Interpreting Correlations

An Interactive Visualization

Created by Kristoffer Magnusson

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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

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

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Please report errors or suggestions by opening an issue on GitHub, if you want to ask a question use GitHub discussions

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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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A huge thanks to the 152 supporters who've bought me a 361 coffees!

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

JDMM bought ☕☕☕☕☕ (5) coffees

You finally helped me understand correlation! Many, many thanks... 😄

@VicCazares bought ☕☕☕☕☕ (5) coffees

Good stuff! It's been so helpful for teaching a Psych Stats class. Cheers!

Dustin M. Burt bought ☕☕☕☕☕ (5) coffees

Excellent and informative visualizations!

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Always the clearest, loveliest simulations for complex concepts. Amazing resource for teaching intro stats!

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For a couple years now I've been wanting to create visualizations like these as a way to commit these foundational concepts to memory. But after finding your website I'm both relieved that I don't have to do that now and pissed off that I couldn't create anything half as beautiful and informative as you have done here. Wonderful job.

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You have an extremely useful site with very accessible content that I have been using to introduce colleagues and students to some of the core concepts of statistics. Keep up the good work, and thanks!

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Keep up the good work!

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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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Great webpage, I use it to illustrate several issues when I have a lecture in research methods. Thanks, it is really helpful for the students:)

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Hard to overstate the importance of this work Kristoffer. Grateful for all you are doing.

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very useful for my students I guess

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Wonderful work!

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Powerlmm was really helpful, and I appreciate your time in putting such an amazing resource together!

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This is very helpful, for my work and for teaching and supervising

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Regina bought ☕☕☕ (3) coffees

Love your visualizations!

Susan Evans bought ☕☕☕ (3) coffees

Thanks. I really love the simplicity of your sliders. Thanks!!

@MichaMarie8 bought ☕☕☕ (3) coffees

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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Amazing illustrations, there is not enough coffee in the world for enthusiasts like you! Thanks!

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🌟What a great contribution - thanks Kristoffer!

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Thank you Kristoffer This is a nice site, which I have been used for a while. Best Prof. Mikhail Saltychev (Turku University, Finland)

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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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Webmentions

Arseny Khakhalin 🇺🇦
Just to illustrate what I mean; take some tool and build a cloud with r=0.7. Like this one: rpsychologist.com/correlation/ Say X is your test score; Y is actual impact. A few top candidates (by Y) are taken by a competitive market. You have a truncated distribution. You cut at X=105...
Tailcalled (tailcalled@schelling.pt)
There are various things that have lead to me developing intuitions for r/beta values, e.g. this site rpsychologist.com/correlation/ or path tracing computation. Are there any recommended ways to get intuition for F_ST values?
Mario Bermonti
Mario Bermonti 2022-11-16
Awesome resource for understanding correlations Interpreting correlations - an interactive visualization by @krstoffr rpsychologist.com/correlation
Derek Wilson
Derek Wilson 2022-11-12
Interpreting correlations - an interactive visualization by @krstoffr rpsychologist.com/correlation
Matthew B Jané
Matthew B Jané 2022-11-05
It’s a great app for teaching basic statistics. I’m TAing a methods course and i find it quite helpful and intuitive rpsychologist.com/correlation/
Tailcalled
Tailcalled 2022-10-21
rpsychologist.com/correlation/
A.N. Atomist
A.N. Atomist 2022-09-20
These apps are pretty nifty. Great from intros for students.
Alexander Wuttke
Alexander Wuttke 2022-09-19
btw: I love the app and use it rather frequently
Peter Clayson
Peter Clayson 2022-03-10
Interpreting correlations - an interactive visualization by @krstoffr rpsychologist.com/correlation Just a shout out. I'll be pulling this page up in my undergrad class today to drive home the impact of outliers on correlations... This is such a useful tool! Thank you!
Dr. Mar Gonzalez-Franco
Interpreting correlations - beautiful interactive visualization by @krstoffr rpsychologist.com/correlation
Alex Shackman
Alex Shackman 2022-02-19
oldy goody - rpsychologist.com/correlation/
Gracia Brückmann
Have I ever told you how much I like this tool? Interpreting correlations - an interactive visualization by @krstoffr rpsychologist.com/correlation
Xiao Jean Chen
Xiao Jean Chen 2021-08-23
The pithiest explanation of correlation coefficient I've ever seen, with awesome interactive visualization you can play with. #statistics made fun by @krstoffr rpsychologist.com/correlation
Masha Kubyshina
Masha Kubyshina 2021-05-23
Interpreting correlations - an interactive visualization by @krstoffr rpsychologist.com/correlation
Guido
Guido 2021-05-23
Interpreting correlations - an interactive visualization by @krstoffr rpsychologist.com/correlation Para acompañar lectura del mejor proyecto de open learning @freeCodeCamp freecodecamp.org/news/what-is-a…
Juan Ramón
Juan Ramón 2021-03-23
Esto es una correlación de 0.30. A puro ojo no es tan fácil saber si la línea habría de ser creciente, decreciente o con pendiente nula. El porcentaje de varianza explicada es de solo el 9%. (Tomado de aquí). rpsychologist.com/correlation/
Jamie Lingwood
Jamie Lingwood 2021-03-05
I've been using this fantastic interactive resource from @krstoffr to help my first year students visualise what different Correlations look like. Particularly handy for explaining tricky concepts such as shared variance: rpsychologist.com/correlation/
Thùy Vy T Nguyễn, PhD ☕️💻📄
I was in a talk by @MalvikaSharan; she mentioned #OpenScience jargons can make you feel you can't keep up. To me, jargons is challenging b/c I learn better w images I really appreciate those who create tools to break down complicated concepts like this rpsychologist.com/correlation/
Dr. #ResearchLiteracy 📊📈
Just found this great data visualization teaching tool created by @krstoffr. Will be using the one on #correlation in my graduate research methods course this week. #ResearchLiteracy @AcademicChatter @OpenAcademics rpsychologist.com/correlation/

(Webmentions sent before 2021 will unfortunately not show up here.)

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