Using the crude measures of literacy and numeracy discussed in a previous post, it is possible to quantify the cognitive ability gap for US Black-White in the 1800s. The data come from:
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A’Hearn, B., Baten, J., & Crayen, D. (2009). Quantifying quantitative literacy: Age heaping and the history of human capital. The Journal of Economic History, 69(3), 783–808.
And look like this:
Following the pass rate to normal conversion (qnorm in R), we can derive relative z-score gaps from the pass rates. These are:
| Year | W literacy | W numeracy | B literacy | B numeracy | BW literacy | BW numeracy | BW mean |
| 1850 | 0.86 | 0.88 | 0.58 | 0.70 | 0.87 | 0.64 | 0.75 |
| 1870 | 0.89 | 0.88 | 0.35 | 0.70 | 1.63 | 0.68 | 1.15 |
| 1900 | 0.94 | 0.95 | 0.62 | 0.86 | 1.22 | 0.60 | 0.91 |
Notes:
- 1850s data is based on free slaves only, hence these were likely above average cognitive ability, explaining the smaller gap. Corollary of this is that Black literacy decreases from 1850 to 1870 due to the release of the southern slaves.
- Samples were small.
- The White pass rates are close to the ceiling introducing ceiling effects and extra imprecision.
- Large-scale immigration of Whites probably reduces their literacy, despite these data being based on natives only.
All in all, the mean gap in the 1850-1900 period comes out at 0.94 d.