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Lecture 14: Factorial ANOVA Practice Laura McAvinue School of Psychology Trinity College Dublin Effectiveness of Therapy on Depression Type of Therapy CBT Gender Males Females Psychoanalytic Drug 10 16 24 8 18 26 6 20 28 22 6 20 20 4 22 18 8 24 Software / Kevin Thomas / Factorial ANOVA dataset The variables in SPSS… • How many variables are there? – 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 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 • How many women got psychoanalytic therapy? – 3 Have a look at the data… Mean Number of Depressive Symptoms for Men & Women receiving Three Kinds of Therapy CBT Male Female Total Psycho- Drug analytic Total 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 Have a look at the data… Mean Number of Depressive Symptoms for Men & Women receiving Three Kinds of Therapy CBT Psycho- Drug analytic 18 26 Male 8 Female 20 6 22 Total 14 12 24 Total 17.33 16 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 Examine the Means Table… Which Means do we compare when investigating if there is a main effect of Gender? CBT Psycho- Drug analytic 18 26 Male 8 Female 20 6 22 Total 14 12 24 Total 17.33 16 Examine the Means Table… Which Means do we compare when investigating if there is a main effect of Therapy? CBT Psycho- Drug analytic 18 26 Male 8 Female 20 6 22 Total 14 12 24 Total 17.33 16 Examine the Means Table… Which Means do we compare when investigating if there is an Interaction between Gender & Therapy? CBT Psycho- Drug analytic 18 26 Male 8 Female 20 6 22 Total 14 12 24 Total 17.33 16 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 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 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? Check the Assumptions Levene's Test of Equality of Error Variancesa Dependent Variable: depress F .000 df1 df2 5 12 Sig. 1.000 Tes ts the null hypothes is that the error variance of the dependent variable is equal acros s groups . a. Des ign: Intercept+gender+therapy+gender * therapy • Is Levene’s statistic significant? • What can we conclude from this? Examine the Tests of Between-Subjects Effects Tests of Between-Subjects Effects Dependent Variable: depres s Source Corrected Model Intercept gender therapy gender * therapy Error Total Corrected Total Type III Sum of Squares 952.000 a 5000.000 8.000 496.000 448.000 48.000 6000.000 1000.000 df 5 1 1 2 2 12 18 17 Mean Square 190.400 5000.000 8.000 248.000 224.000 4.000 F 47.600 1250.000 2.000 62.000 56.000 Sig. .000 .000 .183 .000 .000 a. R Squared = .952 (Adjusted R Squared = .932) • Is there a main effect of Gender? – No! • Report this… – There was no effect of Gender, F (1, 12) = 2, p = .183 Examine the Tests of Between-Subjects Effects Tests of Between-Subjects Effects Dependent Variable: depres s Source Corrected Model Intercept gender therapy gender * therapy Error Total Corrected Total Type III Sum of Squares 952.000 a 5000.000 8.000 496.000 448.000 48.000 6000.000 1000.000 df 5 1 1 2 2 12 18 17 Mean Square 190.400 5000.000 8.000 248.000 224.000 4.000 F 47.600 1250.000 2.000 62.000 56.000 Sig. .000 .000 .183 .000 .000 a. R Squared = .952 (Adjusted R Squared = .932) • Is there a main effect of Therapy? – Yes! • Report this… – There was a main effect of Therapy, F (2, 12) = 62, p <.001 Examine the Tests of Between-Subjects Effects Tests of Between-Subjects Effects Dependent Variable: depres s Source Corrected Model Intercept gender therapy gender * therapy Error Total Corrected Total Type III Sum of Squares 952.000 a 5000.000 8.000 496.000 448.000 48.000 6000.000 1000.000 df 5 1 1 2 2 12 18 17 Mean Square 190.400 5000.000 8.000 248.000 224.000 4.000 F 47.600 1250.000 2.000 62.000 56.000 Sig. .000 .000 .183 .000 .000 a. R Squared = .952 (Adjusted R Squared = .932) • 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 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 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 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? Hypotheses • Ho regarding Age: – There is no effect of age – Old and young participants have the same mean level of recall across all conditions of processing • Halt regarding Age: – There is a main effect of age – Old & young participants’ mean level of recall differs significantly across all conditions of processing Hypotheses • Ho 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 • Halt 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 Hypotheses • Ho regarding an Interaction between Age & Depth of Processing: – There is no interaction between age & depth of processing • Halt 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 Run the ANOVA… • Analyse>General Linear Model>Univariate • Plots • Options – Descriptive statistics • Continue • OK Have a look at the data… Mean Level of Recall for old & young participants learning material under three conditions Counting Adjective Imagery Total Old Young Total Have a look at the data… Mean Level of Recall for Old & Young Participants learning Material under Three Conditions Counting Adjective Imagery Total Old 7 11 13.4 10.47 Young 6.5 14.8 17.6 12.97 Total 6.75 12.9 15.5 Does there appear to be a main effect of age? Count Adj Image Total 7 11 13.4 10.47 Young 6.5 14.8 17.6 12.97 Total 12.9 15.5 Old 6.75 Does there appear to be a main effect of learning strategy? Count Adj Image Total 7 11 13.4 10.47 Young 6.5 14.8 17.6 12.97 Total 12.9 15.5 Old 6.75 Does there appear to be an interaction between age & learning strategy? Count Adj Image Total 7 11 13.4 10.47 Young 6.5 14.8 17.6 12.97 Total 12.9 15.5 Old 6.75 What does the ANOVA tell us? • Main effect of age Tests of Between-Subjects Effects – F (1, 54) = 11.08, p = .002 Dependent Variable: rcall Type III Sum Source of Squares Corrected Model 969.283 a Intercept 8236.817 age 93.750 conditio 807.633 age * conditio 67.900 Error 456.900 Total 9663.000 Corrected Total 1426.183 df Mean Square 5 193.857 1 8236.817 1 93.750 2 403.817 2 33.950 54 8.461 60 59 a. R Squared = .680 (Adjusted R Squared = .650) F 22.911 973.491 11.080 47.726 4.012 Sig. .000 .000 .002 .000 .024 • Main effect of Condition – F (2, 54) = 47.726, p < .001 • Interaction between Age & Condition – F (2, 54) = 4.012, p = .024 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.