Counternull

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]

• assuming that failure to reject the null hypothesis at the chosen level of statistical significance means that the observed size of the "effect" is zero; and
• assuming that rejection of the null hypothesis at a particular p-value means that the measured "effect" is not only statistically significant, but also scientifically important.

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]

See also

• Publication bias