Interpreting Correlations

An Interactive Visualization

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 Bluesky or on Twitter.

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:

x,y
10.0, 11.0
12.0, 12.0
..., ...

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. (2023). Interpreting Correlations: An interactive visualization (Version 0.7.1) [Web App]. R Psychologist. https://rpsychologist.com/correlation/

BibTex

@software{magnussonCorrelation,
    author = {Kristoffer Magnusson},
    title = {Interpreting Correlations: An Interactive Visualization},
    url = {https://rpsychologist.com/correlation/},
    version = {0.7.1},
    date = {2023},
  }

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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There are many ways to contribute to free and open software. If you like my work and want to support it you can:

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A huge thanks to the 175 supporters who've bought me a 422 coffees!

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I love your visualizations. Some of the best out there!!!

Jason Rinaldo bought ☕☕☕☕☕☕☕☕☕☕ (10) coffees

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

Shawn Bergman bought ☕☕☕☕☕ (5) coffees

Thank you for putting this together! I am using these visuals and this information to teach my Advanced Quant class.

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Hi Krisoffer, these are great applets and I've examined many. I'm writing a chapter for the second edition of "Teaching statistics and quantitative methods in the 21st century" by Joe Rodgers (Routledge). My chapter is on the use of applets in teaching statistics. I could well be describing 5 of yours. Would you permit me to publish one or more screen shots of the output from one or more of your applets. I promise I will be saying very positive things about your applets. If you are inclined to respond, my email address if Chip.Reichardt@du.edu.

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Nice work! Saw some of your other publications and they are also really intriguing. Thanks so much!

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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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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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Hi Kristoffer, Some time ago I've come up with a similar illustration about CIs as you have produced, and I'm now also referring to your work:<br>https://hugoquene.github.io/QMS-EN/ch-testing.html#sec:t-confidenceinterval-mean<br>With kind regards, Hugo Quené<br>(Utrecht University, Netherlands)

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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! 😃

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brilliant simulations that can be effectively used in training

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