Common Errors in Statistics (and How to Avoid Them), 4th Edition

RATES AND PERCENTAGES

Consider the statement “Sixty percent of the children in New York City read below grade level.” Some would say we can not tell whether this percentage is of practical significance without some means of comparison. How does New York City compare with other cities its size? What about racial makeup? What about other environmental factors compared with other similar cities?

In the United States in 1985, there were 2.1 million deaths from all causes, compared to 1.7 million in 1960. Does this mean it was safer to live in the United States in the 1960s than in the 1980s? We do not know the answer because we do not know the relative sizes of the population of the United States in 1960 and 1985.

If a product had a 10% market share in 1990 and 15% today, is this a 50% increase or a 5% increase? Not incidentally, note that market share may increase even when total sales decline.

How are we to compare rates? If a population consists of 12% African-Americans, and a series of jury panels contain only 4%, the absolute disparity is 8%, but the comparative disparity is 66%.

In Davis v. City of Dallas⁴, the court observed that a “7% difference between 97% and 90% ought not to be treated the same as a 7% difference between, e.g. 14% and 7%, since the latter figure indicates a much greater degree of disparity.” Not so, for pass rates of 97% and 90% immediately imply failure rates of 3% and 10%.

The consensus among statisticians is that one ought use the odds ratio for such ...