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I ran an experiment with two factors each with two levels, 5 replicates each combination and one response variable. My data are non-normal and heterocedastic. Transformations didn't help. I ran a permutation ANOVA (aovp - package lmperm - R), but I am not sure this is the right way to go and I don't know what to do about a post hoc test, because I have a significant interaction. This is what my data look like: 

F1 F2 BIOMASS
A C 0.66
A C 0.31
A C 0.88
A C 0.55
A C 0.81
A D 0.39
A D 0.21
A D 0.17
A D 0.15
A D 0.18
B C 0.00
B C 0.18
B C 0.05
B C 0.00
B C 0.02
B D 0.16
B D 0.04
B D 0.21
B D 0.15
B D 0.06
gung - Reinstate Monica
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Mariana
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  • What is your response variable? Is it a continuous variable that just happens to fall between 0 & 1? Is it the proportion of successes from some number of Bernoulli trials? Is it a continuous proportion? – gung - Reinstate Monica Jun 11 '14 at 20:42
  • Your permutation test will assume equal distributions under the null. If you're after a location-shift alternative that won't be suitable (but it might work for a scale-shift). My first instinct would be to consider something like a GLM but it partly depends on what your response is. – Glen_b Jun 11 '14 at 23:59

1 Answers1

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Your response variable is suspicious. If it is a continuous proportion, you may want to pursue beta regression (I have an example of a BR in R here: Remove effect of factor on continuous proportion data using regression in R. If it is the outcome of some number of Bernoulli trials (and you know the number), you should disaggregate and use logistic regression (or use a weighted LR). The following assumes the data are simply from a continuous variable, and happen to be within the (0, 1) interval.

I think most of this may be covered by my answer here: Alternatives to one-way ANOVA for heteroscedastic data. In general, permutation tests are not recommended when you have heteroscedasticity. In your case, I might suggest using ordinal logistic regression. Since you have a 2x2, the post-hoc tests are just two 2-group comparisons, which could be done by repeating the original analysis on the stratified data. Under the assumption that the global test of the initial model is significant, I wouldn't even worry about multiple comparisons.

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gung - Reinstate Monica
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    My response variable is plant biomass... it just happened to be between 0 and 1. I took a look at the alternatives to one-way ANOVA, but I have two factors to analyse. I also checked the ordinal logistic regression but I don't think it makes sense for my data. I'll keep searching. Thanks anyways! – Mariana Jun 13 '14 at 13:31
  • I recognize that that question was about one-way ANOVA & you have a two-way ANOVA, but most of the methods will generalize to >1 factor. OLR is the most general non-parametric approach. All you need is for your data to be ordinal in nature, ie you need to be able to confidently say .66>.31, if you can say that, you can use OLR. – gung - Reinstate Monica Jun 13 '14 at 14:39