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.
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 0.6.4) [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!
Contribute/Donate
There are many ways to contribute to free and open software. If you like my work and want to support it you can:
A huge thanks to the 64 supporters who've bought me a 143 coffees!
SCCT/Psychology bought ☕☕☕ (3) coffees
Keep the visualizations coming!
@noelnguyen16 bought ☕ (1) coffee
Hi Kristoffer, many thanks for making all this great stuff available to the community!
Eran Barzilai bought ☕ (1) coffee
These visualizations are awesome! thank you for creating it
Someone bought ☕ (1) coffee
@elena_bolt bought ☕☕☕ (3) coffees
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.
A random user bought ☕☕☕ (3) coffees
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!
@hertzpodcast bought ☕☕☕ (3) coffees
We've mentioned your work a few times on our podcast and we recently sent a poster to a listener as prize so we wanted to buy you a few coffees. Thanks for the great work that you do!Dan Quintana and James Heathers - Co-hosts of Everything Hertz
Chris SG bought ☕ (1) coffee
Very nice.
@whlevine bought ☕☕ (2) coffees
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.
Someone bought ☕☕ (2) coffees
Cameron Proctor bought ☕☕☕ (3) coffees
Used your vizualization in class today. Thanks!
@Daniel_Brad4d bought ☕☕☕☕☕ (5) coffees
Wonderful work!
Gray Church bought ☕ (1) coffee
Thank you for the visualizations. They are fun and informative.
eshulman@brocku.ca bought ☕☕☕ (3) coffees
My students love these visualizations and so do I! Thanks for helping me make stats more intuitive.
Qamar bought ☕ (1) coffee
Someone bought ☕☕☕ (3) coffees
Adrian Helgå Vestøl bought ☕☕☕ (3) coffees
David Loschelder bought ☕☕☕☕☕ (5) coffees
Terrific work. So very helpful. Thank you very much.
Tanya McGhee bought ☕ (1) coffee
@neilmeigh bought ☕☕☕☕☕ (5) coffees
I am so grateful for your page and can't thank you enough!
@schultemi bought ☕ (1) coffee
@giladfeldman bought ☕☕☕☕☕ (5) coffees
Wonderful work, I use it every semester and it really helps the students (and me) understand things better. Keep going strong.
Dean Norris bought ☕☕☕☕☕ (5) coffees
@misteryosupjoo bought ☕☕☕ (3) coffees
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!!!
Sal bought ☕☕☕☕☕ (5) coffees
Really super useful, especially for teaching. Thanks for this!
Neilo bought ☕ (1) coffee
Really helpful visualisations, thanks!
Chi bought ☕☕☕ (3) coffees
You Cohen's d post really helped me explaining the interpretation to people who don't know stats! Thank you!
Someone bought ☕☕☕ (3) coffees
You doing useful work !! thanks !!
@ArtisanalANN bought ☕☕☕ (3) coffees
Enjoy.
Someone bought ☕ (1) coffee
This is amazing stuff. Very slick.
Someone bought ☕ (1) coffee
Sarko bought ☕ (1) coffee
Thanks so much for creating this! Really helpful for being able to explain effect size to a clinician I'm doing an analysis for.
@jsholtes bought ☕☕☕ (3) coffees
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!
@DominikaSlus bought ☕ (1) coffee
Thank you! This page is super useful. I'll spread the word.
Someone bought ☕ (1) coffee
dde@paxis.org bought ☕☕☕☕☕ (5) coffees
Very helpful to helping teach teachers about the effects of the Good Behavior Game
@notawful bought ☕☕☕ (3) coffees
Thank you for using your stats and programming gifts in such a useful, generous manner. -Jess
Mateu Servera bought ☕☕☕ (3) coffees
A job that must have cost far more coffees than we can afford you ;-). Thank you.
Melinda Rice bought ☕ (1) coffee
Thank you so much for creating these tools! As we face the challenge of teaching statistical concepts online, this is an invaluable resource.
@tmoldwin bought ☕ (1) coffee
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.
@cdrawn bought ☕☕☕ (3) coffees
Thank you! Such a great resource for teaching these concepts, especially CI, Power, correlation.
Someone bought ☕ (1) coffee
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?
@akreutzer82 bought ☕☕☕☕☕ (5) coffees
Amazing visualizations! Thank you!
@rdh_CLE bought ☕☕☕☕☕ (5) coffees
So good!
@jackferd bought ☕ (1) coffee
Incredible visualizations and the best power analysis software on R.
Julia bought ☕☕☕ (3) coffees
Fantastic work with the visualizations!
@felixthoemmes bought ☕☕☕ (3) coffees
@dalejbarr bought ☕☕☕ (3) coffees
Your work is amazing! I use your visualizations often in my teaching. Thank you.
@notawful bought ☕☕ (2) coffees
Thank you for sharing your visualization skills with the rest of us! I use them frequently when teaching intro stats.
Cameron Proctor bought ☕ (1) coffee
Great website!
Someone bought ☕ (1) coffee
Hanah Chapman bought ☕ (1) coffee
Thank you for this work!!
Someone bought ☕ (1) coffee
Jayme bought ☕ (1) coffee
Nice explanation and visual guide of Cohen's d
Bart Comly Boyce bought ☕ (1) coffee
thank you
Dr. Mitchell Earleywine bought ☕ (1) coffee
This site is superb!
Florent bought ☕ (1) coffee
Zampeta bought ☕ (1) coffee
thank you for sharing your work.
Mila bought ☕ (1) coffee
Thank you for the website, made me smile AND smarter :O enjoy your coffee! :)
Deb bought ☕ (1) coffee
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!😍
Someone bought ☕ (1) coffee
@exerpsysing bought ☕ (1) coffee
Much thanks! Visualizations are key to my learning style!
@PsychoMouse bought ☕☕☕ (3) coffees
Excellent! Well done! SOOOO Useful!😊 🐭
Someone bought ☕ (1) coffee
Sponsors
You can sponsor my open source work using GitHub Sponsors and have your name shown here.
Backers ✨❤️
Pull requests are also welcome, or you can contribute by suggesting new features, add useful references, or help fix typos. Just open a issues on GitHub.
Webmentions
0 0
(Webmentions sent before 2021 will unfortunately not show up here.)
More Visualizations
Maximum Likelihood
An interactive post covering various aspects of maximum likelihood estimation.
Cohen's d
An interactive app to visualize and understand standardized effect sizes.
Statistical Power and Significance Testing
An interactive version of the traditional Type I and II error illustration.
Confidence Intervals
An interactive simulation of confidence intervals
Bayesian Inference
An interactive illustration of prior, likelihood, and posterior.
Correlations
Interactive scatterplot that let's you visualize correlations of various magnitudes.
Equivalence and Non-Inferiority Testing
Explore how superiority, non-inferiority, and equivalence testing relates to a confidence interval
P-value distribution
Explore the expected distribution of p-values under varying alternative hypothesises.
t-distribution
Interactively compare the t- and normal distribution.