I have a bit of in interest in politics and something that a few pundits and comedians have pointed out is that the current GOP field of candidates has a ton of children. So, I was curious to try to find out how probable it is that a group of people had so many children.

The relevant statistic I am interested in therefore is the Total Fertility Rate (TFR) of the United States. Currently, that number is sitting at 2.1. This is the average number of children that a woman in the United States would have during her lifetime. Another piece of information I need is the distribution of family size in the United States. I couldn’t really find this information, but I did find a paper saying that family size can be modeled with the geometric distribution. This then, is all the information needed to proceed with our calculations.

The geometric distribution is completely defined by one parameter, p. And the way we can solve for p is by using the value of the TFR. The mean of the geometric distribution is given by

μ=(1-p)/p

So, we just set μ=2.1 and solve for p. This gives a value for p of 0.323. So, that means that the probability density function looks like this:

So, now that we have characterized our distribution, we need to look at the candidates. The candidates and the number of (biological) children each has is given in the below table.

Candidate |
Number of Children |

Newt Gingrich |
2 |

Herman Cain |
2 |

Tim Pawlenty |
2 |

Rick Santorum |
7 |

Michelle Bachmann |
5 |

Mitt Romney |
5 |

Jon Huntsman |
5 |

Gary Johnson |
2 |

Ron Paul |
5 |

Rick Perry |
2 |

So, with 10 candidates there is a total of 37 children. That is an average of 3.7 children per candidate. So, judging by the graph of our probability distribution above and calculating it out explicitly, there is just a 7.6% chance of that happening with a random selection of 10 people in the United States.

Does that mean that the GOP reproduces more than Democrats? Or is it a statement about presidential candidates in general? I don’t really know the answer to that and I don’t really want to invest the time to figure it out. At least in this case, religion seems to play a role with Mormon and Catholic candidates (two religions known for large families).

NOTE: I know that this is not a very good statistical analysis, but it is a first swing just to satisfy my curiosity, that is all.

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