Week 8 Factorial ANOVA (Independent groups) Simple (main) effects and interactions, theoretical stuff

Transcription

1 PSY2004 Week 8 Factorial ANOVA (Independent groups) Simple (main) effects and interactions, theoretical stuff

2 Aims To introduce research questions involving factorial ANOVA To go through theoretical examples of what it looks like Interpretation of main effects (very similar to our old ANOVA) Interpretation of interactions To explain, using example data, how an analysis of simple effects allows an interpretation of potential main effects when an interaction is present.

3 Remember the original one-way ANOVA? E.g. a) Degree subject (3) and student hours of study b) Patients (4) receiving an intervention to reduce anxiety c) Or our example of the 7 groups of cows listening to different music and their milk yield So although we had different levels of the IV, the one-way ANOVA looks at only one IV and one DV- our research question relates to whether group A s score is different to group B s score, different to group C s score, etc

4 We might not always want to look at only one IV Research relates to real life Things are not always so simple that only one IV plays a role in our DV We might want to include other variables What else could play a role in the milk yield of cows?

5 The type of food eaten by cows???

6 Milking time? Day or night?

7 More than one IV Does a combination of IVs influence the value of a DV? The term way describes the number of IVs measured by an ANOVA One-way ANOVA measures the effect of one IV on a DV Two-way ANOVA measures the effect of two IVs on a DV Three-way ANOVA and so on In practice, ANOVA with greater than three independent variables is rarely used because of the complexity of interpreting the results.

8 What s in a name? The name of the ANOVA (one-way, two-way, etc ) tells us how many IVs are being examined: One IV - the design is a one-way ANOVA (e.g., does subject of study influence stigmatization of mental illness) Two IVs - the design is a two-way ANOVA (e.g., does degree subject or culture influence stigmatization of mental illness) Three IVs - the design is a three-way ANOVA (e.g., does degree subject, culture, or gender influence stigmatization of mental illness).

9 You will frequently see factorial ANOVA referred to by numbers, e.g., 2x2 ANOVA, 2x3 ANOVA, 3x3 ANOVA!!!???But what do these numbers mean???!!! Don t panic we simply describe each factor in our design by the number of levels or groups in the design. The examples above are all 2-way ANOVAs, because they have 2 IVs. The numbers represent the levels of our IVs. In a 2x2 ANOVA, we have 2 levels of IV, in a 2x3 ANOVA, we have 2 levels of one IV and 3 levels of the other IV.

10 Between groups factorial ANOVA Repeated measures and mixed designs will be addressed in a future lecture Independent variables are known as FACTORS The simplest factorial design is the 2x2 ANOVA, which just means that both IVs have two levels E.g., cows listen to music/ no music, milked by day/night

11 Another example of factorial design If we were looking at gender and type of exam taken these would be two independent factors GENDER of course has only have two levels: male or female TYPE OF ASSESSMENT might have multiple levels, e.g. MCQ, open book, essay, practical, etc

12 Quick Quiz Milk yield: Cows are milked by day or by night. They listen to rap, techno or classical music. This is an example of a _ x _ ANOVA. Lecturers social skills: Business, psychology and I.T. lecturers. With caffeine-free coffee, regular coffee or no coffee. This is an example of a _ x _ ANOVA. Exam performance: Students study for an exam by reading class notes or listening to a recording of the lecture. They then sit the exam in a very cold room or a comfortable room temperature room. This is an example of a _ x _ ANOVA.

13 Work in pairs (10 minutes) Each pair, take one page Think of examples where a between groups Factorial ANOVA might be used Write a very short paragraph on the research (3 or 4 sentences) Exchange your papers with a neighbouring group The other groups task is to answer the following questions: What is your DV? What are your IVs how many levels do your IVs have?

14 Main effects and interactions The effect of a single IV is known as a main effect The effect of two IVs considered together is known as an interaction For the two-way between groups design, an F- ratio is calculated for each of the following: The main effect of the first IV The main effect of the second IV The interaction between the first and second IV

15 Definitions 2-way ANOVA 2 independent variables (IVs) can have: Main Effect The effects of one independent variable (factor) summed (averaged) over all levels of the other independent variable. Interaction When the effect of one factor is not constant across all levels of the other factors.

16 Example Effect of music and alcohol on driving performance IV 1: Music On vs. Off IV 2: Alcohol None vs. 2 units DV: Mean number of driving errors made Method design (independent groups): music no music Alcohol group 1 group 2 No alcohol group 3 group 4

17 No effect of music or alcohol on driving errors made. Neither of these variables affect the DV Possible Outcomes No main effects No interaction IV2: Alcohol 2units no alcohol off IV1: Music on

18 Possible Outcomes Main effect for factor1 Main effect for factor 2 No interaction IV2: Alcohol 2units no alcohol off on IV1: Music

19 Possible Outcomes Main effect for factor1 No main effect for factor 2 No interaction IV2: Alcohol 2units no alcohol off on IV1: Music

20 Possible Outcomes No main effect for factor1 Main effect for factor 2 No interaction IV2: Alcohol 2units no alcohol off on IV1: Music

21 Possible Outcomes They essentially cancel each other out, so no main effect of music or alcohol No main effects Interaction IV2: Alcohol 2units no alcohol off on IV1: Music

22 Possible Outcomes The two lines are not acting the same across music on and off, they are not parallel. Main effect for factor1 Main effect for factor 2 Interaction IV2: Alcohol 2units no alcohol off on IV1: Music

23 I want to research the effect of therapy on locus of control in people with schizophrenia & people with depression Locus of control is a characteristic of self esteem which we all have and it is markedly low in psychological illness I want to know if therapies will help this one single aspect of psychological illness 3 different levels of therapy (CBT, psychoanalytic, family therapy) & 2 levels of illness types (SZ and depression) My dependent measure is the IMPROVEMENT scores on a test for locus of control by how many they increased from baseline after the therapy (not the raw scores)

24 Example Data- the effect of therapy on locus of control for different patient groups Factor 2: diagnosis Schizophrenia Depression Factor 1: Therapy Therapy A Therapy B Therapy C x 3 x 6 x x 1 x 2 x 3 x x 3 x 4 2

25 Interaction Graph Schizophrenia Mean improvement score Depression therapy A therapy B Type of Treatment therapy C

26 Interpreting Significant Interactions Significant interactions have implications for main effects!! In order to interpret any potential main effects, an analysis of Simple Effects should be conducted A Simple Effect is the effect of one independent variable at a particular level of the other independent variable 2 simple effects for type of therapy and 3 simple effects for type of disorder In order for a main effect to be interpretable, the simple effects for that variable must be the same for all levels of the other independent variable.

27 Let s go back to our Interaction Graph Therapy A and C are not different from each other in the schizophrenia group! Schizophrenia Mean improvement score Depression therapy A therapy B Type of treatment therapy C No difference between conditions for Therapy C!

28 Simple Effects testing for Type of therapy There are two simple effects for type of therapy: 1. The effect of treatment for schizophrenia 2. The effect of treatment for depression 1. The difference between therapies for people with schizophrenia 2. The difference between therapies for people with depression Analysis = Conduct TWO separate one-way independent groups ANOVA. using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the three therapies

29 If the effect of drug is the same for schizophrenics and depressives then there is an interpretable main effect for drug. The question we are addressing here is: - Is the effect for drug consistent (the same) for people with schizophrenia and depression? All we are doing is going back and looking at each group of patients individually, instead of all at once.

30 Simple Effects testing for Type of Disorder/diagnosis There are three simple effects for type of disorder: 1. the differences between patient groups for Therapy A 2. the differences between patient groups for Therapy B 3. the differences between patient groups for Therapy C Analysis = Conduct one-way independent groups ANOVA (or in this case could do post hoc t-tests as only two groups) using the MSerror from the original two-way ANOVA and appropriate degrees of freedom, to assess if there is any difference between the scores of the participants for each therapy alone

31 If differences between schizophrenics and depressives are in the same direction for all three types of drug then there is an interpretable main effect for type of problem. Is there? The question we are addressing here is: - Is the effect for type of problem consistent (the same) for all three types of drug?

32 Interaction Graph Schizophrenia Mean improvement score Depression therapy A therapy B therapy C Type of treatment

33 Summary Introduced factorial ANOVA Have discussed theoretical examples of what it looks like Interpreted main effects and interactions

34 Next week Simple effects