In statistics, and especially in the statistical analysis of

psychological Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries betw ...

data, the counternull is a statistic used to aid the understanding and presentation of research results. It revolves around the

effect size In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the ...

, which is the mean magnitude of some effect divided by the standard deviation. The counternull value is the effect size that is just as well supported by the data as the

null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...

. 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 A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can testable, test it. Scientists generally base scientific hypotheses on prev ...

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 In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means ...

as had the original null hypothesis of “no difference.” Some researchers contend that reporting the counternull, in addition to the ''p''-value, serves to counter two common errors of judgment: * 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 Controversy is a state of prolonged public dispute or debate, usually concerning a matter of conflicting opinion or point of view. The word was coined from the Latin ''controversia'', as a composite of ''controversus'' – "turned in an opposite d ...

. Other researchers prefer

confidence interval In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as ...

s as a means of countering these common errors.

References

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See also

References

Further reading