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Lecture 15: ANOVA Interactions
Laura McAvinue School of Psychology Trinity College Dublin
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Factorial ANOVA Two or more independent variables
Allows us to examine two kinds of ‘effect’. What are these? Main effects The effect of each independent variable, controlling for the other variable Simple effects Interaction between the independent variables The effect of one independent variable at one level of another variable
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Recall our research example
We would like to examine the effectiveness of three kinds of therapy (CBT, psychoanalytic, drug) on depressive symptoms displayed by men & women This design will enable us to investigate three things What are these? Main effect of Gender Main effect of Therapy Interaction between Gender & Therapy
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Recall our research example
Examine the following graphs of possible results for our study and for each one tell me… Is there a main effect of Gender? Is there a main effect of Therapy? Is there an interaction between Gender & Therapy?
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Main effect of Gender Interaction
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Main effect of Therapy Interaction
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No effect of Gender or Therapy
Main effect of Therapy
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Main effect of Gender & Therapy
Interaction
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Graphs of Interactions
No interaction Lines are parallel Interaction Lines are not parallel Lines cross or look like they might cross if the graph was extrapolated Is the interaction significant? ANOVA, significance of F value
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Interactions The independent variables have a combined effect on the dependent variable The effects of one variable differ at different levels of the other variable Renders a main effect less important Often, if there is an interaction, you should focus on this rather than on the main effects
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Interactions So, you have found a significant interaction between the independent variables… But what kind of interaction is it? Examine graph Analysis of Simple Effects Factorial ANOVA enables you to pair each level of one variable with every level of the other variable Analysis of simple effects allows you to tease apart the interaction …allows you to compare the pairings to see where the interaction lies
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Simple Effects The effect of one variable at just one level of a second variable Involves running several One Way ANOVAs You exclude certain parts of the data and just examine the parts you are interested in There are often many simple effects that you can analyse But you increase the risk of making a Type I error Usually, go by the graph and only analyse the simple effects that you think are important
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Our Research Example 30 Can’t say that one type of therapy is better for all clients Depends on gender Can’t say that one gender does better than the other Depends on therapy Need to consider both gender & therapy when interpreting data 25 20 15 male female 10 5 CBT Psycho- analytic Drug
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Simple Effects We need to examine the effects of Gender at all levels of Therapy & The effects of Therapy at all levels of Gender This gives us 5 simple effects to analyse What are these?
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Simple Effects The effects of Gender at all levels of Therapy
The effect of gender in CBT condition Do men & women receiving CBT differ? The effect of gender in psychoanalysis condition Do men & women receiving psychoanalysis differ? The effect of gender in drug condition Do men & women receiving drugs differ? The effects of Therapy at each level of Gender The effect of therapy for males Is at least one therapy mean significantly different from the others for males? The effect of therapy for females Is at least one therapy mean significantly different from the others for females?
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Simple Effect 1: The effect of Gender under CBT condition
Which means do we compare? CBT Psychoanalytic Drug Males 10 16 24 8 18 26 6 20 28 Females 22 4
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Simple Effect 2: The effect of gender under psychoanalysis condition
Which means do we compare? CBT Psychoanalytic Drug Males 10 16 24 8 18 26 6 20 28 Females 22 4
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Simple Effect 3: The effect of gender under drug condition
Which means do we compare? CBT Psychoanalytic Drug Males 10 16 24 8 18 26 6 20 28 Females 22 4
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Simple Effect 4: The effect of therapy for males
Which means do we compare? CBT Psychoanalytic Drug Males 10 16 24 8 18 26 6 20 28 Females 22 4
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Simple Effect 5: The effect of therapy for females
Which means do we compare? CBT Psychoanalytic Drug Males 10 16 24 8 18 26 6 20 28 Females 22 4
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Simple Effects on SPSS Not easy to do on SPSS
To examine the effects of gender at all levels of therapy… Split file Organise output according to therapy One Way ANOVA with gender as independent variable & depression as dependent variable Output will produce three One Way ANOVAs The effects of gender on depression under CBT condition The effects of gender on depression under psychoanalysis The effects of gender on depression under drug condition
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Simple effects of gender at each level of therapy
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Simple Effects on SPSS To examine the effects of therapy at each level of gender… Split file Organise output according to gender One Way ANOVA with therapy as independent variable & depression as dependent variable Output will produce two One Way ANOVAs The effects of therapy on depression for males The effects of therapy on depression for females
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Simple effects of therapy at each level of gender
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Create a new ANOVA table
By hand! Take the average variation (MS) due to each of your simple effects Create a new ANOVA table using these MS & the old MSerror term Compute F ratio for each simple effect by comparing the MS for each simple effect to the original MSerror term Look up the probability of obtaining this F ratio when Ho is true, using the F distribution table
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The original ANOVA Original MSerror = 4
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Simple Effects of Gender at all levels of Therapy
Simple Effects of Therapy at each level of Gender
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Simple Effects ANOVA table
Original ANOVA table Source SS Df MS F Pvalue Gender 8 1 2 .183 Therapy 496 248 62 .000 Gender*Therapy 448 224 56 Error 48 12 4 Simple Effects ANOVA table Source SS Df MS F Critical F Signif? Gender at CBT 216 1 54 4.75 Yes Gender at Psycho Gender at Drug 24 6 Therapy at males 448 2 224 56 3.89 Therapy at females 456 228 57 Error 48 12 4
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What can we conclude? No main effect of gender Main effect of therapy
Interaction between gender & therapy All simple effects are statistically significant
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