This contentious interview of Jordan Peterson, a University of Toronto Psychology Professor, by Cathy Newman of the UK’s Channel 4, has garnered a huge amount of attention. While the interview was nominally to promote Peterson’s upcoming book, Newman clearly believed that she was going to be able to nail him as an ignorant bigot. Unfortunately for her, the general consensus is that Peterson was able to avoid that outcome, and make her look pretty silly in the process.

Much of the conversation (see here, for example has focused on Newman’s interrogatory tactics and how Peterson chose to respond to them, but I there are lessons to be learned here about communicating with statistics. The first time I watched the video my initial reaction was that Peterson clearly understood the statistics he wanted to use to support his points, and the interviewer did not. Those statistics are not all that controversial, even among those who tend to disagree with Peterson’s conclusions, but throughout the interview Newman consistently jumps from his rather modest claims to extreme (and sometimes bizarre) conclusions that she assigns to him.

Even if, as some suggest, Newman’s ignorance here was deliberate, her responses reflect the kind of intuitive interpretation of statistics that I’ve seen many times. Statistics are not intuitive. They are tricky. If you need to communicate with them to a non-statistician—and you will—it’s important to help people understand what the statistics you’re using do and do not imply.

Let’s look at two sections where, with the help of hindsight, we might be able to improve on Peterson’s presentation. First, let’s examine the initial conversation about the pay gap.

Peterson makes two mistakes here. First, in an uncharacteristically imprecise use of language, he says that the pay gap “does not exist,” when that’s not what he means. Over a minute later, he clarifies that he actually means “does not exist solely due to gender”, but by that point a minute of airtime has gone to waste.

The more common mistake Peterson makes in the pay gap discussion, though, is focusing on the method. He starts talking about multi-variate analysis, and the interviewer—and most home viewers—have no idea what it means.. When challenged by Newman on why he keeps talking about it, he enters into a mostly fine description of why controls are important in regression (although he does make it sound like he’s doing a series of one-to-one comparisons rather than a single composite analysis). He’s not wrong, but he’s also not making his point; the only thing that this part of the conversation does for him is make it sound like he knows what he’s talking about, but the lay audience won’t get anything out of it.

Everyone who communicates about regression-type analysis needs to have a stock phrase to describe what’s important about it and move on, and I was a bit surprised Peterson didn’t have one ready. Here’s how I might have phrased the point he was making in a way that could keep the conversation focused on the point Peterson was driving at:

“It does seem that way, but what repeated studies have reliably found is that when you account for an person’s age and their personality and their aptitude and their interest, then the difference their gender makes to their salary is very small. So a man and a woman who are similar in other ways should expect to make about the same amount of money. So we know that the pay gap is not mostly due to gender bias.”

I timed myself and that took 22 seconds to say, without getting the methodology behind the point in the way of the point itself. Peterson and Newman six times that on an unfruitful conversation about how statistics work.

The second difficulty that stood out to me about the interview was the way that Peterson and Newman talked past each other on the subject of population characteristics and individual characteristics.

The best example picks up right where the last stopped:

Again, Peterson makes an unforced error when he says “Women are less agreeable than men,” and again, the problem isn’t that he’s wrong exactly but rather that what he’s saying will be taken differently by the viewers than he means it. The natural implication of “woman are less agreeable than men” is that all women are less agreeable than all men.

This confusion is nicely demonstrated by the exchange that follows. Newman accuses Peterson of “a vast generalization,” by which she means that he’s making a statement about all individual women. He says that “it’s not a generalization,” and what he means is that it’s a statement about the distribution of that trait among the population of all women. The disconnect is that the same words mean something slightly different to the two because one is thinking statistically and the other isn’t. And the onus has to be on Peterson to make his point clear.

At first I thought the best phrase to do that would be “agreeableness is more prevalent among women than men,” but I don’t think that’s quite right, because agreeableness is a continuous variable. You could opt for something less precise like “more women are highly agreeable than men,” but that doesn’t quite fit right either. I think the best solution here is a small modification: “Women tend to be more agreeable than men.” People understand the non-universality of tend, and that avoids the confusion.

This one isn’t so much a question of wasting time as of avoiding confusion. To their credit, Newman and Peterson reach consensus of what they mean fairly quickly with the final exchange in that clip. They just both get a bit annoyed doing it.

Peterson warmed up as the interview went along, and I think he handled a second go at much the same argument much better:

In that exchange, Newman fires off a number of conclusions that she claims are implied by Peterson’s arguments. All of them are predicated on the idea that his population statistics determine what will happen with every woman. Instead of talking about how statistics work, he goes to the concrete example of Newman herself. That allows him to make his point without any confusion: she’s been successful precisely because she’s pursued her career in the way that he says matters more than gender. There’s no way to confuse “you, as a woman, are successful because you have battled for it” with “the need to battle for success means women will never succeed.” Sometimes when you’re talking about statistical truths, the best way to do it is to avoid discussing them statistically at all.

Now, the point of this isn’t that Peterson’s dumb and I’m smart; I’ve had time to consider and edit. The point is that communicating statistics is incredibly difficult, even if you understand them well yourself. It’s a separate skill, and takes practice. When you screw it up, it’s easy to blame the ignorance of our listeners, but that’s too easy; it’s far better in the long run to focus how you can be better at communicating statistical facts. Then people might be more interested in what you have to say.

Some stray other thoughts about the interview: