# 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 “x and y were significantly
different, *p* < .05”, which is another way of saying that “assuming
that the null hypothesis is true, the probability of getting the
observed value simply by chance alone is less than 0.05” But that’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 it’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 Cohen’s *d* or *the standardized
mean difference*. As you can see by the name it’s a measure of the
standardized difference between two means. Commonly Cohen’s *d* is
categorized in 3 broad categories: 0.2–0.3 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
group’s mean if Cohen’s *d* = 0.8. That might sound very intuitive to
some, but I find it’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 Cohen’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 “large” 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.

Published April 23, 2012 (View on GitHub)