Statistics to tell the truth, the whole truth, and nothing but the truth: Formulae, illustrative numerical examples, and heuristic interpretation of effect size analyses for neuropsychological researchers

If, as neuropsychologists, we think of the relationship between brain and behavior as the same as that between truth and reality, we must be equipped with statistical procedures that are coherent in terms of what we measure and what it represents. I believe that this necessary statistical procedure is effect size analysis, and without it, I believe that we fail to tell the truth, the whole truth, and nothing but the truth when describing our neuropsychological research. Accordingly, I review here the standard calculations of commonly employed effect sizes in two group designs and show how to adjust some familiar (and perhaps not so familiar) formulae using illustrative numerical examples. I also put forth an argument to adopt Cohenʹs measure as an expression of effect size based on its apropos to neuropsychological research. It is also argued that the interpretation of the magnitude of an effect size should depend on context, and not on pre-established heuristic benchmarks. It is noted, however, that effect sizes greater than 3.0 (OL%<5) might seem particularly appropriate when evaluating the sensitivity of neuropsychological tasks and in establishing test markers in neuropsychological disorders.