The .05 alpha level has long served as a standard for significance testing in educational research, a tradition that began with Ronald Fisher and Karl Pearson. Unlike previous authors who have criticized this tradition, we attempted to explain empirically why .05 is the preferred alpha level. In five experiments, undergraduate and graduate students were asked to consider after how many consecutive occurrences of either selecting red cards or obtaining "heads" coin flips would they consider the results not likely due to chance. Results showed that the modal stopping points, or most persons' thresholds for the dismissal of results as due to chance, had probabilities close to .05. Thus, the .05 alpha level appears to have a psychological basis.