Adjusting for differential base rates: Lord's Paradox again.

When the responses of 2 or more groups to the relative effects of some stimulus are compared, it is often important to adjust statistically the estimates of those effects for baseline differences among those groups. This is often the case in experiments on heart rate for animals of different ages. How should such adjustment be done? Among the competing methodologies are (a) subtract the base rate, (b) divide by the base rate, and (c) covary out the base rate. Because each can give a different answer, the choice is crucial. This article shows that this is an example of Lord's Paradox and that Rubin's Model for the measurement of causal effects allows researchers to understand what the assumptions are underlying the validity of each adjustment strategy. The answer for heart rate data is almost surely Methodology (a).