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As far as I know, CFU counts from bacterial suspensions should approximately follow a Poisson distribution. So in order to perform a One-way Anova, a mathematical transformation to achieve normality should be done. Am I correct on this? And which transformation would be ideal in this case? .

My issue is to compare means of colony forming unit counts from 3 groups of 8 mice. Each group has a different genotype. Shapiro-Wilks test for normality showed that the counts do not follow a normal distribution.


Thank you very much.

At least some of my counts are very large (mean counts for the three different groups are: G1: 337150; G2: 43000, G3: 16536000. However, I am unsure wether Poisson regression may be performed on counts this large.

The variance of the samples is huge (2.28397E+10^11; 4102357143; 9.29586E*10^14). This would constitute over dispersion, am I correct?

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There is no way to transform count data to a true normal distribution. Counts only have integer, non-negative values, while values from a normal distribution may be any real number.

What you need to do is Poisson regression, as discussed also on this page.

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