# Short R script to plot effect sizes (Cohen's d) and shade overlapping area

Update: I have created an interactive effect size visualization here

## Introduction to effect sizes

Many times you read in a study that βx and y were significantly different, p < .05β, which is another way of saying that βassuming that the null hypothesis is true, the probability of getting the observed value simply by chance alone is less than 0.05β But thatβs not really that interesting, though is it? Say you are reading an intervention study that are comparing a treatment group to a control group, I bet you are more interested in finding out the amount of difference between the groups, rather than the chances of the differences popping up under the null hypothesis. Luckily itβs getting more and more common to also report effect sizes in addition to p-values. Effect sizes, in this case, are metrics that represent the amount of differences between two sample means. One of the most common effect size measure in psychology is Cohenβs d or the standardized mean difference. As you can see by the name itβs a measure of the standardized difference between two means. Commonly Cohenβs d is categorized in 3 broad categories: 0.2β0.3 represents a small effect, ~0.5 a medium effect and over 0.8 to infinity represents a large effect. What that means is that with two samples with a standard deviation of 1, the mean of group 1 is 0.8 sd away from the other groupβs mean if Cohenβs d = 0.8. That might sound very intuitive to some, but I find itβs more explanatory to present different d values visually. Which is really easy to do in R statistical software.

## Some quick R code to visualize Cohenβs d

The thing I actually wanted to try out here was to shade the overlapping area of the two distributions. It turned to be pretty easy to do in R.

## And some plots of the different effect size values

A βlargeβ effect size really look insignificant compared to the ridiculously large effect size reported by Clark et al. (2006) in their study Cognitive Therapy Versus Exposure and Applied Relaxation in Social Phobia: A Randomized Controlled Trial

Written by Kristoffer Magnusson, a researcher in clinical psychology. You should follow him on Twitter and come hang out on the open science discord Git Gud Science.

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Published April 23, 2012 (View on GitHub)

A huge thanks to the 152 supporters who've bought me a 361 coffees!

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I've been looking for applets that show this for YEARS, for demonstrations for classes. Thank you so much! Students do not need to tolarate my whiteboard scrawl now. I'm sure they'd appreciate you, too.l

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You finally helped me understand correlation! Many, many thanks... π

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Good stuff! It's been so helpful for teaching a Psych Stats class. Cheers!

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Excellent and informative visualizations!

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Always the clearest, loveliest simulations for complex concepts. Amazing resource for teaching intro stats!

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For a couple years now I've been wanting to create visualizations like these as a way to commit these foundational concepts to memory. But after finding your website I'm both relieved that I don't have to do that now and pissed off that I couldn't create anything half as beautiful and informative as you have done here. Wonderful job.

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You have an extremely useful site with very accessible content that I have been using to introduce colleagues and students to some of the core concepts of statistics. Keep up the good work, and thanks!

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Keep up the good work!

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I wish I could learn more from you about stats and math -- you use language in places that I do not understand. Cohen's D visualizations opened my understanding. Thank you

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Thank you, Kristoffer

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Great webpage, I use it to illustrate several issues when I have a lecture in research methods. Thanks, it is really helpful for the students:)

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Hard to overstate the importance of this work Kristoffer. Grateful for all you are doing.

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very useful for my students I guess

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brilliant simulations that can be effectively used in training

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Please use GitHub Discussions for any questions related to this post, or open an issue on GitHub if you've found a bug or wan't to make a feature request.

## Webmentions

(Webmentions sent before 2021 will unfortunately not show up here.)

M
Matej 2014-02-12

Graphs are yours or from another author?

B
Brian Hempel 2013-07-15

These are very useful visuals. Thank you for sharing them!

H
henrique 2013-05-07

Outstandind!

Thank you! I have wrapped this script in a function and I show it on my R course for undergrads students.

S
Sithara 2013-01-18

Hi Kristoffer,

I am Sithara from India, just completed my master of public health from Kerala, India. I am very much passionate about new things in R. The details in your blog regarding effect size gives and understanding about bothe topic and the functions in R.

Thank you so much!

Keep up the good spirit

Expect new posts.

F
FelipeCC 2012-04-24

Bookmarking! As an I/O practitioner I usually run into trouble when presenting this kind of information to clients. This looks like it could help out!

Thanks and keep up the good work!