Homework #5 A bit more Factorial ANOVA and Repeated Measures ANOVA

1) Purpose: To strengthen your conceptual understanding of contrast analysis in a factorial ANOVA. To give you hands-on experience using SPSS to conduct that type of analysis.

Recall the “Impact of Valence and Format of emotional expression on physical health” question from the previous homework (Question 4 from HW 4). The data are now available online. Please use SPSS to conduct two contrast analyses evaluating the hypothesis that emotional expression (in general) is better (ie, reduces health problems) than non-emotional (neutral) expression – doing this separately for Written and for Spoken formats.

Please be sure to clearly state your formal conclusions re the hypothesis in each case (is it supported or not) and comment on the effect size. Also, in a nutshell, what do the results generally say about the efficacy of emotional expression in the context of different types of expression? Please turn in the relevant SPSS syntax and output (just the contrast-related output would be fine, assuming you’re getting the right Overall ANOVA results).

A few helpful suggestions:

·  Make sure you’re running the right ANOVA, by comparing the ANOVA summary table to the one you used for HW4.

·  See the “Example 2” UNIANOVA syntax from the class handout “2 x 4 Factorial ANOVA with planned contrasts”. The current question asks only for 2 contrasts, not 6 (as illustrated in the handout); but the logic behind the current question fits the logic behind the handout example (where we looked at a contrast reflecting differences among types of therapy, separately for males and females).

·  Something to help you know you’re on the right track: The Partial eta squared for the “written format” results should be .266, and the Partial eta squared for the spoken format results should be .108. If you’re getting these values, then you know you’ve got the right output.

2) Purpose: To solidify your thinking about the meaning of various effects in a more complex factorial design.

In a three-way ANOVA, we have three independent variables. Imagine that we do a study with type of treatment (prozac, cognitive therapy, placebo), type of disorder (depression, anxiety), and age (below 40, above 40) as the three IVs, and symptom level as the DV.

a)  For such a design, how many main effects are there, how many two-way interactions are there, and how many three-way interactions are there?

b)  For each of the following effects, describe the information that we’ll get from testing the effect (that is, what question would be answered by testing the effect?):

i) main effect of type of treatment,

ii) treatment*disorder interaction,

iii) treatment*disorder*age interaction.

3) Purpose: Practice conducting and interpreting a basic repeated measures ANOVA, along with relevant post-hoc results. Practice conducting planned contrasts in RM ANOVA. Understand the “Tests of Within-subjects Contrasts” that’s a default output of SPSS’s repeated measures ANOVA.

Consider the following data, reflecting scores on a Well-being measure at 4 points in time:

Time

Subjects / 1 / 2 / 3 / 4
1 / 3 / 7 / 4 / 7
2 / 6 / 8 / 5 / 8
3 / 3 / 7 / 4 / 9
4 / 3 / 6 / 3 / 8
5 / 1 / 5 / 2 / 10
6 / 2 / 6 / 3 / 10
7 / 2 / 5 / 4 / 9
8 / 2 / 6 / 3 / 11

a)  Using SPSS, test the null hypothesis that well-being does not change. Please be clear about your formal decision (re the null) and comment on the size of the effect. What does the results mean, psychologically?

b)  Using SPSS, conduct three planned contrasts regarding three hypothesized patterns of change, as illustrated in the figure below (L pattern, Q pattern, and C pattern).

i.  For each hypothesis, describe the pattern being tested , in terms of how well-being is changing.

ii.  Do them all in SPSS, but also confirm your result for the L pattern by hand (please provide SPSS syntax/output and your hand calculations). Again, please be clear about your decisions (re the nulls) and note the effect sizes.

iii.  Based on these results, which hypothesis is most consistent with the changes actually exhibited by participants (note you could facilitate this by using the PLOT subcommand in GLM procedure)?

Hint: To get SPSS to do these contrasts, you can use a single MMATRIX statement, of the form: /MMATRIX = 'L pattern' score1 # score2 # score3 # score4 #; 'Q Pattern’ score1 # score2 # score3 # score4 #; ‘C Pattern ' score1 # score2 # score3 # score4 # (This assumes you name the variables “score1”, “score 2”, etc). Obviously you’d replace the “#” with the relevant contrast weights

c)  Look at the “Tests of Within-Subjects Contrasts” output that’s automatically printed by SPSS. I’m not sure why SPSS reports these particular contrasts by default, but since it does, we might as well know what they refer to. Compare your results from c to this default output and note the similarities – how do your contrasts from (c) match these default contrasts (e.g., in terms of F, p, and eta squared values)? .

4) Purpose: to give you practice conducting and interpreting a fairly standard “2-Way Mixed Factor Design”.

An industrial psychologist is interested in the effect of different kinds of reinforcement on worker productivity. She assigns 4 subjects to a “social reinforcement” condition (they receive personal notes and congratulations from managers for exemplary performance), 4 to a “material reinforcement” condition (they receive a small monetary bonus for exemplary performance), and 4 to a control group that receives no special reinforcement. The dependent variable is performance ratings over a 4 month period - one assessment per month for 4 months. She wants to analyze the relationship between reinforcement and change in performance.

Period
Subjects / 1 / 2 / 3 / 4
1 / 3 / 7 / 4 / 7
Social / 2 / 6 / 8 / 5 / 8
3 / 3 / 7 / 4 / 9
4 / 3 / 6 / 3 / 8
5 / 1 / 5 / 2 / 10
Monetary / 6 / 2 / 6 / 3 / 10
Reinforcement / 7 / 2 / 5 / 4 / 9
8 / 2 / 6 / 3 / 11
9 / 5 / 5 / 4 / 5
Control / 10 / 1 / 2 / 3 / 3
11 / 2 / 4 / 3 / 4
12 / 4 / 5 / 5 / 4

Using SPSS, conduct and interpret the ANOVA for the mixed model, including any appropriate post-hoc analyses. Turn in all relevant syntax and output (you don’t need to worry about multivariate stuff, assumptions, contrasts, etc – just turn in descriptives, anova summaries, and any relevant pairwise comparisons). Be sure to include your psychological conclusions – in a nutshell, what do the results tell us about the effects of reinforcement (e.g., presence of any reinforcement, type of reinforcement) on performance?