## Fun with Statistics

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Each day I get a brief email update from Science in the News, and one of the summaries today was of an article from the Washington Post about how parents of more than one child spend more quality time with first-born children than with later-born siblings. I glanced at the article and found a list of data that, depending on how you look at it, could be used to justify any one of a number of conclusions.

The list showed how many minutes per day (on average) fathers and mothers spend with each child in their families, broken down by how many total children there are in the family. I’ve arranged the same data below as a grid:

How many quality minutes (per day) fathers spend with each child:

1 kid 2 kids 3 kids 4 kids
1st-born 64.6 82.6 81.4 100.3
2nd-born   62.0 64.5 98.4
3rd-born     56.5 67.7
4th-born       58.7

How many quality minutes (per day) mothers spend with each child:

1 kid 2 kids 3 kids 4 kids
1st-born 82.2 119.8 122.3 124.0
2nd-born   93.0 99.5 112.8
3rd-born     81.0 112.7
4th-born       91.4

The two page article essentially just pointed out that the numbers decrease in each column: the earlier born children get a larger quantity of quality time than later-born children. Indeed, the study that this was based on was published in “Parent-Child Quality Time: Does Birth Order Matter?” by Joseph Price (from the Journal of Human Resources earlier this year; abstract here) so you can pretty much see what point is trying to be made.

But what I immediately noticed was that the data increases across rows! In other words, the more kids there are, the more quality time everyone gets. And this leads me to the conclusion that if one of your children is feeling neglected, the best way to increase the quality time is to have another child. Well, I might be mixing up that whole correlation versus causation thing, but I still find it interesting that what seems to be happening is that families with more children spend more time with each one, so that no matter how many children there are the youngest get about the same amount of attention but the older children get more and more!

No doubt there are other confounding factors that didn’t get mentioned in the newspaper summary, but the way it’s presented (with no mention of causation and with at least two very different kinds of conclusions to draw) reminds me of the Mark Twain quote “There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.” (from page 77 of Life on the Mississippi, although I originally found the quote in Ivars Peterson’s MathLand).