Is the Lottery Racist?

Folkbum links to an article in the Milwaukee Journal Sentinel reporting statistical analysis of lottery winnings. The article finds that the lottery has a higher payout in rich zip codes ($0.45 per dollar spent on tickets) than in poor zip codes ($0.06 per dollar spent on tickets). I posted the following as a comment on Folkbum's post, but I will reproduce it here.

I find these statistics unconvincing. The article presents the ratio of total winnings of prizes over $600 to the total lottery sales. Tickets with higher payouts would presumably cost more as well. Therefore, I would expect to see fewer high payout sales in the poor zip codes than in the rich zip codes. It follows that the payout ratio would be higher in the richer zip codes.

Let me put it another way. I would expect to find, generally speaking, residents of rich zip codes buying the high payout tickets and residents of poor zip codes buying the low payout tickets. Therefore, filtering the winnings data to only include those on higher payout tickets introduces a bias into the statistics, rendering any conclusions highly suspect.

This looks to me like a simple function of economic class rather than any designed discrimination by the lottery system. To be a meaningful analysis, the bias in the statistics should be removed and winnings at all levels included. There also would need to be corrections based on the different odds of winning in the different games. Only then are we truly comparing apples to apples.

Update: In astronomy this is called a selection effect, and is one of the most common pitfalls in statistical analysis. One imposes selection criteria on data being analyzed, but does not consider the biases those criteria create. An obvious example would be conducting a poll of Assembly of God members and trumpeting the finding that President Bush is not as unpopular as other polls suggest. Selecting members of such congregations will bias the result toward Bush supporters, presumably, so the conclusions are not meaningful.