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For a one‐sample z‐test, Cohen's d (Cohen, 1988) is defined as the absolute distance between the observed sample mean and the population mean under the null hypothesis, divided by the population standard deviation:

In the above, since is serving as the estimate of μ, the numerator can also be given as μ − μ₀. However, using instead of μ above is a reminder of where this mean is coming from. It is coming from our sample data, and we wish to compare that sample mean to the population mean μ₀ under the null hypothesis.

As an example, where , μ₀ = 18, and σ = 2 Cohen's d is computed as:

Cohen offered the guidelines of 0.20, 0.50, and 0.80 as representing small, medium, and large effects respectively (Cohen, 1988). However, relying on effect size guidelines to indicate the absolute size of an experimental or nonexperimental effect should only be done in the complete and absolute absence of all other information for the research area. In the end, it is the researcher, armed with knowledge of the history of the phenomenon under study, who must evaluate whether an effect is small or large. For instance, referring to the achievement example discussed earlier, Cohen's d would be equal to:

The effect size of 0.1 is small according to Cohen's guidelines, but more importantly, also small substantively, since a difference in means of 1 point is, by all accounts, likely trivial. In this case, both Cohen's guidelines and the actual substantive evaluation of the size of effect coincide. However, this is not always the case. In physical or biological experiments, for instance, one can easily imagine examples for which an effect size of even 0.8 might be considered “small” relative to the research area under investigation, since the degree of control the investigator can impose over his or her subjects is much greater. In such cases, it may very well be that Cohen's d values in the neighborhood of two or three would be required for an effect to be considered “large.” The point is that only in the complete absence of information regarding an area of investigation is it appropriate to use “rules of thumb” to evaluate the size of effect. Cohen's d, or effect size measures in general, should always be used in conjunction with statements of statistical significance, since they tell the researcher what she is actually wanting to know, that of the estimated separation between sample data (often in the form of a sample mean) and the null hypothesis under investigation. Oftentimes meta‐analysis, which is a study of the overall measure of effect for a given phenomenon, can be helpful in comparing new research findings to the “status quo” in a given field. For a thorough user‐friendly overview of the methodology, consult Shelby and Vaske (2008).