adjective72.21 8.53 Age at Imagery88.21 10.424 Learning Cond. Learning at Old209.0672104.53312.35 Learning at Young666.4672333.23339.38 Error456.9548.461

14. Find the Critical F Values for each Simple Effect Use the F Distribution Table… Critical value for simple effects of age –  =.05, 4.02 –  =.01, 7.12 Critical value for simple effects of Condition –  =.05, 3.17 –  =.01, 5.01

15. Simple Effects ANOVA Table Source of Variation SSDfMSFCrit F p<.05 Crit F p<.01 Signif? Age Counting1.251.1484.027.12No! Adjective72.21 8.534.027.12Yes Imagery88.21 10.4244.027.12Yes Learning Cond. Old209.0672104.53312.353.175.01Yes Young666.4672333.23339.383.175.01Yes Error456.9548.461

16. Interpretation Explain the effects of Age & Learning Strategy on Recall, drawing on the results of the ANOVA to back up your explanation. Are there any further analyses that you think might be required? –posthoc

17. Examine the dataset… What is the dependent variable? –‘tpstress’, perceived stress What are the independent variables? –‘sex’ & ‘age’ What are the levels of each variable? –Sex = male / female –Age = 18-29 / 30-44 / 45+ What do you think this study is investigating? –The effects of sex & age on perceived stress Example 2: ANOVA Interactions Dataset

18. Ask for descriptives, homogeneity test & a means plot Run the Two Way Factorial ANOVA

19. Have a look at the means plot Main effect of sex? Main effect of age? Interaction?

20. Have a look at the results of the ANOVA Main effect of sex? Main effect of age? Interaction?

21. Are any other analyses required? Explain the results of the study in your own words. Interpretation