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".
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.” From the Editor, Iacobucci, Dawn, , , Journal of Consumer Research, 2005
Some researchers contend that reporting the counternull, in addition to the ''p''-value, serves to counter two common errors of judgment: The counternull value of an effect size: A new statistic, Rosenthal, R., , , Psychological Science, 1994

★ 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^[3]

Contents

See also

References

Further reading

See also

★ File drawer problem

References

1. Steven's handbook of experimental psychology, Pashler, Harold E.; Stevens, S. S., , , John Wiley & Sons, 2002,
2. Contrasts and effect sizes in behavioral research: a correlational approach, Rubin, Donald B.; Rosenthal, Robert; Rosnow, Ralph L., , , Cambridge University Press, 2000,
3. Pasher (2002), p. 348: "The reject/fail-to-reject [the null hypothesis] dichotomy keeps the field awash in confusion and artificial controversy."

Further reading

★ Rosnow, R. L., & Rosenthal, R. (1996). Computing contrasts, effect sizes, and counternulls on other people's published data: General procedures for research consumers. Psychological Methods, 1, 331-340