Doing the Math on Religious Affiliation
James R. Rogers
December 4, 2012

In the forthcoming issue of the journal Sociology of Religion, sociologist Philip Schwadel reports that between 1974 and 2010, the “probability of reporting a strong religious affiliation declined considerably among Catholics” in the U.S. and “increased among evangelical Protestants.” The thing is, this is not necessarily quite the bad news it might sound to be for Catholics, and not quite the good news it might sound to be for Evangelicals.

Let’s start with the Evangelicals. Using data from the General Social Survey, Schwadel reports the probability that someone who identifies as an Evangelical will also report having a “strong affiliation” with his or her religion. The other affiliation categories for Evangelicals are those who report having a not-very-strong affiliation or only a somewhat strong affiliation. Schwadel combines these latter two groups for the purposes of his analysis.

Now, it is possible that the reason the probability increased that an Evangelical would report having a strong religious affiliation is because more Evangelicals developed a strong affiliation with their religion during that period. But it is also possible that the probability increased even though not a single Evangelical became more strongly affiliated with Evangelical beliefs over this period.

How can that be?

Schwadel calls it “doing more with less.” The result follows from the way that probability is calculated from the sample. To wit, probability depends not only on the number of strongly affiliated Evangelicals (#SA) but also on the total number of Evangelicals. The total number of Evangelicals includes not only those who strongly affiliated with their faith, but also those who report not very strong (#NVS) or only a somewhat strong affiliation (#SS).

So, the probability that an Evangelical reports a strong affiliation is:

From this it is straightforward to see that the proportion of strongly affiliated Evangelicals could increase as a result of an increase in the raw number of strongly affiliated Evangelicals (relative to those reporting NVS and SS affiliations). But note that it is also possible that the proportion of strongly affiliated Evangelicals could increase, even though their numbers do not increase, if the number of Evangelicals reporting not-very-strong or somewhat-strong affiliation decreases.

Without intending to be pedantic (but possibly being so nonetheless), let me provide a simple numerical example for the many misomaths and mathophobes out there (not least including prominent members of the First Things editorial team).

Let’s say that we have a population of five Evangelicals. Two report being strongly affiliated with their faith, two report being not very strongly affiliated with their faith, and one reports having only a somewhat strong affiliation. The probability that a randomly selected Evangelical from this population reports being strongly affiliated with the faith is 0.4.

Now, let’s say that one of the not very strongly affiliated Evangelicals drops out, becoming unaffiliated with the Evangelical faith (perhaps affiliating with a mainline denomination, converting to Catholicism, or becoming unaffiliated with any faith). There is now only one person in the NVS affiliated category rather than two people in that category.

If that happens, the probability that an Evangelical reports being strongly affiliated with the faith increases even though the number of strongly affiliated Evangelicals has not increased at all:

The probability that an Evangelical reports being strongly affiliated with the faith increases from 0.4 to 0.5. As Schwadel reports, “disaffiliation may lead to greater average levels of commitment among the religiously affiliated.”

Reports by Pew and others find that the number of Evangelicals has been decreasing in recent years. As a result, Schwadel’s finding that the number of strong adherents has remained fairly constant over time would hint at the plausibility that the reason for the increase in strength of affiliation results mainly from the loss of marginally affiliated Evangelicals rather than from an increase in the absolute number of strongly affiliated Evangelicals.

Conversely, the reported decline in strongly affiliated Catholics might not be as bad news as it might initially seem by similar reasoning. Schwadel speculates that there could be two reasons for this decline among Catholics: the increasing media attention to the sex abuse scandals in the 1980s and the increasing number of Hispanic Catholics in the U.S. The first cause would be bad news. The argument would be that the absolute number of strongly affiliated Catholics declined in response to the revelation of the sex abuse scandal and the Catholic hierarchy’s response to it. This would cause a decline in the numerator and result in a lower probability that Catholics report a strong affiliation with the faith.

The increasing number of Hispanics, however, would create results that mirror the changing statistics for Evangelicals. According to Schwadel, more Hispanics report a not very strong or only somewhat strong affiliation with Catholicism relative to non-Hispanic Catholics. As a result of the increasing number of Hispanics in the U.S., the denominator increases for Catholics and the probability that a Catholic reports being strongly affiliated with the faith decreases. This would occur even if there were no decrease in the absolute number of U.S. Catholics who report a strong affiliation with the faith.

That said, Schwadel discusses in passing the possibility that the seemingly full integration of Catholics into U.S. public life is not an unalloyed benefit for the institutional health of the Catholic Church. He writes: “As Catholics have moved from a group on the margins of society to playing a central role in American society and culture, the Church has become a less pivotal institution in Catholics’ lives.” Schwadel provides a couple of citations for this claim. The claim is presumably not unique to Catholicism but rather pertains to the strength of member affiliation for any once-excluded group as the barriers to social, economic, and political entry into the mainstream disappear.

Not that exclusion could ever be sought for the incidental effects it might have, however beneficial those effects might be. Schwadel’s observation does posit, however, a bit of a sobering counterpoise to the celebration in recent years for what the robust participation of Catholics in national political life might mean for the Church as an institution.

James R. Rogers is department head and associate professor of political science at Texas A&M University. He leads the “New Man” prison ministry at the Hamilton Unit in Bryan, Texas, and serves on the Board of Directors for the Texas District of the Lutheran Church-Missouri Synod. His previous “On the Square” articles can be found here.