The Numbers Guy Wall Street Journal columnist wrote recently about reporting the average cost of weddings. He said the averages are means, not medians, they don’t include certain groups, and so on. It was one of the better numerical discussions I’ve seen in a newspaper.
However, it was about 25% of an ideal discussion. When I was a freshman in college, I went to a talk about life on other planets. The speaker wrote a bunch of numbers on the board, multiplied them together, and came up with something that was supposed to estimate the number of other planets with life. After the talk, I asked, “What’s the error in that number?” The speaker had no idea.
If the Numbers Guy gave his column as a talk, during the question period I would say: “You’ve told us what’s wrong with those numbers. Thanks. I’d also like to know what’s good about them.” His column and blog contain nothing about this.
Here’s my answer:
1. Sure, the median is more interesting than the mean. Because the distribution is obviously skewed positive (like the distribution of incomes), the mean provides an upper bound on the median. If the mean is $30,000, for example, the median must be less. That’s helpful to know.
2. Assuming the distribution of wedding costs resembles the distribution of incomes, I’d guess that the median is somewhere between half and two-thirds of the mean. So the mean is providing even more useful information.
3. The false precision of some estimates (e.g., “$27,852″) indicates the numerical savvy of their source. That too is helpful to know. I will take the rest of what they say less seriously. In a talk I attended, Richard Herrnstein, the Harvard psychologist, said a certain t value was so large that he had to use a special table to find the associated p value. This was a accurate foreshadowing of the quality of The Bell Curve, which Herrnstein co-authored.
That brings us to about half of a good discussion. The other half would come from eliminating the long discussion of sampling bias. Yes, the wedding industry loves sampling methods that overestimate the average cost. I knew that before I read the column. What I don’t know is a method that will tend to underestimate the average cost and thus provide a lower bound. That’s what I’d like to read about.
Something is better than nothing. Micronutrient requirements.
To me, the real unanswered question is the net cost of weddings after gifts are accounted for. I have heard of a few weddings in the New York area (home of the nice, efficient cash gift) that have turned a profit, so the distribution may not skew positive to the degree expected.
This also means that couples have an interest in keeping the perceived cost of weddings high, to encourage more-generous gifting.