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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.

## Two-Way ANOVA

The Two-Way ANOVA is similar to the One-Way ANOVA, but is used when comparing groups on two different categorical variables (i.e. gender and level of education). The biggest difference between the One-Way and the Two-Way ANOVA is that in a Two-Way ANOVA, you are interpreting main effects and interaction effects.

• Main effects - think of this like a t-test (if only two levels of the IV)  or a One-Way ANOVA (if more than two levels)
• If we were only looking at gender as a factor, is there a significant difference?
• If we were only looking at level of education as a factor, is there a significant difference?
• Interaction effects - this looks at pairings of the levels of each IV to determine if the interaction of those variables leads to a significant difference
• Example: Males with a High School Diploma, Females with an Associate's Degree

Assumptions

1. One continuous (interval or ratio) dependent variable and two categorical (nominal or ordinal) independent variables with two or more levels.
2. Independence of observations - usually evaluated based on the research design - participants only belong in one group of each IV
3. No significant outliers - can be assessed using boxplots, scatterplots, and other methods
4. The dependent variable is approximately normally distributed for each combination of the levels of the independent variables
5. Homogeneity of variances for each combination of the levels of the independent variables

Running One-Way ANOVA in SPSS

1. Analyze > General Linear Model > Univariate
2. Move the continuous variable into the "Dependent Variable" box and the categorical variables into the "Fixed Factor(s)" box
3. Click on the Post Hoc button
• choose the appropriate post hoc analysis for your study
• Select Continue
4. You may select additional output, such as descriptive statistics, using the Options button
5. You may include univariate graphs using the Plots button
6. You may include estimated marginal means using the EM Means button
7. You can select your post hoc test(s) using the Post Hoc button
8. Select 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 Between-Subjects Effects
• Provides the results of the statistical tests
• Main effects - look for your individual IVs (i.e. gender and education level)
• test statistic = F-ratio
• associated probability = Sig.
• Interaction effects - look for the combination of your two IVs (i.e. gender*education level)
• test statistic = F-ratio
• associated probability - Sig.
• Used to make a decision about the null hypothesis
• Multiple 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 Two-Way ANOVA was conducted to determine to what extent gender and education level have an effect on income. There was a statistically significant interaction between the effects of gender and education level on income (F(2, 37) = 5.21, p < .01). Simple main effects analysis showed that females earned significantly lower incomes than males when higher levels of education had been pursued (= .003), but there was no difference noted with only high school (p = .42) or undergraduate levels of education (p = .19).