# Rambling Thoughts

## Religiosity in USAMO

I was recently asked an interesting question: What is the correlation of religiosity to the number of USAMO qualifiers?

Let’s do some data analysis to answer this. First, we measure religiosity using data from a Gallup poll. Since this poll gives religiosity by state, we’ll doing this correlation by state. Instead of computing correlation of religiosity vs number of USAMO qualifiers (which is highly population-dependent), I instead looked at correlation of religiosity vs proportion of USAMO qualifiers in the population. Using population data from Wikipedia, I inputted all of the data into an Excel spreadsheet and asked Excel to compute some correlations, and the results are as follows:

The correlation coefficient of religiosity vs number of USAMO qualifiers is -0.54, which is surprisingly strong; I was expecting a correlation of something around -0.3. This suggests that religiosity is fairly strongly negatively correlated with the number of USAMO qualifiers.

Let’s take a look at religiosity vs the number of AIME qualifiers or AMC participants:

Correlation coefficient: -0.47

Correlation coefficient: -0.42

What does this mean? First of all, it seems that the correlation becomes weaker as the contests become less selective, suggesting that the difference between contest math in states with different religiosities is not just a difference in enthusiasm or participation. There is also a difference in achievement, as students in less religious states have a better chance of becoming a USAMO qualifier. The participation difference is still very significant though, as the correlation coefficient between religiosity and AMC participation is nontrivial.

The data considered is certainly imperfect. For example, the USAMO qualifiers list is not final, and a final list is not expected to be published for a few more days. In addition, the AMC participant data varies from year to year, and the data for the 2010 tests might not be fully representative of a typical year. For example, the snowstorm in February made it very difficult for some students in the Northeast to compete, knocking out a significant number of AMC participants. In addition, some students take the AMC twice and were hence double counted in the AMC or AIME numbers, and the might have given themselves a better chance to qualify for USAMO. I suspect that this behavior is more common in states that were already good at math contests, making the fluctuations in the numbers exaggerated. The rule that every state must have a USAMO qualifier might have inflated the USAMO qualification numbers for some states, and private schools in some states recruit across the country and therefore skew their states’ numbers (which is why this analysis couldn’t be done for Putnam, for example).

Can this phenomenon of correlation between religiosity and USAMO qualifiers be explored further? Some interesting questions still remain. For example, what is the correlation between IMO scores and national religiosities? If there’s anything else I should consider, please comment on this post and tell me.

A disclaimer: Correlation does not imply causation. In this post, I pointed out that religious states tend to do less well at contest math (at least as measured by the AMC series of tests). However, I do not make any claim that religion is the cause of this achievement gap, and I refuse to speculate on why this achievement gap exists. I am not opposing religion in this post, and I’d prefer not to receive hate mail.