Congress and the Zodiac

Birthdays are sufficiently far from uniformly distributed that your base assumption isn't valid.

Here's a couple of immediate search results with "standard birthdate distribution" sets supporting my claim (I actually found several references to the first:
http://www.math.hope.edu/swanson/data/birthdays.txt
http://www.math.hope.edu/swanson/data/birthdays_1.txt

Even with attempting to control for typical age of legislators, it does interesting things to look only at the birthdate distributions for around 50 years ago rather than for ransom snapshots relatively near the present.

It's not a proof, but I think it's enough support to not go down that path.

I dunno.... maybe if I saw that data in graph form I'd be able to see this nonuniform distribution you're talking about. Just looking at the numbers looks pretty uniform to me. I'm perfectly willing to believe there is a nonuniform distribution of birthdays, especially within certain populations (because on top of biological reasons, there may be social reasons for breeding at certain times of the year or something). But I haven't been able to find anything about that online.

I have found a lot of references to a Birthday Paradox, which states that "if there are 23 or more people in a room then there is a chance of more than 50% that at least two of them will have the same birthday." Don't know what implications that might have for the question at hand, though, and can't really take the time to ponder it at the moment.

Hmmm... good point. Assuming the numbers in that first set can be generalized to the population as a whole (which requires you to believe that astrological sign does not influence one’s decision to apply for insurance!), there do seem to be a lot more folks being born in Summer & early Fall (Cancer, Leo, Virgo, Libra) and fewer in the Winter (Sagittarius, Capricorn, Aquarius, Pisces) than would be the case if the distribution were even. There are something like 11% more Virgos than in an average sign, and almost 6% fewer Pisceses.

Still, if we accept this +11%/-6% in a sample of 480,715 as representative of the population at large, what are the odds of getting a +56%/-32% in a sample of 422 legislators if those legislators are picked without regard to their sign? I know that a smaller sample size is likely to produce wider margins, but how much larger?

Data

Aquarius	38841	-1218.58	-3.04%
Pisces	37688	-2371.58	-5.92%
Aries	39397	-662.58	-1.65%
Taurus	38909	-1150.58	-2.87%
Gemini	39546	-513.58	-1.28%
Cancer	41630	+1570.42	+3.92%
Leo	42909	+2849.42	+7.11%
Virgo	44542	+4482.42	+11.19%
Libra	41554	+1494.42	+3.73%
Scorpio	39036	-1023.58	-2.56%
Sagittarius	37694	-2365.58	-5.91%
Capricorn	38969	-1090.58	-2.72%
Average	40059.58

Still more obvious sampling problems. I assume that the average age of people shopping for insurance is lower than the average age of congresscritters. So there's a likely bias there. Especially if one gueses at the average age of congresscritters as putting them as early boomers. I figure there was a significant local sway in birthdates around the late 40's and early 50's that could show the data isn't relevant.

And I didn't get into crunching those numbers (and will continue to resist) because I don't think the samples available represent the population we're looking at. I think they're fine for showing that the distribution of birthdates across the population isn't even, but that doesn't correlate with them being well suited to showing likeliness of the kinds of specific distribution patterns you're looking at.

I think the "Birthday Paradox" (linked above) is more relevant as a train of thought toward considering these groupings.

"Too big a problem to adequately model simply."

Congress and the Zodiac

Mr. Balko responds: Congress and the Zodiac

Odds of this happening by chance about 1 in 1600

The probability is calculated using the binomial distribution. Here is a calculator you can use to determine the probability

http://psych.rice.edu/online_stat/java/binomialProb.html

enter N=79, p=0.5 (50/50) and greater than or equal 55 to get the probability of at least 55 cancers in a sample of 79 tauroid or cancer.

Re: Odds of this happening by chance about 1 in 1600

Maybe it has something to do with the probability that a congressperson's parents were more likely beginning a new school year at the time of conception, than were the general public, and there's some psychological effect going on. Or maybe that a congressperson's parents are more likely to plan the birth of their child for summer break or after their schooling was done. Or a combination of both.

Balko calls in the stats geeks!

Congress and the Zodiac, continued.

Re: Balko calls in the stats geeks!

…and continued further…