Effect Size Calculator

What It Does

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.

Between-subjects Studies

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).

Within-subjects Studies

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.

Calculator for Means and SDs

downloadable Excel version

Mean 1: SD 1:

Mean 2: SD 2:

Required. SD 2 is optional but recommended. See description below.

Correlation between means:

Use for within-subjects data only. See description above.

Calculation Using t score

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.

Calculator for t scores and Sample Sizes

t score:

n for Mean 1: n for Mean 2:

Required. Use for between-subjects data only.

Choice of SD Term

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.

What to Report

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.

Why Report Effect Sizes

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.

Why Make a Calculator

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.

References

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)

Disclaimer

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.