Finding differences in means of not-normally distributed data

Question

I'm new to this forum but already have my first question. I'm a biology student, thus my knowledge about statistics in general is rather low ;)

I've measured the size of cells of different genotypes and treated with different growth factors and got the diagram below:

Each facet represents another genotype whereas the x axis gives the different treatments. Each point represents one cell. As you can see, the groups differ in the number of cells and their size.

I now want to know whether there are significant differences between these groups. My first approach was to simply count the cells, calculate the mean and standard deviation and using the Tukey's Range Test as exemplified for the hTNFtg Genotype.

cdata <- ddply(filter(Osteoclasts, Area < 50000),
           c("Genotype", "Stimulants"),
           summarise,
           N = length(Area),
           mean = mean(Area),
           sd = sd(Area))

Significance.hTNFtg <- aov(Area ~ Stimulants, filter(Osteoclasts, Genotype == "hTNFtg", Area < 50000))

Significance.hTNFtg.Table <- TukeyHSD(Significance.hTNFtg)

However, it came to my mind that one assumption for the Tukey's Test is normally distributed data and this is not the case for my data.

Can anyone help me? A small guide on which test to use would be quite helpful.

Answer 1

Good job noting the normality assumption. Just another note -- your data in each group should also be independent. If you have related data, this test won't work. The two assumptions here are really important.

Based on your data (plot shown), it appears that they are continuous, which makes sense for your cell size in question. Assuming if data in your treatment groups are independent (this is a question for you as the researcher), you can log2-transform your data. Based on the Central Limit Theorem, log transformation will generally allow your data to approach a normal distribution. With that, you will have met the normality assumption. To transform the data, you can run log2(cdata$mean).