Virgos proliferating

It is traditional on my birthday (and as a sign of gratitude) to write an entertaining probability note concerning this same occasion.  2016 is no different!  In this article we look at when all of my friends are born.  Obviously there is some randomness to when we are conceived, how long a pregnancy is, and the ultimate day we were delivered to the world.  Is it all random, where the same number of people (1/365 of all annual births) should generally be born each day?  For this query I scraped over 1000 birthdays for all my friends, and drew them (in the red chart below).  You'll notice vastly jagged monthly patterns.  Of course one can say that February is depressed since it is a short month, however all of this chart data has been adjusted to balance out the fewer versus the more plentiful days in the month.  A uniform distribution of birthdays would of course equal 1/12 (or 8.3%) per month.  There is a general seasonal variation that rises about September, while there is of course a suppression in birthdays among my friends in February.  It is natural to ask a couple questions from this.  The first is, what is the overall global distribution of birthdays?  The second is, how likely are these seasonal-appearing differences likely to be instead be due to chance alone?  It turns out that despite the galling unevenness of the pie distributions, my friends' birthdays are not statistically different from the global distribution (in the blue chart below).  But the global distribution is statistically different from a uniform distribution (so there is seasonality!)  We may also have social preferences for being friends with some zodiac/astrological profiles more so than others, but still we are bound to simply run into (and celebrating birthday with) more Virgos (keen, social) and  Libras (balance, justice).  By the same vein, we run into fewer Capricorns (practical, intelligent) and Aquarii (simple, poetic).  Of course our study of horopscopes have been outdated when it first started many millennia ago, as recently announced by NASA.  We really have 13th zodiac signs (and need to return Ophiuchus into the mix, which would awkwardly squat in December).  Readjusting for 13, instead of the geometrically pleasant 12 that the Romans invented, would imply that I too am a Virgo.  They just keep proliferating!  The last trivia here is that our wonderful current President Obama is none of these profiles mentioned so far.  He is a Leo (power, unassuming).  Both presidential contenders right now also share none of these zodiac signs.  Donald Trump is a Gemini (flexibility, drive), while Hillary Clinton is a Scorpio (secretive, argumentative).

Running a nonparametric Chi-square test and a parametric binomial test across my friends' birthdays, we see that they are different from the global distribution, though not as statistically significant as one might imagine.  A p-value of about 1/3.  On the other hand there are millions of people born each month, year after year, and the pattern here is far more statistically significant, despite the amplitude of differences is not as jagged.  See the chart below that shows how as we cycle through the months, year after year, there is less than a 1/2% standard deviation in the monthly distributions of birthdays globally.  Recall that the average distribution of birthdays in a given month, if random, would be 8.3%.  Yet for my friends it is a 2% standard deviation, and far more erratic around the seasonal pattern, for the 1000 or so birthdays.  Note for my friends there is a slump not in January (as it is for the global distribution), but instead it is in February.  So that would include Pisces (unassuming, intense) as well.

 

Bottom line is that the oscillations are a result of a smaller sample size (tens of thousands instead of tens of millions) and natural for the seasonal patterns, which when taken at the global level are smoothed out more.  Also don't take your horoscopes too gravely!