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)
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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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Wonderful work!
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Terrific work. So very helpful. Thank you very much.
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I am so grateful for your page and can't thank you enough!
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Wonderful work, I use it every semester and it really helps the students (and me) understand things better. Keep going strong.
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Really super useful, especially for teaching. Thanks for this!
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Very helpful to helping teach teachers about the effects of the Good Behavior Game
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Amazing visualizations! Thank you!
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So good!
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🌟What a great contribution - thanks Kristoffer!
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Wow - your website is fantastic, thank you for making it.
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Thank you Kristoffer This is a nice site, which I have been used for a while. Best Prof. Mikhail Saltychev (Turku University, Finland)
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Keep up the nice work, thank you!
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Thanks - this will help me to teach tomorrow!
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Keep the visualizations coming!
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Thank you so much for your work, Kristoffer. I use your visualizations to explain concepts to my tutoring students and they are a huge help.
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Thank you for making such useful and pretty tools. It not only helped me understand more about power, effect size, etc, but also made my quanti-method class more engaging and interesting. Thank you and wish you a great 2021!
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Used your vizualization in class today. Thanks!
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My students love these visualizations and so do I! Thanks for helping me make stats more intuitive.
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For a high school teacher of psychology, I would be lost without your visualizations. The ability to interact and manipulate allows students to get it in a very sticky manner. Thank you!!!
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You Cohen's d post really helped me explaining the interpretation to people who don't know stats! Thank you!
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Enjoy.
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Teaching stats to civil engineer undergrads (first time teaching for me, first time for most of them too) and grasping for some good explanations of hypothesis testing, power, and CI's. Love these interactive graphics!
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Thank you for using your stats and programming gifts in such a useful, generous manner. -Jess
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A job that must have cost far more coffees than we can afford you ;-). Thank you.
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Thank you! Such a great resource for teaching these concepts, especially CI, Power, correlation.
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Fantastic work with the visualizations!
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Your work is amazing! I use your visualizations often in my teaching. Thank you.
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Excellent! Well done! SOOOO Useful!😊 🐭
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Thank you so much for these amazing visualizations. They're a great teaching tool and the allow me to show students things that it would take me weeks or months to program myself.
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Thank you for sharing your visualization skills with the rest of us! I use them frequently when teaching intro stats.
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Thank you for building such excellent ways to convey difficult topics to students!
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Really wonderful visuals, and such a fantastic and effective teaching tool. So many thanks!
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I really like your work.
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You're awesome. I have students in my intro stats class say, "I get it now," after using your tool. Thanks for making my job easier.
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Incredibly useful tool!
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Thanks for the assistance for RSCH 8210.
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Great tools! Thank you very much!
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Hi Kristoffer, many thanks for making all this great stuff available to the community!
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These visualizations are awesome! thank you for creating it
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Very nice.
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Thank you for the visualizations. They are fun and informative.
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Really helpful visualisations, thanks!
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This is amazing stuff. Very slick.
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Thanks so much for creating this! Really helpful for being able to explain effect size to a clinician I'm doing an analysis for.
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Thank you! This page is super useful. I'll spread the word.
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Thank you so much for creating these tools! As we face the challenge of teaching statistical concepts online, this is an invaluable resource.
@tmoldwin bought ☕ (1) coffee
Fantastic resource. I think you would be well served to have one page indexing all your visualizations, that would make it more accessible for sharing as a common resource.
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Fantastic Visualizations! Amazing way to to demonstrate how n/power/beta/alpha/effect size are all interrelated - especially for visual learners! Thank you for creating this?
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Incredible visualizations and the best power analysis software on R.
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Great website!
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Thank you for this work!!
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Nice explanation and visual guide of Cohen's d
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thank you
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This site is superb!
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thank you for sharing your work.
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Thank you for the website, made me smile AND smarter :O enjoy your coffee! :)
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Struggling with statistics and your interactive diagram made me smile to see that someone cares enough about us strugglers to make a visual to help us out!😍
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Much thanks! Visualizations are key to my learning style!
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Archived Comments (5)
Graphs are yours or from another author?
These are very useful visuals. Thank you for sharing them!
Outstandind!
Thank you! I have wrapped this script in a function and I show it on my R course for undergrads students.
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.
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!