Interpreting Cohen's d Effect Size

An Interactive Visualization

The Cohen’s d effect size is immensely popular in psychology. However, its interpretation is not straightforward and researchers often use general guidelines, such as small (0.2), medium (0.5) and large (0.8) when interpreting an effect. Moreover, in many cases it is questionable whether the standardized mean difference is more interpretable than the unstandardized mean difference.

In order to aid the interpretation of Cohen’s d, this visualization offers these different representations of Cohen’s d: visual overlap, Cohen’s U₃, the probability of superiority, percentage of overlap, and the number needed to treat. It also lets you change the standard deviation and displays the unstandardized difference.

Cohen's U₃

% Overlap

Probability of Superiority

Number Needed to Treat

A Common Language Explanation

With a Cohen's d of 0.80, 78.8% of the "treatment" group will be above the mean of the "control" group (Cohen's U₃), 68.9% of the two groups will overlap, and there is a 71.4% chance that a person picked at random from the "treatment" group will have a higher score than a person picked at random from the "control" group (probability of superiority). Moreover, in order to have one more favorable outcome in the "treatment" group compared to the "control" group, we need to treat 3.5 people on average. This means that if there are 100 people in each group, and we assume that 20 people have favorable outcomes in the "control" group, then 20 + 28.3 people in the "treatment" group will have favorable outcomes.¹

¹The values are averages, and it is assumed that 20 (CER) of the "control" group have "favorable outcomes," i.e., their outcomes are below some cut-off. Change this by pressing the settings symbol to the right of the slider. Go to the formula section for more information.

Colors

Dist1

Overlap

Dist2

Click to change colors

Dark mode:

Parameters

Save settings

Save settings locally in browser

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?

Change Cohen’s d

Use the slider to change Cohen’s d, or open the settings drawer and change the parameters. The inputs can also be controlled using the keyboard arrows.

Settings

You can change the following settings by clicking on the settings icon to the right of the slider.

Parameters
- Mean 1
- Mean 2
- SD
- Control group event rate (CER)
Labels
- X axis
- Distribution 1
- Distribution 2
Slider settings
- Slider Max
- Slider Step: Controls the step size of the slider

Save settings

The settings can be saved in your browser’s localStorage and will thus persist across visits.

Pan and rescale

You can pan the x axis by clicking and dragging the visualization. Double-click the visualization to center and rescale it.

Offline use

This site is cached using a service worker and will work even when you are offline.

What are the formulas?

Cohen’s d

Cohen’s d is simply the standardized mean difference,

$δ = \frac{μ _{2} - μ _{1}}{σ}$ ,

where $δ$ is the population parameter of Cohen’s d. Where it is assumed that $σ_{1} = σ_{2} = σ$ , i.e., homogeneous population variances. And $μ_{i}$ is the mean of the respective population.

Cohen’s U₃

Cohen (1977) defined U₃ as a measure of non-overlap, where “we take the percentage of the A population which the upper half of the cases of the Β population exceeds”. Cohen’s d can be converted to Cohen’s U₃ using the following formula

$U_{3} = Φ (δ)$

where $Φ$ is the cumulative distribution function of the standard normal distribution, and $δ$ the population Cohen’s d.

Overlap

Generally called the overlapping coefficient (OVL). Cohen’s d can be converted to OVL using the following formula (Reiser and Faraggi, 1999)

$OVL = 2 Φ (- ∣ δ ∣ / 2)$

where $Φ$ is the cumulative distribution function of the standard normal distribution, and $δ$ the population Cohen’s d.

Probability of superiority

This is effect size with many names: common language effect size (CL), Area under the receiver operating characteristics (AUC) or just A for its non-parametric version (Ruscio & Mullen, 2012). It is meant to be more intuitive for persons without any training in statistics. The effect size gives the probability that a person picked at random from the treatment group will have a higher score than a person picked at random from the control group. Cohen’s d can be converted CL using the following formula (Ruscio, 2008)

$CL = Φ (\frac{δ}{2})$

where $Φ$ is the cumulative distribution function of the standard normal distribution, and $δ$ the population Cohen’s d.

Number Needed to Treat

NNT is the number of patients we would need to treat with the intervention to achieve one more favorable outcome compared to the control group. Furukawa and Leucht (2011) gives the following formula for converting Cohen’s d into NNT

$NNT = \frac{1}{Φ ( δ + Ψ ( C E R ) ) - C E R}$

where $Φ$ is the cumulative distribution function of the standard normal distribution and $Ψ$ its inverse, CER is the control group’s event rate and $δ$ the population Cohen’s d. N.B. CER is set to 20 % in the visualization above. You can change this be pressing the settings symbol to the right of the slider. The definition of an “event” or a “response” is arbitrary and could be defined as the proportion of patients who are in remission, e.g. bellow some cut-off on a standardized questionnaire. It is possible to convert Cohen’s d into a version of NNT that is invariant to the event rate of the control group. The interested reader should look at Furukawa and Leucht (2011) where a convincing argument is given to why this complicates the interpretation of NNT.

R code to calculate NNT from Cohen’s d

Since many have asked about R code for the formula above, here it is

CER <- 0.2
d <- 0.2
1 / (pnorm(d + qnorm(CER))-CER)

References

Baguley, T. (2009). Standardized or simple effect size: what should be reported? British journal of psychology, 100(Pt 3), 603–17.
Cohen, J. (1977). Statistical power analysis for the behavioral sciencies. Routledge.
Furukawa, T. A., & Leucht, S. (2011). How to obtain NNT from Cohen’s d: comparison of two methods. PloS one, 6(4).
Reiser, B., & Faraggi, D. (1999). Confidence intervals for the overlapping coefficient: the normal equal variance case. Journal of the Royal Statistical Society, 48(3), 413-418.
Ruscio, J. (2008). A probability-based measure of effect size: robustness to base rates and other factors. Psychological methods, 13(1), 19–30.
Ruscio, J., & Mullen, T. (2012). Confidence Intervals for the Probability of Superiority Effect Size Measure and the Area Under a Receiver Operating Characteristic Curve. Multivariate Behavioral Research, 47(2), 201–223.

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). A Causal Inference Perspective on Therapist Effects. PsyArXiv. https://DOI

BibTex

@article{magnussonCausalTherapistEffects,
  doi = {XXX},
  url = {XXX},
  year = 2023,
  month = {jun},
  publisher = {PsyArXiv},
  volume = {},
  number = {},
  pages = {},
  author = {Kristoffer Magnusson},
  title = {A Causal Inference Perspective on Therapist Effects},
  journal = {PsyArXiv}
}

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.

The overlap statistic differs from Cohen's calculations

This is intentional, you can read more about my reasons in this blog post: Where Cohen went wrong – the proportion of overlap between two normal distributions

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!

The source code for this page is licensed using MIT, and the text on the page is CC-BY 4.0.

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:

Buy Me a Coffee ☕

(or use PayPal)

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

Steffen bought ☕☕☕☕☕☕☕☕☕☕☕☕ (12) coffees

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.

anthonystevendick@gmail.com bought ☕☕☕☕☕ (5) coffees

I've been using a lot of your ideas in a paper I'm writing and even borrowed some of your code (cited of course). But this site has been so helpful I think, in addition, I owe you a few coffees!

Chip Reichardt bought ☕☕☕☕☕ (5) coffees

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.

Someone bought ☕☕☕☕☕ (5) coffees

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

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!

Someone bought ☕☕☕☕☕ (5) coffees

@metzpsych bought ☕☕☕☕☕ (5) coffees

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

Ryo bought ☕☕☕☕☕ (5) coffees

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.

Diarmuid Harvey bought ☕☕☕☕☕ (5) coffees

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!

Michael Hansen bought ☕☕☕☕☕ (5) coffees

Keep up the good work!

Michael Villanueva bought ☕☕☕☕☕ (5) coffees

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

Someone bought ☕☕☕☕☕ (5) coffees

Thank you, Kristoffer

Pål from Norway bought ☕☕☕☕☕ (5) coffees

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:)

@MAgrochao bought ☕☕☕☕☕ (5) coffees

Joseph Bulbulia bought ☕☕☕☕☕ (5) coffees

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

@TDmyersMT bought ☕☕☕☕☕ (5) coffees

Some really useful simulations, great teaching resources.

@lakens bought ☕☕☕☕☕ (5) coffees

Thanks for fixing the bug yesterday!

@LinneaGandhi bought ☕☕☕☕☕ (5) coffees

This is awesome! Thank you for creating these. Definitely using for my students, and me! :-)

@ICH8412 bought ☕☕☕☕☕ (5) coffees

very useful for my students I guess

@KelvinEJones bought ☕☕☕☕☕ (5) coffees

Preparing my Master's student for final oral exam and stumbled on your site. We are discussing in lab meeting today. Coffee for everyone.

Someone bought ☕☕☕☕☕ (5) coffees

What a great site

@Daniel_Brad4d bought ☕☕☕☕☕ (5) coffees

Wonderful work!

David Loschelder bought ☕☕☕☕☕ (5) coffees

Terrific work. So very helpful. Thank you very much.

@neilmeigh bought ☕☕☕☕☕ (5) coffees

I am so grateful for your page and can't thank you enough!

@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

Sal bought ☕☕☕☕☕ (5) coffees

Really super useful, especially for teaching. Thanks for this!

dde@paxis.org bought ☕☕☕☕☕ (5) coffees

Very helpful to helping teach teachers about the effects of the Good Behavior Game

@akreutzer82 bought ☕☕☕☕☕ (5) coffees

Amazing visualizations! Thank you!

@rdh_CLE bought ☕☕☕☕☕ (5) coffees

So good!

tchipman1@gsu.edu bought ☕☕☕ (3) coffees

Hey, your stuff is cool - thanks for the visual

Hugo Quené bought ☕☕☕ (3) coffees

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)

Tor bought ☕☕☕ (3) coffees

Thanks so much for helping me understand these methods!

Amanda Sharples bought ☕☕☕ (3) coffees

Soyol bought ☕☕☕ (3) coffees

Someone bought ☕☕☕ (3) coffees

Kenneth Nilsson bought ☕☕☕ (3) coffees

Keep up the splendid work!

@jeremywilmer bought ☕☕☕ (3) coffees

Love this website; use it all the time in my teaching and research.

Someone bought ☕☕☕ (3) coffees

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

DR AMANDA C DE C WILLIAMS bought ☕☕☕ (3) coffees

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

Georgios Halkias bought ☕☕☕ (3) coffees

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! 😃

Zakaria Giunashvili, from Georgia bought ☕☕☕ (3) coffees

brilliant simulations that can be effectively used in training

Someone bought ☕☕☕ (3) coffees

@PhysioSven bought ☕☕☕ (3) coffees

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

Cheryl@CurtinUniAus bought ☕☕☕ (3) coffees

🌟What a great contribution - thanks Kristoffer!

vanessa moran bought ☕☕☕ (3) coffees

Wow - your website is fantastic, thank you for making it.

Someone bought ☕☕☕ (3) coffees

mikhail.saltychev@gmail.com bought ☕☕☕ (3) coffees

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

Someone bought ☕☕☕ (3) coffees

Ruslan Klymentiev bought ☕☕☕ (3) coffees

@lkizbok bought ☕☕☕ (3) coffees

Keep up the nice work, thank you!

@TELLlab bought ☕☕☕ (3) coffees

Thanks - this will help me to teach tomorrow!

SCCT/Psychology bought ☕☕☕ (3) coffees

Keep the visualizations coming!

@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

Cameron Proctor bought ☕☕☕ (3) coffees

Used your vizualization in class today. Thanks!

eshulman@brocku.ca bought ☕☕☕ (3) coffees

My students love these visualizations and so do I! Thanks for helping me make stats more intuitive.

Someone bought ☕☕☕ (3) coffees

Adrian Helgå Vestøl bought ☕☕☕ (3) 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!!!

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.

@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!

@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.

@cdrawn bought ☕☕☕ (3) coffees

Thank you! Such a great resource for teaching these concepts, especially CI, Power, correlation.

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.

@PsychoMouse bought ☕☕☕ (3) coffees

Excellent! Well done! SOOOO Useful!😊 🐭

Someone bought ☕☕ (2) coffees

Thanks, your work is great!!

Dan Sanes bought ☕☕ (2) coffees

this is a superb, intuitive teaching tool!

@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

@notawful bought ☕☕ (2) coffees

Thank you for sharing your visualization skills with the rest of us! I use them frequently when teaching intro stats.

Someone bought ☕ (1) coffee

You are awesome

Thom Marchbank bought ☕ (1) coffee

Your visualisations are so useful! Thank you so much for your work.

georgina g. bought ☕ (1) coffee

thanks for helping me in my psych degree!

Someone bought ☕ (1) coffee

Thank You for this work.

Kosaku Noba bought ☕ (1) coffee

Nice visualization, I bought a cup of coffee.

Someone bought ☕ (1) coffee

Thomas bought ☕ (1) coffee

Great. Use it for teaching in psychology.

Someone bought ☕ (1) coffee

It is the best statistics visualization so far!

Ergun Pascu bought ☕ (1) coffee

AMAZING Tool!!! Thank You!

Ann Calhoun-Sauls bought ☕ (1) coffee

This has been a wonderful resource for my statistics and research methods classes. I also occassionally use it for other courses such as Theories of Personality and Social Psychology

David Britt bought ☕ (1) coffee

nicely reasoned

Mike bought ☕ (1) coffee

I appreciate your making this site available. Statistics are not in my wheelhouse, but the ability to display my data more meaningfully in my statistics class is both educational and visually appealing. Thank you!

Jayne T Jacobs bought ☕ (1) coffee

Andrew J O'Neill bought ☕ (1) coffee

Thanks for helping understand stuff!

Someone bought ☕ (1) coffee

Shawn Hemelstrand bought ☕ (1) coffee

Thank you for this great visual. I use it all the time to demonstrate Cohen's d and why mean differences affect it's approximation.

Adele Fowler-Davis bought ☕ (1) coffee

Thank you so much for your excellent post on longitudinal models. Keep up the good work!

Stewart bought ☕ (1) coffee

This tool is awesome!

Someone bought ☕ (1) coffee

Aidan Nelson bought ☕ (1) coffee

Such an awesome page, Thank you

Someone bought ☕ (1) coffee

Ellen Kearns bought ☕ (1) coffee

Dr Nazam Hussain bought ☕ (1) coffee

Someone bought ☕ (1) coffee

Eva bought ☕ (1) coffee

I've been learning about power analysis and effect sizes (trying to decide on effect sizes for my planned study to calculate sample size) and your Cohen's d interactive tool is incredibly useful for understanding the implications of different effect sizes!

Someone bought ☕ (1) coffee

Thanks a lot!

Someone bought ☕ (1) coffee

Reena Murmu Nielsen bought ☕ (1) coffee

Tony Andrea bought ☕ (1) coffee

Thanks mate

Tzao bought ☕ (1) coffee

Thank you, this really helps as I am a stats idiot :)

Melanie Pflaum bought ☕ (1) coffee

Sacha Elms bought ☕ (1) coffee

Yihan Xu bought ☕ (1) coffee

Really appreciate your good work!

@stevenleung bought ☕ (1) coffee

Your visualizations really help me understand the math.

Junhan Chen bought ☕ (1) coffee

Someone bought ☕ (1) coffee

Michael Hansen bought ☕ (1) coffee

ALEXANDER VIETHEER bought ☕ (1) coffee

mather bought ☕ (1) coffee

Someone bought ☕ (1) coffee

Bastian Jaeger bought ☕ (1) coffee

Thanks for making the poster designs OA, I just hung two in my office and they look great!

@ValerioVillani bought ☕ (1) coffee

Thanks for your work.

Someone bought ☕ (1) coffee

Great work!

@YashvinSeetahul bought ☕ (1) coffee

Someone bought ☕ (1) coffee

Angela bought ☕ (1) coffee

Thank you for building such excellent ways to convey difficult topics to students!

@inthelabagain bought ☕ (1) coffee

Really wonderful visuals, and such a fantastic and effective teaching tool. So many thanks!

Someone bought ☕ (1) coffee

Yashashree Panda bought ☕ (1) coffee

I really like your work.

Ben bought ☕ (1) coffee

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.

Gabriel Recchia bought ☕ (1) coffee

Incredibly useful tool!

Shiseida Sade Kelly Aponte bought ☕ (1) coffee

Thanks for the assistance for RSCH 8210.

@Benedikt_Hell bought ☕ (1) coffee

Great tools! Thank you very much!

Amalia Alvarez bought ☕ (1) coffee

@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

Chris SG bought ☕ (1) coffee

Very nice.

Gray Church bought ☕ (1) coffee

Thank you for the visualizations. They are fun and informative.

Qamar bought ☕ (1) coffee

Tanya McGhee bought ☕ (1) coffee

@schultemi bought ☕ (1) coffee

Neilo bought ☕ (1) coffee

Really helpful visualisations, thanks!

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.

@DominikaSlus bought ☕ (1) coffee

Thank you! This page is super useful. I'll spread the word.

Someone bought ☕ (1) coffee

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.

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?

@jackferd bought ☕ (1) coffee

Incredible visualizations and the best power analysis software on R.

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!

Someone bought ☕ (1) coffee