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
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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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Load CSV files
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This site performs no server-side calculations, and the data is only loaded in your browser and not uploaded to my server.
What are the formulas?
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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. (2020). Interpreting Correlations: An interactive visualization (Version 0.6.4) [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! I did not invent plotting two overlapping Gaussian distributions. 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!
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Keep the visualizations coming!
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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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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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Very nice.
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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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Used your vizualization in class today. Thanks!
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Wonderful work!
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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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Terrific work. So very helpful. Thank you very much.
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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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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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Really super useful, especially for teaching. Thanks for this!
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Really helpful visualisations, 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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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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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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Very helpful to helping teach teachers about the effects of the Good Behavior Game
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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 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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Thank you! Such a great resource for teaching these concepts, especially CI, Power, correlation.
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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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Amazing visualizations! Thank you!
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So good!
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Incredible visualizations and the best power analysis software on R.
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Your work is amazing! I use your visualizations often in my teaching. Thank you.
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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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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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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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