statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, and especially in the statistical analysis of

psychological Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...

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 In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...

. The counternull value is the effect size that is just as well supported by the data as the

null hypothesis The null hypothesis (often denoted ''H''0) is the claim in scientific research that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data o ...

. 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 (: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess o ...

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 op ...

. Other researchers prefer confidence intervals as a means of countering these common errors.

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Further reading