| Abstract: | Larkin and Rainard's (1984) article was sufficiently interesting not only to have me recommending it to others but also to re-read it for a third time. Unhappily I then realized that as a biproduct I had been giving my students an entrée into the old fallacy of inverse probability (see R. A. Fisher's, The Design of Experiments, Chapter 1). The fallacy occurs on pages 252 and 253. The authors say: “ ? sample size is rarely important to generalizability. Suppose, for example, 500 or 10 individuals are tested out of a population of 5000. Testing 500 (instead of 10) decreases the standard error of the mean by only a factor of 1.1 = (1–10/5000)/(1–500/5000)]. Most research does not use large samples to increase generalizability. Instead the function is either to estimate many parameters in a detailed model, or to increase statistical significance, a factor sensitive to sample size.” |
