Probably Overthinking It

This tweet from John Burn-Murdoch links to an article in the Financial Times (FT), “A new global gender divide is emerging”, which includes this figure:

The article claims:

In the US, Gallup data shows that after decades where the sexes were each spread roughly equally across liberal and conservative world views, women aged 18 to 30 are now 30 percentage points more liberal than their male contemporaries. That gap took just six years to open up.

The figure says it is based on General Social Survey data and the text says it’s based on Gallup data, so I’m not sure which it is. UPDATE: In this tweet Burn-Murdoch explains that the figure shows Gallup data, backfilled with GSS data from before the Gallup series began.

And I don’t know what it means that “All figures are adjusted for time trend in the overall population”. UPDATE: In this tweet, Burn-Murdoch explains that the adjustment mentioned in the figure is to subtract off the overall trend. In the notebook for this article, I apply the same adjustment, but it does not change my conclusions.

Anyway, since I used GSS data in several places in Probably Overthinking It, this analysis did not sound right to me. So I tried to replicate the analysis with GSS data.

I conclude:

• The GSS data does not look like the figure in the FT.
• Women are a more likely to say that they are liberal, by 5-10 percentage points.
• The only evidence that the gap is growing depends entirely on a data point from 2022 that is probably an error.
• If we drop the 2022 data and apply moderate smoothing, we see no evidence that the gap is growing.

Most of the functions in this notebook are the ones I used to write Probably Overthinking It. All of the notebooks for that book are available in this repository.

Click here to run this notebook on Colab

GSS Data

I’m using data from the General Social Survey (GSS), which I previous cleaned in this notebook. The primary variable we’ll use is polviews, which asks:

We hear a lot of talk these days about liberals and conservatives. I’m going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal–point 1–to extremely conservative–point 7. Where would you place yourself on this scale?

The points on the scale are Extremely liberal, Liberal, and Slightly liberal; Moderate; Slightly conservative, Conservative, and Extremely conservative.

I’ll lump the first three points into “Liberal” and the last three into “Conservative”

All respondents

The following figure shows the percentage who says they are liberal minus the percentage who say they are conservative, grouped by sex.

In the general population, women are more likely to say they are liberal by 5-10 percentage points. The gap might have increased in the most recent data, depending on how seriously we take the last two points in a noisy series.

Just young people

Now let’s select people under 30.

The trends here are pretty much the same as in the general population. Women are more likely to say they are liberal by 5-10 percentage points.

It’s possible that the gap has grown in the most recent data, but the evidence is weak and depends on how we draw a smooth curve through noisy data.

Anyway, there is no evidence the trend for men is going down — as in the FT graph — and the gap in the most recent data is nowhere near 30 percentage points.

With Sampling Weights

In the previous figures, I did not take into account the sampling weights, partly to keep the analysis simple and partly because I didn’t expect them to make much difference.

And I was mostly right, except for men in 2022 – and as we’ll see, there is almost certainly something wrong with that data point.

In this figure, the shaded area is the 90% CI of 101 weighted resamplings, the line is the median of the resamplings, and the points show the unweighted data. We only have weighted data since 1988, since that’s how far back the wtssps variable goes.

In most cases, the unweighted data falls in the CI of the weighted data, but for male respondents in 2022, the weighting moves the needle by almost 30 percentage points.

So something is not right there. I think the best option is to drop the 2022 data, but just for completeness, let’s see what happens if we apply some smoothing.

Resampling and smoothing

Here’s a version of the same plot with moderate smoothing, dropping the unweighted data.

You could argue that this figure shows evidence for an increasing gap, but the error bounds are very wide, and as we’ll see in the next figure, the entire effect is due to the likely error in the 2022 data.

Resampling and smoothing without 2022

Finally, here’s the analysis I think is the best choice, dropping the 2022 data for both men and women.

In summary:

• Since the 1990s, both men and women have become more likely to identify as liberal.

• Women are more likely to identify as liberal by 5-10 percentage points.

• There is no evidence that the ideology gap is growing.

To celebrate one month since the launch of Probably Overthinking It, I’m releasing the Jupyter notebooks I used to create the book. There’s one per chapter, and they contain all of the code I used to do the analysis and generate the figures. So if you are curious about the details of anything in the book, the notebooks are here!

If you — or someone you love — is teaching statistics this semester, please let them know about this resource. I think a lot of the examples in the book are good for teaching.

And if you are enjoying Probably Overthinking It, please help me spread the word:

• Recommend the book to a friend.
• Write reviews on Amazon, Goodreads, or your favorite book site.
• Talk about it on social media.
• Request it from your local library.
• Order it from your local bookstore or suggest they carry it.

It turns out that writing a book is the easy part — finding an audience is hard!

In May 2022, Elon Musk tweeted this cartoon:

The creator of the cartoon, Colin Wright, explained it like this:

At the outset, I stand happily beside ‘my fellow liberal,’ who is slightly to my left. In 2012 he sprints to the left, dragging out the left end of the political spectrum […] and pulling the political “center” closer to me. By 2021 my fellow liberal is a “woke ‘progressive,’ ” so far to the left that I’m now right of center, even though I haven’t moved.”

The cartoon struck a chord, which suggests that Musk and Wright are not the only ones who feel this way.

As it happens, this phenomenon is the topic of Chapter 12 of Probably Overthinking It and this post from April 2023, where I use data from the General Social Survey to describe changes in political views over the last 50 years.

The chapter includes this figure, which shows how beliefs have changed among people who consider themselves conservative, moderate, and liberal.

All three groups give fewer conservative responses to the survey questions over time. (To see how I identified conservative responses, see the talk I presented at PyData 2022. The technical details are in this Jupyter notebook.)

The gray line represents a hypothetical person whose views don’t change. In 1972, they were as liberal as the average liberal. In 2000, they were near the center. And in 2022, they were almost as conservative as the average conservative.

Using the same methods, I made this data-driven version of the cartoon.

The blue circles show the estimated conservatism of the average self-identified liberal; the red squares show the average conservative, and the purple line shows the overall average.

The data validate Wright’s subjective experience. If you were a little left of center in 2008 and you did not change your views for 14 years, you would find yourself a little right of center in 2022.

However, the cartoon is misleading in one sense: the center did not shift because people on the left moved far to the left. It moved primarily because of generational replacement. On the conveyor belt of demography, when old people die, they are replaced by younger people — and younger people hold more liberal views.

On average people become a little more liberal as they age, but these changes are small and slow compared to generational replacement. That’s why many people have the experience reflected in the cartoon — because the center moves faster than them.

For more on this topic, you can read Chapter 12 of Probably Overthinking It. You can get a 30% discount if you order from the publisher and use the code UCPNEW. You can also order from Amazon or, if you want to support independent bookstores, from Bookshop.org.

Or you might like this talk I presented at PyData NYC, this podcast, and this online article at Brilliant.org.