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# Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

## Repeated Measures ANOVA

The Repeated Measures ANOVA is similar to the One-Way ANOVA, but is used when comparing groups made up of the same people. In technical terms, each participant experiences each level of the independent variable, rather than a typical one-way ANOVA where each participant belongs to only one group.

Assumptions

1. One continuous (interval or ratio) dependent variable and one categorical (nominal or ordinal) independent variables with two or more dependent groups.
2. No significant outliers - can be assessed using boxplots, scatterplots, and other methods
3. Dependent variable is approximately normally distributed for each level of the independent variable
4. Sphericity - tested using Mauchly's test of sphericity

Running One-Way ANOVA in SPSS

1. Analyze > General Linear Model > Repeated Measures
2. Edit the Within-Subject Factor Name (default "factor1") to something more meaningful (i.e. IV name)
3. Enter the number of levels for that factor. Click "Add".
4. Edit the "Measure Name" to something more meaningful (i.e. DV name). Click "Add".
5. Click "Define" to move to the next window.
6. Transfer the variable for each level of the IV into their respective places in the Within-Subjects Variables box.
7. You may select additional output, such as descriptive statistics, using the Options button
8. You may include univariate graphs using the Plots button
9. You may include estimated marginal means using the EM Means button
10. You can select your post hoc test(s) using the Post Hoc button
11. Click OK to run the analysis

Interpreting the Output

• Descriptives (if you opted to include them)
• provides means and standard deviations based on combinations of levels of the IVs
• Tests of Within-Subjects Effects
• provides the results of the statistical tests
• test statistic = F-ratio
• associated probability = Sig.
• which value you report depends on the results of your sphericity test
• used to make a decision about the null hypothesis
• Pairwise Comparisons
• provides the results of the post hoc analysis
• allows you to determine exactly which groups are significantly different than each other
• compare the Sig. to your level of significance (i.e. .05)

Reporting Results in APA Style

A Repeated Measures ANOVA determined that word recall performance varied significantly across points in time (F(1.382, 21.813) = 25.21, p < .01). A post hoc analysis showed that while there was not a significant difference between recall performance at 12 hours (M = 32, SD = 8) and 24 hours (M = 28, SD = 7), recall performance at 48 hours (M = 12, SD = 3) was significantly lower than the previous checks.