Tuesday, April 9, 2013

Freshman hordes regress to the mean

More nones, no nuns

For several years I have been following one of the most under-reported stories of the decade: the fraction of college freshmen who report no religious preference has tripled since 1985, from 8% to 24%, and the trend is accelerating.

Two years ago I wrote Freshman hordes more godless than ever; last year I updated it with Freshman hordes even more godless.  Each year, the number of students with no religious preference increased, and the number attending religious services decreased.

In last year's installment, I made the bold prediction that the trend would continue, and that the students starting college in 2012 would again, be the most godless ever.  It turns out I was wrong: attendance went up slightly, and the fraction of "Nones" dropped slightly, in both cases reverting toward long-term trends.

My analysis is based on survey results from the Cooperative Institutional Research Program (CIRP) of the Higher Education Research Insitute (HERI).  In 2012, more than 190,000 students at 283 colleges and universities completed the CIRP Freshman Survey, which includes questions about students’ backgrounds, activities, and attitudes.

In one question, students select their “current religious preference,” from a choice of seventeen common religions, “Other religion,” or “None.”

Another question asks students how often they “attended a religious service” in the last year. The choices are “Frequently,” “Occasionally,” and “Not at all.” Students are instructed to select “Occasionally” if they attended one or more times.

The following figure shows the fraction of Nones over more than 40 years of the survey:

The blue line shows actual data through 2011; the red line shows a quadratic fit to the data.  The dark gray region shows a 90% confidence interval, taking into account sampling error, so it reflects uncertainty about the parameters of the fit.

The light gray region shows a 90% confidence interval taking into account both sampling error and residual error.  So it reflects total uncertainty about the predicted value, including uncertainty due to random variation from year to year.

We expect the new data point from 2012, shown as a blue square, to fall within the light gray interval, and it does.  In fact, at 23.8% it falls almost exactly on the fitted curve.

Here is the corresponding plot for attendance at religious services:

Again, the new data point for 2012, 26.8%,  falls comfortably in the predicted range.  Don't listen to Nate Silver; prediction is easy :)

Predictions for 2013

Using the new 2012 data, we can generate predictions for 2013.  Here is the revised plot for "Nones":
The prediction for next year is that the fraction of Nones will hit a new all-time high at 25% (up from 23.8%).

And here is the prediction for "No attendance":

The prediction for 2013 is a small decrease to 26.6% (from 26.8%).  I'll be back next year to check on these predictions.

Other updates

1) This year the survey repeated two questions from 2010, asking students if they consider themselves "Born again Christian" or "Evangelical".  The fraction reporting "Born again" dropped from 22.8% to 20.2%.  The fraction who consider themselves Evangelical dropped from 8.9% to 8.5%.  But it's too early to declare a trend.

2) As always, more males than females report no religious preference.  The gender gap increased this year, but still falls in the predicted range, as shown in the following plot:
Evidence that the gender gap is increasing is strong.  The p-value of the slope of the fitted curve is less than 10e-5.

Data Source

The American Freshman: National Norms Fall 2012
Pryor, J.H., Eagan, K., Palucki Blake, L., Hurtado, S., Berdan, J., Case, M.H.
ISBN: 978-1-878477-22-4     90 pages.
Jan 2013

This and all previous reports are available from the HERI publications page.


  1. I would have thought a time series (ARIMA) model would have been more appropriate than a quadratic model, since these are after all time series data.

    1. Yes, that would probably be a better model for prediction. The model I used here has the regrettable property that it gives substantial weight to the earliest data points.

      I started out with a quadratic model because I was interested in testing whether there is a slope and (since there is) whether there is evidence of acceleration. With the quadratic model, I can run simple tests on the coefficients.

      Obviously the quadratic model can't go on forever, but it has been holding up better than expected.

  2. I don't think modeling the temporal correlation will change the conclusions. Confidence and prediction intervals would be a bit wider. There appears to be evidence of moderate temporal correlation in no attendance, maybe some in no religion, and little to none in gender gap.