Variants of a widely discussed problem related (but not restricted) to causal inference are called Simpson’s paradox. In one version, the paradox is that while a new drug may be better than the old drug for both male and female patients, when the data are combined, for all individuals, the old drug appears better. In these cases, the odds ratio is used to determine which treatment is better. First, the paradox is illustrated, and a brief overview of some of the published arguments is given, which aim at explaining what is wrong. Most of these theories say that the paradox occurs as a result of properties of the data or of the data collection procedure. This chapter takes a different position. It is argued that the odds ratio may not be appropriate to measure effect size, because it fails to take into account how popular the compared treatments were, which is a relevant information collected in observational studies. A competing, consistent measure of effect (and a concept of effect) is developed, which never commits the paradox. Finally, the last section does not suggest neither the odds ratio nor the measure developed in the previous section to be used universally; rather, it is argued that for a good choice of the better treatment, additional aspects, not only the numbers of positive and negative responses, need to be taken into account.
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