Given a significance test, How large a sample size is large enough?

“The sample size n is too small” is an often‐devastating criticism widely expressed in evaluating research. Researchers are often not aware, however, that, for reasons described herein, whether n be 2 or 2,000, rejection of the null hypothesis ( H 0 ) by a significance test immediately establishes that n is acceptably adequate to support the conclusion(s) that must then be drawn. Those conclusions amount to accepting an alternative hypothesis given the protocols followed in evaluating H 0 . Traditional fears of small n , however, really are warranted when H 0 is not rejected.