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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**

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

**Running One-Way ANOVA in SPSS**

- Analyze > General Linear Model > Univariate
- Move the continuous variable into the "Dependent Variable" box and the categorical variables into the "Fixed Factor(s)" box
- Click on the Post Hoc button
- choose the appropriate post hoc analysis for your study
- Select Continue

- You may select additional output, such as descriptive statistics, using the Options button
- You may include univariate graphs using the Plots button
- You may include estimated marginal means using the EM Means button
- You can select your post hoc test(s) using the Post Hoc button
- 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.

- Main effects - look for your individual IVs (i.e. gender and education level)
- Used to make a decision about the null hypothesis

- Provides the results of the statistical tests
- 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 (*p *= .003), but there was no difference noted with only high school (*p* = .42) or undergraduate levels of education (*p* = .19).

- Last Updated: Sep 12, 2023 12:38 PM
- URL: https://resources.nu.edu/statsresources
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