## Saturday, May 28, 2011

### Less variation in family size

Using General Social Survey (GSS) data, I calculated the mean number of offspring for women ages 45 to 64 for each decade since the 1970s. I display these numbers below, along with standard deviations--a measure of variation--and estimates of kurtosis--the degree to which a distribution is flatter or more peaked than a normal distribution:

1970s
Mean 2.77
SD 2.04
Kurtosis .19

1980s
Mean 3.07
SD 2.05
Kurtosis -.09

1990s
Mean 2.54
SD 1.75
Kurtosis .86

2000s
Mean 2.14
SD 1.54
Kurtosis 1.38

2010
Mean 2.05
SD 1.60
Kurtosis 2.35

We all know that family size has shrunk over the past few decades: according to GSS data, from 2.77 children in the 1970s to 2.05 last year. The standard deviations indicate a reduced amount of variation in completed number of offsapring. In the 1970s, SD was 2.04, meaning that if we grabbed two random  women who had completed their families, our best guess is that one mom would have two more kids than the other. Moving forward to the 2000s, SD has dropped to roughly 1.5 which tells us that the two hypothetical moms differ by one and a half kids. In other words, families have become more similar in size. They are more and more converging on the number two.

If the kurtosis number is one or greater, that means that the distribution is more peaked than a normal curve. While there is no problem through the 1990s, one appears in the last decade. What this means in plain English is that a lot of women are having two children, and that puts a skyscraper right in the middle of the bell-shaped curve. In the 1970s, 24 percent of women had two children. By 2010, it was 34 percent.

Why am I interested in this? Well for one thing, reduced variation in family size means that people are contributing a more equal amount of genes to the next generation than in the past. A few decades ago, some people would have zero kids, some would have ten. Of course, we still have diversity, but there is greater convergence on having two offspring. If that convergence became complete (it won't) every woman would have two children and would contribute the same number of genes to the next generation. Since almost all children (not including fetuses) nowadays make it to adulthood (thank God), there is even less differential mortality than differential fertility. It looks like the evolutionary process ain't what it used to be.

But what about the male contribution, you ask. That's next.

1. I'm not sure about the interpretation.

As I understand it, a greater proportion of women are having zero children over the decades - probably related to the increasing average length of formal education.

The more years of formal education, the higher the percentage of women with zero children - and of course the proportion of women going to college, and on to graduate programmes, has been increasing.

2. I am surprised that mean, variance, and kurtosis (a degree to which, apparently, distributions diverge from the normal curve) are considered at all relevant in the first place, when the distribution of the number of children per woman must be one of the most non-normal distributions within all of social sciences. Mean, of course, remains somewhat relevant for any distribution, even when it ceases to be a very good marker of central tendency. But what does SD tell us here? It can of course be computed, but for a distribution that is probably closer to a negative exponential than normal, SD loses its intuitive feel.

I mean, sure, if women averaged 50 children per lifetime, then the normal might be a fairly good approximation.

But order statistics and/or quintiles are probably more explanatory for social science statistics like these.

All this seems to be saying that yes, the mean is decreasing, and yes, so is the variance. And yes, maybe all of that doesn't bode well for civilization. But I think that can be shown without reference to a type of distribution completely unrelated to these data.

### New study: High rate of underweight black newborns due to genes, not racism

A new study finds that several gene variants in African-Americans help explains why they have underweight newborns twice as often as whites...