Hello Sarah,

Have you had a look at the distribution of model residuals from your proposed ancova? It's the residuals that need to be normally distributed, not the observed DV scores themselves.

If model errors aren't normally distributed, and you can't figure a way to transform the continuous variable scores so that they are, you could:

1. Use bootstrap/resampling methods to estimate effects and their confidence intervals; these do not require any distributional assumptions.

2. Have a look at some hybrid methods that have been around for some time (see references below). Each involves: (a) ranking scores; (b) applying the parametric test; and (c) interpreting significance either via the L criterion of Puri and Sen, or the ordinary p-value method of Iman and Conover.

Good luck with your work.

References:

Puri, M. L., & Sen, P. K. (1985). Nonparametric methods in general linear models. New York: Wiley.

Conover, W. J., & Iman, R. L. (1981). Rank transformation as a bridge between parametric and nonparametric statistics. The American Statistician, 35, 124-129. doi:10.2307/2683975

As David Morse has noted, it is the errors that are assumed to be (approximately) normal, not the DV. I will add quantile regression to the list of alternatives he suggested (in case the model errors are too far from normal, and there is no sensible transformation). But bear in mind that the fitted values from quantile regression (with the default settings) are conditional medians, not conditional means. HTH.

I would definitely disagree with Bruce Weaver. Quantile Regression is for quantile estimation which is not what you want. Another robust alternative is M estimation which is described in the first attachment here. An R version of my ancient BASIC can be found in Venables and Ripley Modern Applied Statistics available in the z-library. An excellent intro to R is also found there by Jared Lander R for Everyone, which contains much research grade code. Best wishes David Booth

Now there's a surprise. You always agree with me, David. :-O

What does the outcome look like? If its a count then I think this would lend itself to a GLM such as Poisson or Negative binomial regression possibly with zero inflation. I'm guessing the issue is there is severe skew in the outcome in which case a transformation may be sufficient but a generalized linear model (GLM) is often preferable .