Lecture 10: One Way ANOVA Between Subjects: Practice! Laura McAvinue School of Psychology Trinity College Dublin

Example 1: ANOVA by hand Our research interest is the treatment of social anxiety We would like to evaluate different therapies for social anxiety We took a sample of 15 people suffering from social anxiety & randomly assigned them to three groups – Placebo – Cognitive Behavioural Therapy (CBT) – Gestalt Therapy Did any of the treatments significantly improve social anxiety? Are any of the means significantly different?

Steps Group AGroup BGroup C PlaceboCBTGestalt Mean141 1.Sum of Squares 2.Degrees of Freedom 3.Mean Square 4.F Ratio 5.P Value What is the grand mean of these observations? 2

SS Total (0-2) 2 + (1-2) 2 + (3-2) 2 + (1-2) 2 + (0-2) (4-2) 2 + (3-2) 2 + (6-2) 2 + (3-2) 2 + (4-2) (1-2) 2 + (2-2) 2 + (0-2) = 46 ∑ (X ij – Grand mean) 2

SS Between = 30 n∑ (Group mean – Grand mean) 2 5 ∑ (1-2) 2 + (4-2) 2 + (1-2) 2 5 ( ) 5 (6)

SS within = 16 ∑ (X ij – Group mean j ) 2 SS placebo (0-1) 2 + (1-1) 2 + (3-1) 2 + (1-1) 2 +(0-1) = 6 SS CBT (4-4) 2 + (3-4) 2 + (6-4) 2 + (3-4) 2 + (4-4) = 6 SS gestalt (1-1) 2 + (2-1) 2 + (0-1) = 4

Degrees of Freedom Df total N – 1 15 – 1 14 Df between K – 1 3 – 1 2 Df within K (n – 1) 3 (5 – 1) 12

Mean Square MS between SS between / df between 30 / 2 15 MS within SS within / df within 16 /

F Ratio MS between / MS within 15 / Is F > 1? Yes! Is F big enough to reject Ho? Compare your F value to the F distribution Df numerator = Df between Df denominator = Df within = 2 = 12

F Ratio What is the critical value of F when  =.05? – 3.88 What is the critical value of F when  =.01? – 6.93 Is your F value greater than the critical values? – Yes! Can you reject Ho? At what alpha level? – Yes! At P <.01

Example 2: ANOVA by computer GroupSocial Anxiety 1 (Placebo) (CBT) Enter the data into SPSS...

Run the ANOVA Analyse, Compare Means, One Way ANOVA – Dependent List:Social Anxiety – Factor:Group – Options:Descriptives Homogeneity of variance test Means plot

Examine the means plot Are the means more or less the same or does one seem a little different?

Examine the test for Homogeneity of Variance Is Levine’s statistic significant? Can we assume homogeneity of variance among groups?

Examine the ANOVA table Is it similar to the one you created? What is the p value? Is it statistically significant? What can you conclude from this ANOVA? At least one mean is significantly different from the others

Multiple Comparisons According to the Bonferroni & Tukey posthoc tests, which means are significantly different from the others?

Example 3: T tests v ANOVAs Software/ Kevin Thomas/ ANOVA data set Analyse the ‘age’ & ‘adherence’ variables using an independent samples t test & an ANOVA Similar results? T 2 = ?

Example 4: Research example –Eysenck (1974) used three groups to investigate the impact of levels of processing (Craik & Lockhart, 1972) on incidental learning - learning in the absence of expectation that the material will need to be recalled later Group 1 - count number of letters in each word - lowest level of processing Group 2 - think of an adjective that might be used to describe the word Group 3 - form a vivid image of the word –What are H o & H 1 ? H o : There is no difference between the groups Level of processing has no effect on recall H 1 : At least one group is significantly different As level of processing increases, incidental memory increases

Run the ANOVA ANOVA dataset: Group & Recall variables What is the F value? Is F > 1? Is it statistically significant? What can we conclude? Conclude: At least one of the means is significantly different from the others Level of processing does significantly affect incidental recall

Which means are different? What does the means plot suggest?

Which means are different? What do the posthoc tests suggest?

Effect Size Calculate Eta squared Calculate Omega squared / =.44

Fully reporting the analysis –A one-way (or one-factor) analysis of variance (ANOVA) compared the mean number of words recalled across three groups who processed the words differently: count, adjective or imagery. With an alpha level of.05, the analysis was statistically significant, F(2,27) = , p 10).