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.
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APA 7
Magnusson, K. (2020). Interpreting Correlations: An interactive visualization (Version 0.6.4) [Web App]. R Psychologist. https://rpsychologist.com/correlation/
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I fund a bug/error/typo or want to make an suggestion!
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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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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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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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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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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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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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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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Hi Kristoffer, many thanks for making all this great stuff available to the community!
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Really helpful visualisations, thanks!
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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 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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Incredible visualizations and the best power analysis software on R.
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