It's easy to misunderstand gaps and mistake good fortune for a crisis

At the 5th Nordic Health Promotion Research Conference, held in Esbjerg, Denmark, in June 2006, I gave a paper titled "The Misinterpretation of Health Inequalities in Nordic Countries."

I had been wanting to give such a paper since 2001. That year, at a conference in Oslo, Norway, I learned of a perception that, despite being comparatively egalitarian societies, Norway and Sweden were home to some of Western Europe's largest socioeconomic differences in rates of disease and death. Precisely because they are societies that prize equality, the disparities caused great concern in Norway and Sweden.

This issue captured my attention at the Oslo conference because I was there to explain a pattern in statistics that can prove confusing in situations exactly like this. It's a pattern whereby reducing the overall frequency of any adverse outcome tends to increase the relative difference between the rates at which advantaged and disadvantaged groups experience that outcome.

(Simultaneously, reducing overall frequency of an outcome reduces the difference between the rates at which different groups experience the opposite outcome.)

For example, reducing overall death rates tends to increase relative differences in mortality while reducing relative differences in survival.

The pattern can be illustrated with hypothetical scores from tests on which minorities score lower than whites. Suppose that, at a particular threshold for passing a test, failure rates are 20 percent for whites and 37 percent for minorities. The minority failure rate is 1.85 times the white rate (37 ÷ 20). Meanwhile, the white pass rate is 1.27 times the minority rate (80 ÷ 63).

If the score needed to pass is lowered to a point where the white failure rate becomes 5 percent, the minority failure rate (assuming normal test-score distributions) would become about 13 percent. With these better pass rates overall, the minority failure rate would now be 2.6 times the white rate (13 ÷5), while the white pass rate would be only 1.09 times the minority rate (95 ÷ 87).

This pattern is not peculiar to test score data. It is inherent in the shapes of risk distributions for virtually any outcome on which advantaged and disadvantaged groups differ in average susceptibility.

Many examples of this pattern, along with the implications of failing to understand it, may be found in my 2000 Society magazine article, "Race and Mortality," on which the Oslo paper was based. It is readily available online. (For more on the issues, see my website, jpscanlan.com.)

"Race and Mortality" also explained why racial-group differences in adverse outcomes like infant mortality tended to be particularly large within advantaged subpopulations like the well-educated. This pattern occurs simply because adverse outcomes tend to be less common in advantaged groups.

This is what piqued my interest when I heard about the concerns over large socioeconomic differences in health outcomes in Norway and Sweden. Those searching for causes for these differences were overlooking the implications of the simple fact that these are healthy countries.

Since that time, I have taken special interest in disparities issues in places like Minnesota. The connection is not that many Minnesotans have roots in Norway and Sweden. Rather, it's that Minnesota ranks very high on health and other social indicators.

Even the report's transmittal letter reflects a mistaken belief that improvements in health should reduce relative differences in adverse outcomes. Media commentary on the report sees a contradiction between the state's low overall infant mortality rate and its comparatively large racial difference on infant mortality.

But a large racial difference in infant mortality should hardly be surprising in a state with the sixth-lowest white and seventh-lowest black infant mortality rates. In fact, many patterns identified in the report should be unsurprising — but they only will be if one knows what to expect in the circumstances.

Like Norway and Sweden, Minnesota devotes substantial resources to studying disparities. Such study can only be useful if it's undertaken with an understanding of the ways that measures of differences are affected by the frequency of an outcome.