I’m always going around saying that graphs are comparisons. For example, see Section 2.3 of Regression and Other Stories or the discussion here.
“All graphs are comparisons” has four implications:
1. If you’re considering making a graph, think of how to construct it to focus on the comparisons you want to examine and to convey.
2. If you’re doing research or writing up results, think about what are the comparisons you care about, and then figure out how to make graphs to show these.
3. To evaluate a graph you’ve already made, think about what comparisons it is displaying.
4. To understand a graph produced by someone else, think of it as displaying a comparison.
The graphs-as-comparison idea is relevant for both research and presentation graphics. Indeed, I’ve argued that research graphics and presentation graphics are pretty much the same thing. In a research graph, you still have an audience–it is you and your collaborators–and in a presentation graph you want convey some understanding to your reader.
Anyway, the other day I came across this old post where Dale Lehman in the comment thread points to this quote from Edward Tufte:
To be truthful and revealing, data graphics must bear on the question at the heart of quantitative thinking: “Compared to what?”
And Chandrasekhar Ramakrishnan points to this other Tufte line:
Small multiple designs, multivariate and data bountiful, answer directly by visually enforcing comparisons of changes, of the differences among objects, of the scope of alternatives.
I read these Tufte books many years ago, so I guess that’s where my “Graphs are comparisons” mantra came from.
Apologies for being off-topic, but what is the planned relationship between this blog and the Substack effort.
https://statmodeling.substack.com
For example, I was reading this post, and wanted to comment:
https://statmodeling.substack.com/p/howard-lutnick-gives-top-cantor-fitzgerald
But the substack is set (?) to not allow comments. Will that post appear here eventually?
D:
Yes, the posts on Substack will appear here eventually.
Here’s the story:
This blog is the main place. It has comment threads and 20+ years of past posts.
But a year or two ago someone told me that there are people who don’t read blogs and don’t follow twitter links, but they do read newsletters. So the advice was given to me to start a newsletter. I already have a blog, so the natural thing for the newsletter is to post weekly links to the blog. Which is what I do. So if you subscribe to the newsletter you’ll get links to all our blog posts. But then I wanted to encourage people to subscribe, so approximately once a week I post a scheduled blog post earlier on the newsletter.
The current end of the blog queue is in early July, so the recent newsletter posts should appear here in a few months.
Very sensible. This gives me several months to prepare high(er) quality comments! ;-)
You’d still be behind
I just thought you should know, I hope you don’t mind
‘Cause I’ve got a carrier pigeon instead of a newsletter, blog post, or twitter link
That arrives even earlier at the window near my kitchen sink
And on a little note attached to its leg
It shows an overview on what’s on deck
D:
Yes, the commenters are to this blog as this blog is to the internet: free content that improves the overall experience.
Quote from above: “Yes, the commenters are to this blog as this blog is to the internet: free content that improves the overall experience.”
For me, this blog and the comments here are sometimes like a door to some hallway
Where there are other doors to open, or rooms to briefly stay
The comments by Mr. Kane and Mr. Gelman opened such a door
Which I walked through, and ended up on some other floor
I walked around, and saw and heard
Some interesting story about a certain bird:
Cher Ami
A carrier pigeon that showed things that might be worthwhile to see
And that in turn led me to another hallway and another door
Via another staircase I ended up on a different floor:
“Mon ami”
Which people might often use incorrectly, apparently
I supposed this is as good a place as any to share an exercise I used in teaching called “What’s the denominator?” You give some numbers to the students in a handout, divide them into teams, and ask each team to come up with what they think a good denominator would be. After time for deliberation, each team presents its answer and why it chose it.
One obvious learning objective is to understand the relationship between comparisons and questions of interest. Are you interested in growth? Then compare, say, a country’s number about something to what it was in an earlier period. Are you interested in the effect of different environmental factors or policies or something else? Then choose comparators that span those differences. And so on.
But deeper is a version of Tufte’s idea, that numbers are meaningful only in relation to other numbers, and this ought to be conscious and not haphazard. The nice thing about this exercise is that it can be tailored to classes at all levels and in all subject areas. Sometimes the answers you get are surprising, and you learn something valuable from the different perspectives students bring with them.
When interested in growth, I’m skeptical whenever the denominator is the number in an earlier period. Why was that particular period chosen?
If a sequence s is growing at a rate of r per unit of time, that means s_{n+1}/s_n – 1 = r, right? So that order seems natural enough to me.
And please use grayscale, not colors, on graphs.
Hey, I like colors!
I disagree. Sparingly, perhaps – to highlight in some cases. But in general colors have no natural interpretation (except on weather maps or in accounting statements). If you color 6 categories in a line chart, you need to keep going back and forth to the legend which is destructive to understanding. Now, if you have sufficient room on the graph to label the lines directly, then color will help distinguish them from each other, although it does introduce a visual distinction that goes beyond simply identifying the separate lines. Can you explain a bit more what you mean by liking colors? Under what circumstances?
p.s. grayscale is sort of dull, so I’ve taken to using a blue scale – one color but with different intensities.
Dale:
I have lots and lots of examples where color is useful. See for example here, here, and here.
I agree that it’s bad to make a graph where the reader has to go back and forth between the display and the legend. That’s bad whether it uses color, symbols, different patterns of dashes, or anything else. I recommend putting the labels directly on the graph.
tl;dr. When done poorly, color can make graphs harder to read. When done well, color can make graphs much clearer.
A single scaled color can be a good choice if the categories have a natural order, but if they don’t it doesn’t seem like using a grayscale (or blue scale) will make it any easier for the reader to internalize the mapping between the different lines and the data they represent.
The folks at Storytelling with Data make frequent use of greyscale plus a highlight colour (they like cornflower blue) and I think that’s often very effective. But it seems extreme to discard colour scales entirely. For example, I don’t think the map of US unemployment rates by county that appears in the introduction to the viridis R package would be better in greyscale. It’s easy enough to put the two options side-by-side and decide for yourself which design conveys the story in the data more effectively.
Tufte is not opposed to color but thought it must be used judiciously. His maxim regarding color is: “Above all, do no harm.”
If you have four to eight discrete categories then colors are better than grayscale (and better than any single color with different intensities). Red/green/blue/purple/orange/yellow are much easier to distinguish than six shades of gray. If you doubt this, say so in the comments and I’ll do a short blog post on the subject in the next week or so.
I’m sure you know, but always worth remembering advice in:
https://en.wikipedia.org/wiki/Color_blindness
This is a real concern, but using hue as a redundant encoding can still speed interpretation for most people without leaving behind folks who perceive it differently.
One additional way I like to think about it as well is in terms of causality and conditional probabilities, especially for proportion/rate type charts (like pie graphs or area graphs or stacked bar charts).
For example, say you show a stacked bar graph of the proportion of age categories (young,middle,old) on the Y axis, and the X axis is the flavor of ice cream they ate. This shows `P(Age | Ice Cream Flavor)` – the probability of the age category conditional on the ice cream flavor chosen. This is probably backwards from what you want if you are a marketing person — you want `P( Ice Cream Flavor | Age)`, you think maybe the age demographic influences the ice cream choice (and you want to market your product to the correct segmentation).
So in that scenario, you maybe want a set of small multiple bar or line plots, with the Y axis the percent in each category, and the X axis the ice cream flavor.