Statistical measures like P-Values and R Squares are dragged out to prove a number of things. But caution should be considered. This Nature article does a good job of explaining the needed cautions:
" ... Scientific method: Statistical errors
P values, the 'gold standard' of statistical validity, are not as reliable as many scientists assume.
by Regina Nuzzo ... "
The final quote in the article brings us back to how any study, analytic or statistical should be considered. It is about the process involved.
" .... Statistician Richard Royall of Johns Hopkins Bloomberg School of Public Health in Baltimore, Maryland, said that there are three questions a scientist might want to ask after a study: 'What is the evidence?' 'What should I believe?' and 'What should I do?' One method cannot answer all these questions, Goodman says: “The numbers are where the scientific discussion should start, not end. .... "
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