I have an experiment like this: control group (n=3), treatment group 1(n=3), and treatment group 2 (n=3). I have one readout for all 3 groups: plasma IL-6 level. do I have to do a normality test such as Shapiro-Wilk test for each group before we perform one-way ANOVA test? In fact, the minimal sample number per group for running Shapiro-Wilk test is 6. so, that means I have to do nonparametric ANOVA test instead? what about post hoc Turkey test? do we need to run this Turkey test after we pass a normality test for each group?
I'm really confused on this and looking forward to your help. Thanks,
Li,
Checking normality of the residuals suffices. If so, no need for checking normality of the original data of each group separately.
When you have such small groups no normality test has any meaning at all.
On the other hand the myth of 'normality' is too pervasive in applications, see attached file...
It is about IL-6 levels.
This is very well known to not being normal distributed. It is known - from a large body of empirical data and from theoretical work as well - that it is approximately log-normal (or gamma) distributed.
Testing the normal distribution makes no sense here at all. First, because an appropriate distribution model for variables like this is known, and second, because a formal test to test assumptions is logically flawed.
Using non-parametric analyses is essentially powerless for such small samples. Since you don't have homoscedasticity, test like KW, MW, or Dunn do not test location shifts per se. You might reject a hypothesis, but it is unlikely to pin down the meaning of the rejected hypothesis. In principle, bootstrapping could be used to estimate the sampling distribution of mean difference or ratio of IL-6 levels, but there is nothing much to bootstrap with just n=3 per group.
Why do some researchers always ask how the statistic fits to my convenience sample? Instead of having planned the experiment beforehand to determine how much sample would be enough to detect a certain effect with the treatments. With n = 3 you can't do anything. I sometimes ask myself "What is being teaching in basic Statistics courses?"
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