# Interpretation of ANCOVA interaction term

I have some doubts in how to interpret the interaction term in an ANCOVA using R since in other statistical programs this term is not provided. If I am right, one assumption of ANCOVA is the Homogeneity of regression slopes (that is, they must be parallel). Not following this assumption means you cannot use ANCOVA.

My question is, can the interaction term be interpreted as a test for the homogeneity of regression slopes? I meant, if is significance is because the slopes are not parallel and the model cannot be ran. If not, how can I test for it?

Here is an example

Thanks,

## 1 Answer

1- can the interaction term be interpreted as a test for the homogeneity of regression slopes?

Yes, you can. An essential aspect is to verify the homogeneity of slopes between groups defined by the categorical variable. In this case, sex.

2- I meant, if is significance is because the slopes are not parallel and the model cannot be ran. If not, how can I test for it?

One of the assumptions of ANOVA it is the covariable (weight) has the same slope for each group. So if the interaction term it is not significant, the slopes of the 2 groups are not significantly different from each other and therefore there is a common, general slope between sex and weight.

It means you couldn't reject the null hypothesis. The slopes are parallels. On the other hand, if the interaction term it is significant, the slopes are not parallel and you can run a more simple model, only with the single terms.

In your particular example, your model outcome shows the interaction between sex and log(weight) is not significant. So you can dispense with the interaction term and use the single terms to interpret your results. In this case, your variable response depends separately on sex and log(weight) but not on the interaction.

To understand a little bit more of how ANCOVA works, please see Ancova it is a linear regression model.