1. Lecture 14: Factorial ANOVA Practice Laura McAvinue School of Psychology Trinity College Dublin

2. CBTPsychoanalyticDrug Males101624 81826 62028 Females22620 422 18824 Type of Therapy Gender Effectiveness of Therapy on Depression Software / Kevin Thomas / Factorial ANOVA dataset

3. The variables in SPSS… How many variables are there? –3–3 What are they? –Gender, Therapy, Depress Which are the independent & dependent variables? –Independent = Gender, Therapy –Dependent = Depress How many levels does each independent variable have? –Gender = 2 –Therapy = 3

4. The variables in SPSS… How many people took part in the study? –18 How many men and how many women? –9 men & 9 women How many men got CBT? –3–3 How many women got psychoanalytic therapy? –3–3

5. Have a look at the data… CBTPsycho- analytic DrugTotal Male Female Total Mean Number of Depressive Symptoms for Men & Women receiving Three Kinds of Therapy

6. Have a look at the data To obtain the ‘totals’ –Analyse, Descriptive Statistics, Explore –Dependent list = depress –Factor list = gender, therapy To obtain the cell means –Data, split file, organise output by groups –Groups based on gender –File is already sorted –Analyse, Descriptive Statistics, Explore –Dependent list = depress –Factor list = therapy

7. Have a look at the data… CBTPsycho- analytic DrugTotal Male8182617.33 Female2062216 Total141224 Mean Number of Depressive Symptoms for Men & Women receiving Three Kinds of Therapy

8. Three kinds of Effects When we run the Factorial ANOVA, we will be interested in investigating if there are three kinds of effects that are causing the data to vary. What are these? –Main effect due to Gender –Main effect due to Therapy –An Interaction between Therapy & Gender

9. Examine the Means Table… CBTPsycho- analytic DrugTotal Male8182617.33 Female2062216 Total141224 Which Means do we compare when investigating if there is a main effect of Gender?

10. Examine the Means Table… CBTPsycho- analytic DrugTotal Male8182617.33 Female2062216 Total141224 Which Means do we compare when investigating if there is a main effect of Therapy?

11. Examine the Means Table… CBTPsycho- analytic DrugTotal Male8182617.33 Female2062216 Total141224 Which Means do we compare when investigating if there is an Interaction between Gender & Therapy?

12. Run the ANOVA… Analyse>General Linear Model>Univariate –Dependent Variable: depression –Fixed Factors: these are our two IVs (gender & therapy) Plots –Horizontal axis: put one IV on this axis (typically, put IVs that have more than two levels here) –Separate Lines: put the other IV in this window (typically, put IVs that have only two levels here) –Don’t forget to click Add Options –Descriptive statistics and –homogeneity tests Continue OK

13. Scroll through the output… Between-subjects factors –The independent variables in the analysis & the number of levels in each Descriptive Statistics –Means, SDs & n for each level of the independent variables Levene’s test –Test for homogeneity of Variance Test of Between-Subjects Effects –Significance of Main Effects & Interactions Profile Plots –Plot of the means

14. Examine the Means Plot Does there appear to be a main effect of gender? Does there appear to be a main effect of Therapy? Does there appear to be an interaction?

15. Check the Assumptions Is Levene’s statistic significant? What can we conclude from this?

16. Examine the Tests of Between-Subjects Effects Is there a main effect of Gender? –No! Report this… –There was no effect of Gender, F (1, 12) = 2, p =.183

17. Examine the Tests of Between-Subjects Effects Is there a main effect of Therapy? –Yes! Report this… –There was a main effect of Therapy, F (2, 12) = 62, p <.001

18. Examine the Tests of Between-Subjects Effects Is there a significant interaction between Gender & Therapy? –Yes! Report this… –There was a significant interaction between Gender & Therapy, F (2, 12) = 56, p <.001

19. Example 2, Eysenck’s Study Factorial ANOVA dataset –Variables: age, condition, recall Have a look at the dataset… What is the dependent variable? –Recall What are the independent variables? –Age & Condition What are the levels of Age? –Old & Young

20. Example 2, Eysenck’s Study What are the levels of Condition? –Counting, Adjective, Imagery Describe this ANOVA in two ways –Two Way Factorial ANOVA –2x3 Factorial ANOVA How many people participated in this experiment? –60 How many old & how many young? –30 old & 30 young

21. Example 2, 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. What are the null and research hypotheses for this study?

22. Hypotheses H o regarding Age: –There is no effect of age –Old and young participants have the same mean level of recall across all conditions of processing H alt regarding Age: –There is a main effect of age –Old & young participants’ mean level of recall differs significantly across all conditions of processing

23. Hypotheses H o regarding Depth of Processing: –There is no effect of depth of processing –For both young and old participants, mean recall is the same under each condition of processing H alt regarding Depth of Processing: –There is a main effect of depth of processing –For both young and old participants, at least one processing condition mean is significantly different from the others

24. Hypotheses H o regarding an Interaction between Age & Depth of Processing: –There is no interaction between age & depth of processing H alt regarding an Interaction between Age & Depth of Processing : –There is a significant interaction between age & depth of processing –Age & depth of processing have a combined effect on recall

25. Run the ANOVA… Analyse>General Linear Model>Univariate Plots Options –Descriptive statistics Continue OK

26. Have a look at the data… CountingAdjectiveImageryTotal Old Young Total Mean Level of Recall for old & young participants learning material under three conditions

27. Have a look at the data… CountingAdjectiveImageryTotal Old71113.410.47 Young6.514.817.612.97 Total6.7512.915.5 Mean Level of Recall for Old & Young Participants learning Material under Three Conditions

28. Does there appear to be a main effect of age? CountAdjImageTotal Old 71113.410.47 Young 6.514.817.612.97 Total 6.7512.915.5

29. Does there appear to be a main effect of learning strategy? CountAdjImageTotal Old 71113.410.47 Young 6.514.817.612.97 Total 6.7512.915.5

30. Does there appear to be an interaction between age & learning strategy? CountAdjImageTotal Old 71113.410.47 Young 6.514.817.612.97 Total 6.7512.915.5

31. 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

32. In your own words, explain what is happening in these data? There is a main effect of Age and Condition and a significant interaction between Age & Condition. It seems that overall, greater depth of processing leads to better recall. Also, older participants tend to show poorer recall than younger participants. However, this is only during conditions of deeper processing of material. In the counting condition, which involved a very shallow level of processing, older and younger participants performed equally well. This finding suggests that older participants do not benefit as much as the younger participants do from deeper processing of the material.