I am involved in the teaching of statistics to non-specialists and am concerned about improving practice within the sciences in particular. The problem with which I am confronted is that of non-specialists teaching students to use t-tests and ANOVA (including multiple comparisons tests) to test for a difference or association whilst ignoring the fact that their sample sizes are way too small for this to be sensible.
Clearly, confidence intervals are a good indicator of the lack of validity of any generalizations which are made on the basis of the results obtained. However, I suggest that given the small groups sizes, the scientists need to be pointed towards alternative, albeit more simplistic, approaches to demonstrating the possibility of a difference occurring (in fluorescence intensity, say) across two groups.
I am aware of a few possibilities such as plotting graphs and, where one wishes to compare consistency of measurements across two groups, considering the ratio of the variances. However, with a view to pointing non-specialists to a comprehensive list of good practice, I would be most grateful for any suggestions as to useful examples (found in textbooks but better still, publications) where research objectives have been achieved effectively in the absence of a t-test or an ANOVA, albeit a temptation to use them.
Perhaps also there is a paper on the very subject I am discussing which I could point people to when I feel less inclined to preach a sermon.
I look forward to receiving your replies.
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