## What is homogeneity of regression slopes?

When an ANCOVA is conducted we look at the overall relationship between the outcome (dependent variable) and the covariate: we fit a regression line to the entire data set, ignoring to which group a person belongs. This assumption is very important and is called the assumption of homogeneity of regression slopes.

**How do you test for homogeneity of slopes?**

How to Test

- Conduct a correlation analysis between the dependent variable(s) and the covariate(s). They should be highly correlated.
- A scatter plot of the dependent variable(s) and the covariate(s) by factor group should show that all lines have a similar slope.

**Can covariates in ANCOVA be categorical?**

Note: You can have more than one covariate and although covariates are traditionally measured on a continuous scale, they can also be categorical. However, when the covariates are categorical, the analysis is not often called ANCOVA. If you have two independent variables rather than one, you could run a two-way ANCOVA.

### What if Levene’s test is significant in ANCOVA?

Levene’s test is significant, indicating that the group variances are not equal (hence the assumption of homogeneity of variance is likley been violated). This value is greater than 2 indicating that our variances are probably heterogeneous!

**What is a repeated measures ANCOVA?**

The repeated measures ANCOVA compares means across one or more variables that are based on repeated observations while controlling for a confounding variable. Again, a repeated measures ANCOVA has at least one dependent variable and one covariate, with the dependent variable containing more than one observation.

**What does homogeneity of slopes mean?**

#### How do you check for homogeneity of regression slopes in R?

Use Anova() to test homogeneity of regression slopes To test the assumption of homogeneity of regression slopes we need to run the ANCOVA again, but include the interaction between the covariate and predictor variable.

**Is ANCOVA the same as multiple regression?**

ANCOVA and multiple linear regression are similar, but regression is more appropriate when the emphasis is on the dependent outcome variable, while ANCOVA is more appropriate when the emphasis is on comparing the groups from one of the independent variables.

**Can a covariate be nominal?**

As explained by Kolawole, a nominal variable can be used as covariate but interpretation of the results need some reference range, i.e. what type of labeling of the original variable (or dummy )is used.

## What to do if the Levene test is significant?

Levene’s test is often used before a comparison of means. When Levene’s test shows significance, one should switch to more generalized tests that is free from homoscedasticity assumptions (sometimes even non-parametric tests). Welch’s t-test, or unequal variances t-test is a more conservative test.

**What makes a Levene’s test significant?**

For now, let’s just assume it’s met. Next, our sample sizes are sharply unequal so we really need to meet the homogeneity of variances assumption. However, Levene’s test is statistically significant because its p < 0.05: we reject its null hypothesis of equal population variances.