Correlation is one of the most widely used tools in statistics. The correlation coefficient summarizes the association between two variables. In this visualization I show a scatter plot of two variables with a given correlation. The variables are samples from the standard normal distribution, which are then transformed to have a given correlation by using Cholesky decomposition. By moving the slider you will see how the shape of the data changes as the association becomes stronger or weaker. You can also look at the Venn diagram to see the amount of shared variance between the variables. It is also possible drag the data points to see how the correlation is influenced by outliers.
Correlation: 0.00
Shared variance: 0%
y = 100.00 + 0.00*x
Mean(y) = 100.00
Mean(x) = 100.00
SD(y) = 3.00
SD(x) = 5.00
Loading visualization
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.
FAQ
How do I use this visualization?
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Probability Ellipses
You can toggle probability ellipses in the settings drawer. The ellipse probabilities are: 0.5, 0.8, 0.95, 0.99. Protip: You can click on the ellipses if you disable “Edit points”.
What are the formulas?
This section is not finished.
How do I cite this page?
Cite this page according to your favorite style guide. The references below are automatically generated and contain the correct information.
APA 7
Magnusson, K. (2023). Interpreting Correlations: An interactive visualization (Version 0.7.1) [Web App]. R Psychologist. https://rpsychologist.com/correlation/
BibTex
I fund a bug/error/typo or want to make an suggestion!
Please report errors or suggestions by opening an issue on GitHub, if you want to ask a question use GitHub discussions
I'm gonna ask a large number of students to visit this site. Will it crash your server?
No, it will be fine. The app runs in your browser so the server only needs to serve the files.
Can I include this visualization in my book/article/etc?
Yes, go ahead! This visualization is dedicated to the public domain, which means “you can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission” (see Creative common’s CC0-license). Although, attribution is not required it is always appreciated!
The source code for this page is licensed using MIT, and the text on the page is CC-BY 4.0.
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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... 😄
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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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Wonderful work!
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I am so grateful for your page and can't thank you enough!
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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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Love this website; use it all the time in my teaching and research.
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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!
Susan Evans bought ☕☕☕ (3) coffees
Thanks. I really love the simplicity of your sliders. Thanks!!
@MichaMarie8 bought ☕☕☕ (3) coffees
Thanks for making this Interpreting Correlations: Interactive Visualizations site - it's definitely a great help for this psych student! 😃
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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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🌟What a great contribution - thanks Kristoffer!
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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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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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Thank you for using your stats and programming gifts in such a useful, generous manner. -Jess
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Thank you! Such a great resource for teaching these concepts, especially CI, Power, correlation.
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this is a superb, intuitive teaching tool!
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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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Thanks for helping understand stuff!
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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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Thanks a lot!
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Thanks mate
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Thank you, this really helps as I am a stats idiot :)
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Your visualizations really help me understand the math.
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Great work!
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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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Incredibly useful tool!
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Thanks for the assistance for RSCH 8210.
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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
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