Mathematical fact check: Quartz — “All this talk of ‘inner cities’ is missing a bigger problem affecting the African-American middle class”

Often I see articles misunderstanding or misrepresenting statistics or mathematical results in an otherwise well-written article. This is my attempt to start calling them out.

From Quartz, regarding wage disparity between blacks and whites in the US:

Yet middle-class African Americans continue to suffer discrimination. The wage of a typical black college graduate is only 81% that of a white college graduate: an average of $26 an hour for African Americans, versus $32 for whites. The gap is even greater for those with advanced degrees — 84%. The old adage that African Americans have to be twice as good to succeed still seems to apply in 2016. (Quartz, Oct 12, 2016)

This paragraph seems to be confusing what the black wage is in terms of percentage of white wage (calculated as black wage/white wage), and the percentage gap between black and white wages (calculated as difference in wages/white wage). Black wages going from 81% of white wages for college graduates to 84% for advanced degree holders represents a 3% decrease in the gap. So African Americans with an advanced degree are closer to wage parity (though still unacceptably far) than those with only a college degree.

I suspect that the confusion may come from the title of the source report: Black-white wage gaps expand with rising wage inequality. However, if you look at the data, the wage gap increase is with respect to absolute number of dollars, not percentage. Below, I’ve reproduced the data in the report, and added the calculated wage gap in dollars and percentage:

Education level | White | Black | Gap($) | Gap(%)
<High School | $13.57| $11.25| $2.32 | 17%
High School | $18.00| $14.24| $3.76 | 21%
Some college | $19.80| $15.85| $3.95 | 20%
College | $31.83| $25.77| $6.06 | 19%
Advanced degree | $39.82| $33.51| $6.31 | 16%

We see that while the gap increases with education level in terms of dollars, the percentage that this gap represents actually tends to decreases with education level. The notable exception is African Americans with less than a high school education; this group is the second closest to wage parity, making “only” 17% less than whites (after advanced degree holders who make 16% less). However, this result is hardly encouraging, seeing as a primary reason for the relatively small gap is that the minimum wage sets a floor on how low wages can get. That is, black wages aren’t much lower than whites’ in this category because they’re not legally allowed to get any lower. The report finds that increasing minimum wage improves wage parity for those with lower education levels, but more needs to be done to address the gap for those with higher education.

None of this invalidates any of the points that the article makes. Wage disparity is a significant issue that requires serious discussion, research, and policy to address, and we will require different solutions tailored to different parts of the demographic. However, when articles make careless statistical mistakes, it makes it that much easier for detractors to dismiss the conclusions and ignore the issues.