THE COUNTERNULL VALUE OF AN EFFECT SIZE - A NEW STATISTIC

We introduce a new, readily computed statistic, the counternull value of an obtained effect size, which is the nonnull magnitude of effect s ize that is supported by exactly the same amount of evidence as suppor ts the null value of the effect size. In other words, if the counternu ll value were taken as the null hypothesis, the resulting p value woul d be the same as the obtained p value for the actual null hypothesis. Reporting the counternull in addition to the p value, virtually elimin ates two common errors: (a) equating failure to reject the null with t he estimation of the effect size as equal to zero and (b) taking the r ejection of a null hypothesis on the basis of a significant p value to imply a scientifically important finding. In many common situations w ith a one-degree-of-freedom effect size, the value of the counternull is simply twice the magnitude of the obtained effect size, but the cou nternull is defined in general, even with multi-degree-of-freedom effe ct sizes, and therefore can be applied when a confidence interval cann ot be. The use of the counternull can be especially useful in meta-ana lyses when evaluating the scientific importance of summary effect size s.