Statistics - It's Best to Be Skeptical First

Candice Watters over at The Line writes on a Wall Street Journal analysis of wedding costs. It is common for people to parrot the belief that the average wedding costs almost 30,000. The statistic is misleading, though. The mean doesn't really capture what most weddings cost because it's susceptible to corruption if the set from which it's drawn includes even one wildly different example. The article gives this example:

One $1 million wedding put into the mix with 54 weddings costing $10,000 each would boost the mean to $28,000, although among the 55 couples, $10,000 would seem a much better representation of the typical cost.

This is a typical problem with statistics, but the real problem lies with people. First, we're impressed by the statistic because it sounds believable, so we carelessly repeat it. Then the cycle begins again with others being impressed and then carelessly repeating. Stop the madness!

A comment on the blog gives another example:

I know this is unrelated, but this wedding cost miscalculation is similar to how the average wage for men and women is derived. Instead of comparing the wages for the same job (i.e., male writer to female writer, or whatever other job), they just put all of the wages together for each gender and call that the average. Of course, more men work full-time and men also work the majority of the dangerous, blue-collar jobs, so just comparing the total gender wages does not make much sense. This is why the supposed stat of women making 77 cents for every dollar that make men is so ludicrous.

I'm at the risk here of doing exactly what I criticized above: parroting another statistic about women's wages because it sounds more believable than some other statistic. After all, I haven't studied this.

The point here is not to say that women typically make equal wages to men. If you have some data on that question, please share it with us in the comments section. I offer the example here to point out that statistics, unless explained and elaborated, are very often misleading. The value of an explanation like the one above about the women's wage statistic is that it leads us to examine the facts themselves. Ideally, the statistic itself, when we first heard it, would have motivated us to do that before the whole mess got started.

Since it's easy to be misled by statistics, it's best to be skeptical about them until we've examined them.

Comments

[alan aronson]

Most tables will state if the average reflects the mean or median. I don't know where the commenter got his data. There is a large body of data that breaks down wages by gender, occupation, race, level of education, etc. - below are a few links.

http://www.bls.gov/cps/cpswom2000.pdf

http://www.bls.gov/cps/cpsaat39.pdf

http://www.bls.gov/bls/blswage.htm

http://www.womensmedia.com/new/Lips-Hilary-gender-wage-gap.shtml

http://gstudies.asp.radford.edu/sources/wage_gaps/wagegap.htm#backslide

This is from the Journal article where the median cost of a wedding is also listed.

"The so-called average cost -- between $27,400 and $28,800, according to the latest iteration of these surveys -- is a mean. That's the kind of average you might remember from grade-school math: In this case, it's the sum of all the survey responses, divided by the number of people surveyed. The mean is especially susceptible to a single lavish exception: One $1 million wedding put into the mix with 54 weddings costing $10,000 each would boost the mean to $28,000, although among the 55 couples, $10,000 would seem a much better representation of the typical cost.

For the three surveys, the median wedding cost is closer to $15,000. The median is the middle figure when you line up a set of numbers in order of size. It is a popular choice for social statistics because it is unperturbed by very small or very large numbers.

[KS]

For further information on women's wages, I recommend checking the Independent Women's Forum website, iwf.org. Look under Issues, then Women and Work, then Wage Gap.

[Jon]

I've read that 79.6% of all statistics are made up.

[Douglas Westfall]

That's very funny Jon.

[Mike Westfall]

Lies, Damn Lies, and Statistics!

[Agilius]

The average American doesn't factor in to the average statistic.

o.O

[Colin]

1. 95% of people will believe a statement if it is backed up by a statistic.

2. I just made that up.

[Rick Ianniello]

Another statistic for you ... half of the people are below average ...