I have a three-factorial experiment, and I am going to use three-way ANOVA, however, some of the response variables dot not fit in the assumption of normality (I use residuals), no matter how I transform the data, it just does not work. Then I thought I need to do a non-parametric test, but later I found out the non-parametric test is not valid for testing interactions. I am looking for the effect of each factor and also their interactions. Are there any methods to analyze these non-normal distributed data?
Use the Kruskal–Wallis test and/or Mood’s median test instead of ANOVA.
yes, that should work. at least if you've independent groups. Otherwise Friedman should be used.
Think about merging the factors. If one factor is gender and another one group with 2 levels each, you can combine them to one factor with 4 levels! If the overall effect is not significant, the interaction won't be, too. Use post hoc the Wilcoxon rank sum test.
AFAIK rank-based models can NOT model interactions. So I doubt that the previous answers are useful.
Lulu, what data do you have? How severe is the non-normality of the residuals?
Maybe the kind of data will suggest a different model (Beta, Gamma, Poisson, negative binomial, ...). Maybe the severity of the non-normality is not relevant.
If you still don't succeed and you have enough data (>20 values per cell - just to give a rough orientation), it is always possible to do bootstrapping.
Lulu, the response variable does not have to be normally distributed (in most linear model problems, they typically are not), the residuals from the linear model need to be normally distributed. If the residuals turn out to be non-normal, you could use Robust Regression, and if the error variance is not-constant, you can correct for that. This is easily done in the statistical programming language R (which is free, and you can easily find tutorials/examples) on the web. One place that has examples is
www.stats24x7.com
Hello, A.K.Singh, in my data, the residuals are not normally distributed. A statistician told me that the homogeneity is the most important thing for drawing conclusion from ANOVA, the normality somehow can be ignored. Is that true? This is the first time for me to hear the Robust Regression, but I need to do ANOVA not regression. I will check the Robust Regression.
ANOVA is a subset of linear models so what I wrote earlier applies in your case.
You can also use Robust OLS to fit linear model (for example, rlm of package R). See the link below:
http://www.ats.ucla.edu/stat/r/dae/rreg.htm
Run Mood's median test or Levene test. Otherwise you can run Cp/Cpk analysis. best of luck.
Hello, A.K.Singh, I just read some information about robust regression. The regression only can detect the single factor effect. In my experiment, I also need to see whether there are interactions among three factors. Do we have a method is able to detect the interactions as well?
If you have enough observations, robust regression will work for you. If you want to email me the data, I can take a look.
Hello, A.K.Singh, that would be great. Thank you so much. Is this your email address? [email protected]
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