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?
This section is not finished.
Load CSV files
You can load your own data from a CSV file. The CSV file must have this structure:
The first row is the column names, where the first column is assumed to be the x variable and the second the y variable - all other columns are ignored.
Your data is not uploaded
This site performs no server-side calculations, and the data is only loaded in your browser and not uploaded to my server.
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. (2020). Interpreting Correlations: An interactive visualization (Version 0.6.5) [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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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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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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Keep the visualizations coming!
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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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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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Really wonderful visuals, and such a fantastic and effective teaching tool. So many thanks!
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