8 - Muddied waters: the challenge of confounding

Summary

Box 8.1 Are university admissions biased towards men?

Table 8.1 shows that in one year a prestigious university admitted 52% of male applicants compared with only 45% of female applicants, suggesting that there was a bias in favour of men. When quizzed about this, the two main faculty heads said that it couldn't be true, they had both admitted a higher proportion of women than men: the success rate in arts was 38% for women and only 32% for men and that in science was 66% for women compared with only 62% for men. How can this be?

This is an example of Simpson's paradox, an extreme form of confounding where an apparent association observed in a study is in the opposite direction to the true association. In this example it arose because women were much more likely to apply to arts courses, for which applicants had a lower overall success rate.

(Based on an analysis of graduate admissions data conducted at the University of California, Berkeley (Bickel et al., 1975).)

In Chapters 6 and 7 we considered two reasons why the results of a study might not be the truth, namely chance and error or bias. In this chapter we will consider a third possible ‘alternative explanation’ – confounding.

Confounding refers to a mixing or muddling of effects that can occur when the relationship we are interested in is confused by the effect of something else, just as we see in the striking example in Box 8.1.