follow-up to My Friends’ Birthdays
The main conclusion I drew from examining my Facebook friends’ birthdays is that I didn’t have enough data to see the birth month effect – when your month of birth influences your success in a field because it decides your relative age to your peers early on in sports or school.
The birth month effect is real in some circumstances. Just now, I searched for “US junior baseball team” and found this roster.
In Outliers, Malcolm Gladwell explained that the cutoff date for youth baseball leagues in the US is July 31. (It’s now changed to May 1, so in ten years we can do this experiment over and see the effect.) Thirteen players on the roster were born in the half of the year directly following July 31 (August through January), and only five were born in the next half (February through July). With data like that, even a sample of eighteen people is enough to see the strong effects that birth month has on athletic success. The odds of such lopsidedness occurring by random chance are about 5%.
If 18 baseball players is enough to see a significant birth month effect in sports, then shouldn’t more than 100 Facebook friends have been plenty to see it in education?
In American education, there is no firm, uniform cut-off date like there is with baseball. Different states have different dates. Also, parents may have a choice about when to send their child to kindergarten if the child is born in a certain window. I was born in December in Maryland, where entering kindergarteners must be five years old by December 31. I could have been one of the youngest students in my grade, but my parents held me back, making me one of the oldest. Their stated reason was that they thought I’d appreciate being one of the first kids with a driver’s license come high school.
Mixed-up birth months, along with other obfuscating factors the reader may imagine, could easily make a real signal difficult to pick up, so I asked the Caltech registrar’s office for data on all the domestic Caltech students. They kindly obliged, with birth months tallied for the 5083 students enrolled since 1985. I was asked not to release the data directly, but I can report on its statistics.
Since September to December babies can be either old or young when entering kindergarten, let’s leave them out. The hypothesis is that entering Caltech students are more likely to be born in the January to April time frame than May to August. (If you want to be a stickler for experimental design, we could say that the null hypothesis is that students are equally likely to be in those categories.)
There were 3399 students whose birth months fell into one of these two ranges. If each student were a simple binomial variable with even probability we’d expect a standard deviation of 29 in the number of students in each range. We should also take into account that these periods aren’t perfectly equal in numbers of births. According to a Google result, a baby born anywhere from January to August has a 51.85% chance of being born in the May-August window, due partially to the three extra days and partially to higher birth rates. Thus, we expect that if domestic Caltech students have birth month patterns that mirror the American population at large, there should be 1762 +/- 30 students born in the May-August window. If there are fewer than 1700, we have evidence that Caltech students are less likely to be born in the summer.
The statistic is 1713 born in those months, compared to 1686 in January – April. The discarded period, from September to December, has 1684. There is no significant evidence to suggest that Caltech students are more likely to be born in any particular month.
This certainly doesn’t disprove the idea that your month of birth impacts your success in school, but the effect, if present, is not as powerful in education as it is in organized sports.