One salient feature of randomized clinical trials is that patients are randomly allocated to treatment groups, but not randomly sampled from any target population. Without random sampling parametric analyses are inexact, yet they are still often used in clinical trials. Given the availability of an exact test, it would still be conceivable to argue convincingly that for technical reasons (upon which we elaborate) a parametric test might be preferable in some situations. Having acknowledged this possibility, we point out that such an argument cannot be convincing without supporting facts concerning the specifics of the problem at hand. Moreover, we have never seen these arguments made in practice. We conclude that the frequent preference for parametric analyses over exact analyses is without merit. In this article we briefly present the scientific basis for preferring exact tests, and refer the interested reader to the vast literature backing up these claims. We also refute the assertions offered in some recent publications promoting parametric analyses as being superior in some general sense to exact analyses. In asking the reader to keep an open mind to our arguments, we are suggesting the possibility that numerous researchers have published incorrect advice, which has then been taught extensively in schools. We ask the reader to consider the relative merits of the arguments, but not the frequency with which each argument is made.