If the uncertainty of the test result is unknown, the result is unreliable. It is therefore important to know the statistical precision of the analysis. A statistical test based on a sample size of 3 is not likely to provide sufficient statistical power. Figure 1. shows the relationship between statistical power and effect size (i.e. the mean difference relative to the standard deviation) when using Student’s t-test and dependent on the distribution of analysed variables.
Figure 1. The relation between statistical power and effect size with n=3.
One problem is that the statistical power depends on the distribution of the variable, and the statistical power to detect a non-Normal distribution (with the Shapiro-Wilk test) is minute with n=3. As a consequence, a huge effect size is necessary for testing with sufficient statistical power, and this means that the sensitivity to detect even a moderate difference in mean values is low, probably much lower than many lab investigators realise.
In addition, inadequate solutions to the multiplicity issue problem discussed here, leads to equally low specificity in the tests of mean values. The research results produced by such a methodology should not be taken too seriously.