If you study contemporary religion and are interested in religious trends in America, data is not a problem. There's a wealth of data. A surplus. Lots and lots of raw info, which one can only be grateful for.
The problem isn't numbers, but interpretations of numbers.
It could be a full time job, questioning and challenging and correcting interpretations of this data.
Part of this is just because so many of the interpretations are political, and are essentially hack work. If your mission, in reading the numbers, is to show why your side is right and "winning," whatever winning means or is supposed to mean, you're going to be able to make the numbers say what you want them to say. But that will be a shallow and facile reading. Numbers aren't so simple as to just prove straightforwardly that a certain theology is the right theology, or to allow for easy extrapolations of truth beyond the brute fact of one number or another. Ultimately, it will involve implications you're not actually comfortable with, and will involve accepting premises which, as they say on cop shows, can and will be used against you.
So be forewarned.
In that spirit, three things to think about when interpreting contemporary statistics for U.S. religious participation:
1. For an explanation to explain one thing, it has to explain many things.
Case in point, if "accommodating the culture" explains why Episcopal numbers declined from the '70s onward, why did "accommodating the culture" apparently have no negative consequences from the gilded age to '66?
Or, if "holding true to orthodoxy" and "maintaining traditional, conservative faith" explains Southern Baptist success from the mid '30s to 2000, what happened then?
Another way to think about this is that explanations all have implications, and if you query some of those implications, making them more explicit, you can get a better sense of whether or not the argument is something more than an ad hoc guess.
So, for example, William M. Briggs, the Cornell University statistician who put the above graphs together follows Douthat's commentary on "liberal Christianity," which is changing and changing and dying for that reason. Worked into a rule, the thesis proposes: when a religion becomes indistinguishable from the surrounding culture, in an environment where religions compete for adherents, said religion will lose adherents.
It's actually a really interesting thesis. What "the surrounding culture" consists of needs clarification, of course, and it would be helpful if the corollary thesis were also considered, that when religious stand out from or oppose the surrounding culture, in an environment where religions compete for adherents, said religions will gain adherents. I can think of a number of religions that seem more oppositional to American culture than, say, Southern Baptists, which have not done so well in gaining adherents. Especially in places where the "surrounding culture" actually is most accurately described as "Southern Baptists."
The point being, if this explanation is going to account for why there are so many Southern Baptists in the American South, it is also going to need to explain why Hare Krishna and Zoroastrianism are not so popular in that same region.
If the explanation can't explain anything except the one particular point, it's not a particularly good explanation. It's likely just hackery, an ad hoc, not-really-serious argument that supports a pre-conclusion, i.e., that one side is right, "winning" because they should be winning, etc., etc.
2. There are internal changes and external changes. Changes in thought and ideas and changes in conditions and contexts. Remember to also consider the later. Many interpretations of graphs like the above emphasize or focus on only changes (or purported changes) in theology. But that's not all that's going on.
While many have, e.g., said things like Briggs says about the above graphs, that,
"those denominations which are roughly 'conservative' are strengthening, while those which are roughly 'liberal' or 'progressive' are weakening. And it doesn’t take a keen eye to see when the trouble started. With your finger, draw a vertical line at 1960 or so on each of these plots, and then allow yourself a slight 'Ah,'"that only takes changes of ideas into consideration. What other external factors changed in the mid '60s? It's true that the 1960s saw a leftward lean for many churches, but it was also a time when America's immigration policies changed, which meant that the racial make-up of the country changed. One could plausibly "draw a vertical line at 1960 or so on each of these plots" and then think about the 1965 Immigration and Nationality Act and how that has dramatically reshaped the demographics of the US. In the cases of Catholicism and Pentecostalism, here represented by the Assemblies of God, it's quite possible to argue that growth has everything to do with that immigrant influx. Methodists and Episcopalians, on the other hand, are nearly 90 percent white.
I don't know why it's so hard to imagine that culture is not just mental and psychological, but also material, but it is. Changes that happen -- in religion or anything -- are often better explained by charting changes in context and conditions than by accounts of how people have suddenly transformed.
3. Correlation and causation are not the same thing.
Anyone who interprets contemporary religious numbers should have to have this tattooed on the insides of their eyelids.