Created by Kristoffer Magnusson

The Cohen's *d* effect size is immensely popular in psychology. However, its interpretation is not straightforward for clinicians and laypersons, as it requires prior knowledge about what a standard deviation is. Even practicing scientists often turn to general guidelines, such as small (0.2), medium (0.5) and large (0.8) when interpreting the effect of an intervention.

These cut-offs were introduced by Cohen himself, but with a strong caution that "this is an operation fraught with many dangers" (Cohen, 1977). Just like *p*-values, these arbitrary cut-offs seem to be used mindlessly today. I believe that such "canned effect sizes" (Baguley, 2009, p. 613) should be avoided. Findings from studies need to be interpreted by their practical and clinical significance. Factors like the quality of the study, the uncertainty of the estimate and results from previous work in the field need to be appraised before declaring an effect "large".

In order to aid the interpretation of Cohen’s *d* this visualization offers these different representations of Cohen's *d*: Visually, Cohen’s U_{3}, Probability of superiority, Percentage of overlap and Number needed to treat.

^{1} It is assumed that % of the control group have "favorable outcomes", i.e. improve below some predefined cut-off. Change this by pressing the symbol above the slider. Go to the formula section for more information.

If you enjoy my work, or maybe even use it in your own teaching, please consider supporting me on Patreon. My visualizations will always be free to use, but you can show your support by donating a dollar or two for every new visualization I create.

Here are some books that I have found useful both in understanding effect sizes and calculating them.

- Statistical Power Analysis for the Behavioral Sciences (2nd Edition)
- The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results
- Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis (Multivariate Applications Series)
- Effect Sizes for Research: Univariate and Multivariate Applications, Second Edition
- Introduction to Meta-Analysis
- Practical Meta-Analysis (Applied Social Research Methods)

CER <- 0.2 d <- 0.2 1 / (pnorm(d + qnorm(CER))-CER)

- Baguley, T. (2009). Standardized or simple effect size: what should be reported?
*British journal of psychology, 100*(Pt 3), 603–17. - Cohen, J. (1977).
*Statistical power analysis for the behavioral sciencies.*Routledge. - Furukawa, T. A., & Leucht, S. (2011). How to obtain NNT from Cohen's d: comparison of two methods.
*PloS one, 6*(4). - Reiser, B., & Faraggi, D. (1999). Confidence intervals for the overlapping coefficient: the normal equal variance case.
*Journal of the Royal Statistical Society, 48*(3), 413-418. - Ruscio, J. (2008). A probability-based measure of effect size: robustness to base rates and other factors.
*Psychological methods, 13*(1), 19–30. - Ruscio, J., & Mullen, T. (2012). Confidence Intervals for the Probability of Superiority Effect Size Measure and the Area Under a Receiver Operating Characteristic Curve.
*Multivariate Behavioral Research, 47*(2), 201–223.

Date | Changes |
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2014-02-03 | Added "settings". Let the user change CER, step size and slider's max value |

2014-01-13 | Initial release |