I am performing an ANCOVA. My dependent variable is the number of days a student is absent from school. As one can imagine, this variable is not normal, so I performed a log10 transformation. When I run the analysis with the transformed variable, I find no significant relationship with my variable of interest. However, when I run it with the original dependent variable the relationship is significant. Also, the homogeneity assumption is violated with the original dependent variable, but not with the transformed variable. Given the violations, I was under the impression that statistical power should be reduced. Why is it that I only find significant results when these assumptions are violated? Can someone help explain this to me? I should also mention that my sample sizes are quite unequal and in this case the smaller cell has a smaller variance on the dependent variable.
Solved – Non-normality and heterogeneity in ANCOVA
ancovadata transformationmodeling
Best Answer
First, without seeing the data, it is difficult, if not impossible, to tell exactly why you get significance with the model that violates the assumptions but not with the one that doesn't. However, one possible (likely) reason is that you had some students with a large number of absences that also had an unusual value on the independent variable (whatever it is - you could tell us). This would then be an influential point and cause a strange relationship.
Second, it is not the dependent variable that has to be normal, it is the residuals from the model. Have you tested those?
Third, days absent is a count variable. Therefore, unless the mean number of days absent is fairly high, you should not be doing ANCOVA at all, you should be doing some form of count regression. Possibly Poisson but more likely negative binomial regression. If this is over a relatively short time period, then you might even need a zero-inflated model, but it's hard to tell without the data.
Fourth, how did you take the log of the number of days absent? Surely some students had no days absent? Log(0) is undefined.