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I am trying to compare the effect of two treatments (planting distance) on the growth of plants (multiple species), using the variable growth rate in diameter for multiple years. I have 4 sets of values for the growth rate (growth rate for each treatment and data for 2 years), but with different sample sizes (by including every plant). I understand that the sample sizes can be the same if I choose plants randomly. However, on checking for normality and homogeneity of variances, I found that one set of values are non-normal but have homogenous variances, whereas the others are non-normal and have heterogeneous variances. Which test would be the most suitable for such data values?

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  • $\begingroup$ I think there is no general answer without understanding your data more. Providing a histogram for each set of values would be a good start, some more mathematical theory of plant growth would also be great (if available). Note that it is not surprising that growth rates are non-normal as (I assume) negative growth rates do not occur while normal distribution would assume they are OK. $\endgroup$ Jan 24 '19 at 14:06
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If you're just trying to test for statistical significant difference between the two treatments you could use bootstrapping to do random sample-tests.

I also highly suggest reading this article by Allen Downey on the subject of statistical testing: There is still only one test as well as Jake Vanderplas' presentation at PyCon2016 on the same subject: Statistics for Hackers - PyCon 2016

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You could try a mixed model approach since it seems you have repeated measures (actually I do not understand your experiment design), if you don't have repeat measures you can use a linear model with treatments as explanatory variables. In the modelling approach you must concern only with residuals normality and variance homogeneity, even if your response are not normally distributed.

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