By: Kristin Hunter-Thomson
Looking at 3 variables at once
I am willing to bet that few would say that the divorce rate in Maine over time is driven by the per capita consumption of margarine, but this great graph by Spurious Correlations certainly leads you to make sense of the data in that way.
And here in lies a fundamental struggle with using two y-axes…how in the world do you interpret the data?
Double y-axes: why the temptation
There are many reasons why scientists, and even your students, would want to make a graph with two y-axes:
- you have three distinct variables
- you have one independent and potentially two dependent variables
- your dependent variables have completely different scales
So, for example you can get a graph like this [let’s ignore for a moment the content of what is being displayed in the graph]. Technically the graph designer here has employed some good techniques to help us understand the graph better. For example, the color of the axes and axis labels aligns with the color of the data points. This helps solve one of the biggest struggles with two y-axes graphs, which data go with which axis/scale?
However, I don’t know about you but I am still left scratching my head to figure out what this graph is trying to convey to me about the data. Is it important that the green is all to one side and is higher than the red and blue? Is it important that the blue goes below the red?
Well, here is lies another common struggle with two y-axes graphs…our eyes are drawn to points where lines and data cross. And before we know it our brain has raced ahead trying to make meaning of that connection/cross point. But where the data cross is actually a reflection of the scales that you chose for your axes not anything relevant to your data (think back to the divorce rates and margarine consumption).
For example, the conception risk around 8 and 17 days of a menstrual cycle has no relevance to being “below” or “above” a level of political conservatism. Bur our brains want to find meaning in that relationship because we are hard wired to think that when things cross it means something.
Our brain wiring makes it hard for us to truly make sense of the data, yet people often think that using two y-axes graphs is a more “slick” or “sophisticated” to show their data.
Food for thought on how to avoid the confusion
What can you do if your students really want to make them? I would suggest asking them questions like:
- Why do you want to put two y-axes on your graph?
- What are you hoping this graph will communicate about your data?
- Why are two y-axes the best way to communicate that?
- What do your two y-axes graph not communicate about your data? Or what confusions may be communicated about your data?
- Is there another way you could communicate that message about your data?
By asking these questions we start to teach our students how to make their own decisions. Also how what data they have and what they are trying to communicate/answer/explain with their data determines the best choice in graph types.
Rather than just telling them not to make a two y-axes graph, ask them the questions so they decide why not to do it and why to do something else.
Searching for more?
Check out the “But, which graph is the “right” one?” post from last year to explore how to help your students make their own choices of which graph to use.