Assumptions in ANCOVA, and consequences of violating them


New Member
I ran an ANOVA with 4 predictors (2 categorical, 2 continuous) and 1 covariate (continuous). Including the covariate did not significantly alter the main effects of the ANOVA when it was run without the covariate, so I concluded that the covariate did not need to be included in the overall model, as it had no added benefit.

When investigating possible reasons why it might have had no benefit, I played around with the data a bit and found that one of the categorical variables had a significant effect on the original covariate when I ran an independent samples t-test (i.e. scores on the covariate were significantly lower in the 'Low' categorical condition, compared to 'Control'). I assumed this meant that the homogeneity of regression slopes assumption had been violated, so I was going to conclude that it was possible that the covariate had no benefit in the initial ANOVA because it had already been captured within the categorical variable.

However, when I actually found out how to test for homogeneity of regression slopes (this is all above the level of stats that I've been required to learn, so I'm doing lots of guesswork), the categorical*covariate interaction in my custom GLM was non-significant. Does this mean that the homogeneity of regression slopes was not actually violated? If so, why did I find the significant effect on the covariate when using it as a DV in the t-test? And does that make my conclusion wrong?

As you can probably tell I'm pretty confused here, so all help is greatly appreciated. I've probably also not been very clear writing this out because I don't really understand what I'm talking about, so I'd be happy to clarify anything.