We find that a ten percentage-point increase in state-level female sports participation generates a five to six percentage-point rise in the rate of female secularism, a five percentage-point increase in the proportion of women who are mothers, and a six percentage-point rise in the proportion of mothers who, at the time that they are interviewed, are single mothers.
Andrew finds these claims implausible, so do I.
Ayres uses the econometrics methodology called instrumental variables regression to support these claims. Since the data is observational, and as Andrew pointed out, there wasn't even a period of time in which one could find exposed and unexposed populations (since the TItle IX regulation was federal), one must treat such regression results with a heavy dose of skepticism.
It is useful to understand that causal claims are possible here only if we accept all the assumptions of the instrumental variables method.
Besides, plausibility is assisted by the ability to outline the causal pathways. It should be obvious that more females competing in college sports does not directly cause more females to become secular. The data on sports competition and on secularism come from different sources and this presents a hairy problem. The analysis would have been more convincing if it found that among the women who participated in college sports, more became secular; what the analysis linked was higher participation rate and higher secularism among all women in the state.
What is it about sports participation that would cause people to become secular? (The visual evidence from professional American sports would lead me to hypothesize the opposite--that sports participation may be associated with higher religosity!) Is this specific to the female gender? Do we find male secularism increase as sports participation by men went up?
As Andrew pointed out, the magnitude of the estimated effect seems too large to believe. I'd prefer to see these effects reported at more realistic increments. A jump of 10% participation is very drastic. For example, according to the chart here (the one titled "a dramatic, 40-year rise"), the percent of women participating in high school sports has moved just 2 percent from 1995 to 2011.
Andrew is right that this is an instance of "story time". And we are not saying that statisticians should not tell stories. Story-telling is one of our responsibilities. What we want to see is a clear delineation of what is data-driven and what is theory (i.e., assumptions). The plausibility of a claim depends on the strength of the data, plus whether we believe the parts of the theory that are assumed.
See how Andrew articulates these--and other--concerns on his post.