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 βx and y were significantly different, p < .05β, which is another way of saying that βassuming that the null hypothesis is true, the probability of getting the observed value simply by chance alone is less than 0.05β But thatβs 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 itβs 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 Cohenβs d or the standardized mean difference. As you can see by the name itβs a measure of the standardized difference between two means. Commonly Cohenβs d is categorized in 3 broad categories: 0.2β0.3 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 groupβs mean if Cohenβs d = 0.8. That might sound very intuitive to some, but I find itβs more explanatory to present different d values visually. Which is really easy to do in R statistical software.
Some quick R code to visualize Cohenβs 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 βlargeβ 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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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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Some really useful simulations, great teaching resources.
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Thanks for fixing the bug yesterday!
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This is awesome! Thank you for creating these. Definitely using for my students, and me! :-)
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very useful for my students I guess
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Preparing my Master's student for final oral exam and stumbled on your site. We are discussing in lab meeting today. Coffee for everyone.
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What a great site
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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!Β Β
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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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Powerlmm was really helpful, and I appreciate your time in putting such an amazing resource together!
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This is very helpful, for my work and for teaching and supervising
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Love your visualizations!
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Thanks. I really love the simplicity of your sliders. Thanks!!
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Thanks for making this Interpreting Correlations: Interactive Visualizations site - it's definitely a great help for this psych student! π
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brilliant simulations that can be effectively used in training
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Amazing illustrations, there is not enough coffee in the world for enthusiasts like you! Thanks!
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πWhat 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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Thank you for this great visual. I use it all the time to demonstrate Cohen's d and why mean differences affect it's approximation.
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This tool is awesome!
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I've been learning about power analysis and effect sizes (trying to decide on effect sizes for my planned study to calculate sample size) and your Cohen's d interactive tool is incredibly useful for understanding the implications of different effect sizes!
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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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Thanks for the assistance for RSCH 8210.
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Hi Kristoffer, many thanks for making all this great stuff available to the community!
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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.
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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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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!