Thursday, May 16, 2013

Race and wealth, relative or absolute?

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: 
                       Average               Median 
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.  


  1. If the category for race had included an "Oriental" option, what would the chart have looked like?

  2. I know that the graphing interested you, but I was interested in the assumptions. Unspoken, but clearly thought, is that this disparity is (entirely) a product of the American system, rather than the actions of individuals.

    It does suggest the systemic problem of federal encouragement of bad housing loans did hurt minorities harder when the market collapsed, however.

    1. It's interesting because Tim and I were discussing how we had no problems with people challenging the reasons. It was part of why the graphic was display the numbers and start a discussion about the reasons behind them.

      I think what perplexed both of us was people who (quite clearly based on commenting history) took issue with the causes being offered decided not to criticize the causes, but the numbers.

      I'm not sure why someone would do that actually, it really confused me.