Normality violations - still use ANOVA?

[jhartsho]

Hi all,

I am having some trouble deciding which test to run for a chapter of my thesis. The brief intro is that I felled trees, cut them into an even number of logs and then randomly assigned those logs to a treatment (i.e. a treatment could have 2 A logs, 1 B and 2 C or 1 A, 3 Bs and 1 C etc...). My treatments were time left in the field. The first set was brought in immediately, second set after 15 days, third after 30 days and final set after 45 days. I cut them at 3 points (both ends and the center) to look at the decrease in moisture content. This way I can look at how moisture changes over time as well as how it changed along the length of the log.

After looking at the distribution of my final moisture measurements, my data are not normal. It is fairly even across and not really skewed one way or the other. I plotted a qq plot but that is kind of an eyeball type of thing so I also ran a shapiro test which returned a sig p value.

Even though my p value there is significant, my advisor still wants me to use a one-way ANOVA bc normality is the only violation and, in his eyes, is not violated "enough" to warrant a non-parametric. I have also transformed the data and cannot get a normal distribution that way either.

I have performed a regular ANOVA with sig results. I also performed a kruskal-wallis with sig results. I am wondering, since it looks to be sig in any situation - do I stick with the ANOVA to have an easier time of interpretation? I would not be able to explain why I still used it after failing a normality test - unless someone here as a reason why it would be okay.

I think for my thesis and defense it would be okay but this should be publishable and I do not want to have to change everything with a letter from the editor telling me i'm an idiot and that I can't publish with my stats the way they are....

Any suggestions?

[duskstar]

Its an interesting question that you raise. I guess a lot depends on how much the normality assumption is being violated, many people would just quote that the test is robust and leave it at that. However, I think you are right to question it. Maybe this paper will help you:

Lix L. M., Keselman J. C., Keselman H. J. (1996). Consequences of assumption violations revisited: a quantitative review of alternatives to the one-way analysis of variance F test. Rev. Educ. Res. 66, 579–620. doi: 10.3102/00346543066004579.

[Dason]

Note that the normality assumption is on the error term. Do the residuals from your analysis look approximately normally distributed?