One-way within (repeated measures) groups ANOVA with post hoc comparisons

Activity 1A

One-way between groups (independent measures) ANOVA with post hoc comparisons

Synopsis: Researchers have administered a survey that measures the behavioural trait impulsivity to a sample of 90 drug users. The researchers are interested in examining whether there are any differences in impulsivity according to age, and have coded each of the age groups where Group 1: adolescent(n= 30),Group 2:younger adult(n=30),Group 3:older adult(n= 30).

• Inspect the assumption of normality for the variable impulsivity for each age group (i.e., split the file by age group and inspect histograms for the variable impulsivity). The DV is not normally distributed within each age group, and therefore the assumption of normality has been violated. As the sample size is greater than 30, and there are an equal number of subjects in each group (levels of the IV), we will continue with the analysis as ANOVA is robust to violations of normality under these conditions.

In order to conduct a One-Way between groups ANOVA with post hoc comparisons:

• Select Analyze
• Select Compare Means
• Select One-Way ANOVA...
• A dialog window will open
• Select the DV impul and move to the Dependent List
• Select the IV agegp and move to the Factor (IVs are called ‘factors in ANOVA)
• Click on Options...
• Under Statistics Select Descriptive, Homogeneity of variance test
• Select Means plot
• Click Continue
• Click on Post Hoc...
• Under Equal Variances Assumed select LSD and Tukey 
• Click Continue
• Click OK

The results for the analysis will be generated in an output viewer. There is alot of information displayed:

Descriptives: The mean and standard deviation of the DV (impulsivity) for each level of the IV (age group) are presented.

Test-of-Homogeneity-of-Variances: The results of Levenes test for homogeneity of variances are presented. If this sig value is greater than .05 there are no significant differences in the variances between the groups and the assumption is not violated.

ANOVA: The Sums of Squares, df, Mean Square, F value and Sig level is presented. This is the omnibus test that informs if there are any significant differences between the groups in the model overall. It does not inform where the significant differences are (which groups/levels of the IV significantly differ).

Post-Hoc-Tests: Only Inspect the table Multiple Comparisons if the omnibus test was significant. Both Tukeys HSD and LSD were requested (if you compare the two, the only difference is the confidence intervals surrounding the mean difference). This table presents the mean difference between each group, and significant differences are flagged with an asterisk, the exact level of significance is presented in the column sig.

Answer the following questions:

1. What is the null hypothesis?
2. What is the alternative hypothesis?
3. What is the independent variable?
4. How many levels of the independent variable are there?
5. What is the dependent variable?
6. Is Levene's Test for Equality of Variance non-significant?
7. What is the mean (and standard deviation) for Group 1?
8. What is the mean (and standard deviation) for Group 2?
9. What is the mean (and standard deviation) for Group 3?
10. Is there a significant difference between age groups on level of impulsivity? (Hint: Inspect omnibus test in ANOVA table)
11. What level of statistical significance has been achieved?
12. Should the null hypothesis be rejected?
13. What is the F-value?
14. What are the between groups df?
15. What are the within groups/error df?
16. What is the value for the between groups sums of squares (SSBetween)?
17. What is the value for the total sums of squares (SSTotal)?
18. What is ?2?
19. Is this considered a small, medium or large effect?
20. What percentage of the variation in impulsivity can be accounted for by age group?
21. What does the post hoc analysis inform?
22. Are there significant differences between Group 1 adolescent and Group 2 younger adult?
23. What is the mean difference?
24. What level of significance has been achieved?
25. What is Cohens d?
26. Are there significant differences between Group 1 adolescent and Group 3 older adult?
27. What is the mean difference?
28. What level of significance has been achieved?
29. What is Cohens d?
30. Are there significant differences between Group 2 younger adult and Group 3 older adult?
31. What is the mean difference?
32. What level of significance has been achieved?
33. What is Cohens d?

Activity 1 B

Synopsis: Researchers have administered a survey that measures the behavioural trait impulsivity to a sample of 50 drug users, before, during and after a rehabilitation program that aimed to treat impulse control disorders. The researchers are interested in examining whether there are any changes in the level of impulsivity as the drug users progress through the program.

In order to conduct a One-way within groups ANOVA with post hoc comparisons:

• Select Analyze
• Select General Linear Model
• Select Repeated Measures...
• A dialog window will open
• In the Within-Subject Factor name box, type "time"
• In the Number of Levels box, type 3 (as there are 3 testing times)
• Click Add
• Click on Define
• Select all three variables (impul1, impul2, impul3) and move them to the Within-Subjects Variables (time) box
• Click on Options
• Move the variable time to the box Display Means for
• Tick the Compare main effects box
• From the Confidence interval adjustment select: dropdown list, choose Bonferroni
• Under Display, select Descriptive statistics and Estimates of effect size
• Click on Continue
• Click OK

Answering the following questions:

1. What is the null hypothesis?
2. What is the alternative hypothesis?
3. What is the independent variable?
4. How many levels of the independent variable are there?
5. What is the dependent variable?
6. Are the variables impul1, impul2, impul3 normally distributed?
7. What is the mean (and standard deviation) impulsivity level at time 1?
8. What is the mean (and standard deviation) impulsivity level at time 2?
9. What is the mean (and standard deviation) impulsivity level at time 3?
10. Is Mauchlys Test of Sphericity non-significant?
11. Is there a significant difference in the levels of impulsivity across the testing times overall? (Hint: as the assumption of Sphericity has been violated, you should read the row Greenhouse-Geisser in the Tests of Within-Subjects Effects table.)
12. What level of statistical significance has been achieved?
13. Should the null hypothesis be rejected?
14. What is the F value?
15. What are the between groups df?
16. What are the within groups/error df?
17. What is ?2? (note: SPSS has calculated this, inspect column partial Eta squared)
18. Is this considered a small, medium or large effect?
19. What percentage of the variation in impulsivity can be accounted for by testing time?
20. What does the post hoc analysis inform?
21. Are there significant differences in impulsivity between Time 1 and Time 2?
22. What is the mean difference?
23. What level of significance has been achieved?
24. What is Cohens d?
25. Are there significant differences in impulsivity between Time 1 and Time 3?
26. What is the mean difference?
27. What level of significance has been achieved?
28. What is Cohens d?
29. Are there significant differences in impulsivity between Time 2 and Time 3?
30. What is the mean difference?
31. What level of significance has been achieved?
32. What is Cohens d?