Visually quantitative Venn diagrams

I bet that you have included a Venn diagram in your scientific article, poster or presentation at least once in the past. You probably did it to visually show the intersection of two groups, datasets, etc. This is a very good idea, as visual elements help your audience understand and remember the facts. However, you have likely been doing it wrong.

In this article you will discover what you are doing wrong in your Venn diagrams and how you can draw Venn diagrams that are more visually accurate and appealing.

Bad Venn diagrams

We have the tendency to create Venn diagrams that are very symmetrical: two perfectly equal circles, that intersect super symmetrically in the middle. Our data, on the other hand, are almost never symmetrical.

Look at this diagram, for example. The green set contains less than half the elements with respect to the purple one, but the size of the circles that represent them is the same. And look at the intersection: does it look like it’s less than one fifth of the purple set?

You can see the problem: what our eyes see clashes with the numbers we read, making the graphics confusing. How can we fix this?

The solution: visually quantitative Venn diagrams

How would the diagram above look if the area of each section was proportional to the number of elements in it? Let’s take a look.

In this image, you can get a solid idea of the size of the sets by just taking a look at the picture, without reading the numbers. You can immediately see that set A is smaller than set B, and that their intersection is quite large compared to set A and quite small compared to set B.

If you still want to know the precise numbers, you can read them, of course, but this time they won’t conflict with what your eyes see. Pretty cool, uh?

This upgraded version of Venn diagrams makes your communication much more effective by presenting the information visually as well as analytically. You can even do this with three-group Venn diagrams, although here getting the proportions right is a bit trickier. Fortunately, I’ve got a solution for you.

How to create your own cool Venn diagrams

Everything about these visually quantitative Venn diagrams sounds good and all, but how do you actually create one? You could do it by roughly estimating the areas yourself, or you could dive into some geometry calculations if you’re a math person. This could prove a bit frustrating or time-consuming, though.

So, here is a free tool that will help you create your own visually quantitative Venn diagrams in a few clicks:

On this page, you can find a tool where you can enter the sizes of three sets and their intersections, and it will automatically create a visually quantitative Venn diagram for you. If you want to generate a two-set diagram only, just set the sizes involving set C to zero.

I recommend that you use this resource as a starting point to get the areas of the sets right, and then customize your diagram using some graphic software. For example, you can take a screenshot of the website output, import it into your software, and re-create the sets using the Ellipse Tool. You can then customize labels, colors, and anything else you wish.

Let’s recap!

Traditional Venn diagrams represent a certain number of sets as circles of the same size, and their intersection is usually drawn symmetrically. This, however, gives no visual representation of the numbers of unique and shared elements of the groups: shouldn’t a set with more elements look larger?

The solution to this is visually quantitative Venn diagrams. In these graphics, the area of each sector is proportional to the number of elements it contains. This immediately makes your scientific figure easier to read and to remember.

You can use this free tool to create visually quantitative Venn diagrams that include two or three sets.

So here you go! I hope you will start integrating more of these cool Venn diagrams in your science communication. I would love to see your creations! You can share them with me by tagging @tales_of_science on Instagram!

If you feel a bit overwhelmed and would like me to help you with your scientific graphic, just drop me a line! I’ll be happy to help you!

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