This calculator evaluates the effect size between two means (i.e., Cohen's
*d*; Cohen, 1988), which is the difference between means divided by
standard deviation.

Enter the two means, plus SDs for each mean. To compute effect size using pooled or control condition SD, only enter one SD (computed as appropriate, of course).

For within-subjects studies, one must correct for dependence among means in order to make direct comparisons to effect sizes from between-subjects studies. To do this, you also need to enter the correlation between the two means, so that Morris and DeShon's (2002) equation 8 can be applied.

downloadable Excel version

Alternatively, enter the *t* score and sample size for each condition.
In this case, Ray and Shadish's (1996) equation 2 will be used, which produces
an equivalent effect size to using pooled SD. See the paper, and please don't
combine effect sizes using different SD terms.

I prefer to use the average of each mean's individual SD, as opposed to pooled or control condition SD. This decision is based on reading more than a dozen statistics papers on the topic (note that I am a psychologist, not a statistitian). I believe average SD is the best choice because this resulted in the greatest number of studies being included in my 2006 meta-analysis (and will do so in future meta-analyses, as well) and also because I found arguments for use of control condition or pooled SD inadequately strong to justify throwing out a large portion of studies. There is debate among statisticians about which SD term should be used, and I encourage you to read the literature on this issue if you want to be more fully informed.

Report the *d* value that gets output from this calculator. Also,
please report your choice of SD term. I encourage all researchers to report
effect sizes for their primary (and even secondary) comparisons.

Future researchers and meta-analysis producers should be fully informed about many aspects of your data. Effect sizes are one tool that will help researchers move beyond null hypothesis testing.

I am trying to encourage all researchers to include (proper) effect sizes in their papers. I want to make doing so as easy as possible. Even if you choose not to report effect sizes in your papers, please please include the information needed to compute effect sizes for your primary (and even secondary) comparisons, so that as many studies as possible can be included in future meta-analyses. Note that additional information is required for within-subjects studies, above and beyond current common practice, in order to compute within-subject effect sizes that are directly comparable to between-subjects effect sizes.

Cohen, J. (1988). *Statistical power analysis for the behavioral
sciences* (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates.

Morris, S. B., & DeShon, R. P. (2002). Combining effect size estimates
in meta-analysis with repeated measures and independent-groups designs.
*Psychological Methods*, *7*, 105-125.

Ray, J. W., & Shadish, W. R. (1996). How interchangeable are different
estimators of effect size? *Journal of Consulting and Clinical
Psychology*, *64*, 1316-1325. (see also “Correction to Ray and
Shadish (1996)”, *Journal of Consulting and Clinical Psychology*,
*66*, 532, 1998)

While every effort has been made to ensure that computations and claims are correct, no warranty is being provided. It is up to you to double check my calculations and read and evaluate the source articles. Source code is available upon request. If you notice an error, please let me know (ncepeda at yorku dot ca), so that I can look into the issue, and fix it as needed.