schussman.com logo

Weight and See

Tim Lambert continues to document the case of John Lott's Mysterious Survey. Others have commented recently on the current state of affairs, and I have little to add. However, Lambert's recent entry is a great, brief description of some of the mechanics of sample weighting:

bq. Suppose that we just weight by race and sex and 90% of the population is white and 10% is black. We take a sample of ten people, getting nine whites (four men and five women) and one black (a man). The four white men constitute 40% of the sample and 45% of the population so get weight 45/40=1.13. The five white women are 50% of the sample and 45% of the population so get weight 45/50=0.9. The black man is 10% of the sample and 5% of the population so gets weight 5/10=0.5. Notice that the total weight of the whites in the sample is 4x1.13+5x0.9=9, 18 times the total weight of the blacks, even though they are only 9 times as frequent in the general population. In this example whites were weighted twice as heavily, but with 1836 (=36x51 states+DC) categories Lott's procedure could cause even worse discrepencies.

_Now_ I get it! Thanks, Prof. Lambert!