In statistics, and especially in the statistical analysis of psychological data, the counternull is a statistic used to aid the understanding and presentation of research results. It revolves around the effect size, which is the mean magnitude of some effect divided by the standard deviation.[1]
The counternull value is the effect size that is just as well supported by the data as the null hypothesis.[2] In particular, when results are drawn from a distribution that is symmetrical about its mean, the counternull value is exactly twice the observed effect size.
The null hypothesis is a hypothesis set up to be tested against an alternative. Thus the counternull is an alternative hypothesis that, when used to replace the null hypothesis, generates the same p-value as had the original null hypothesis of “no difference.”[3]
Some researchers contend that reporting the counternull, in addition to the p-value, serves to counter two common errors of judgment:[4]
These arbitrary statistical thresholds create a discontinuity, causing unnecessary confusion and artificial controversy.[5]
Other researchers prefer confidence intervals as a means of countering these common errors.[6]