Recently, my brother was a contributor to an infographic his organization put together about race and the wealth gap. Despite knowing that I am inherently biased against infographics, he called me and asked my opinion on some criticism it had received. The whole thing’s fairly large, so I’m only posting the piece that caused the controversy:
The graph at the top had caused some commenters to question the use of “average” in lieu of median, and if it was skewing the results.
Luckily, since my brother has listened to me rant for years about people not sourcing their facts, he had mad sure this graphic included the source of the numbers…a report from the Urban Institute that can be found here.
I was interested to see that they not only acknowledge that they use average over median, but also give the median numbers to show that the trend is essentially the same. Here they are for 2010:
White 632,000 124,000
Black 98,000 16,000
Hispanic 110,000 15,000
Using average numbers, the absolute gap between incomes is larger…however I was interested to see that using median the ratio of incomes would have looked larger (8 times lager vs 6 times larger). Honestly, there’s pluses and minuses to using either angle.
Absolute inequality generally favors the gap (higher value – lower value) as the important measure. This can make sense in some situations, but it tends to depend on where you start. The difference between a person who makes $20,000/year and someone who makes $90,000/year is very different from the difference between someone who makes $90,000/year and someone who makes $160,000/year.
Relative inequality looks more at the ratio between two numbers. It also really depends on where you start, and is skewed by small starting numbers. If I change the price of something from 50 cents to a dollar, it’s doubled, but you still can likely afford it. If I change it from $20 to $40, I’m going to lose some customers.
So given that, did they use the right one here? Well, I think it was probably a toss up choice. Picking average made the graph and some numbers below look larger, but they made the 2010 ratio numbers look smaller. If they had switched from average to median depending on what was more substantial, I would have taken issue, but as it is I don’t think there was anything deceptive going on. After all, had they used the median numbers, they would have also changed the axis and the difference would have looked just as dramatic.
There’s always the possibility that they could have put both to prove this point, but I’m pretty sure only someone like me would have enjoyed that.