ABSTRACT: Uses the data of B. D. Layton and B. Turnbull's (see PA, Vol 54:Issue 2) 2 ESP experiments to illustrate Bayesian hypothesis tests that provide more useful information than is obtained from significance tests. It is noted that the use of significance tests has tended to foster negative evaluation of "nonsignificant" findings relative to "significant" findings. The present Bayesian hypothesis tests indicate that Layton and Turnbull's findings should generally be taken as support for their null hypotheses (no ESP effects) rather than for the weakest alternatives that their experiments had reasonable power to detect.