Lord's Paradox: An essay on causal inference

In 1967 Frederic Lord published a two page paper on weight changes over time by two groups. A scientist would surely conclude that the data show individuals in both groups were fluctuating in weight but not gaining or losing. Yet an analysis of covariance (ANCOVA) seemed to lead to a conclusion that the initially heavier group was gaining more than the initially lighter group. Lord seemed to present this as an example showing that inappropriate use of ANCOVA leads to absurd conclusions, yet statisticians and causal modelers have been re-examining this paradox ever since, sometimes concluding that one cannot reach a valid conclusion, sometimes concluding that the correct conclusion is more weight gain for the initially heavier group. I use this example to highlight the importance of using science to guide the way we do statistics, rather than using statistics to tell us how to do science. More generally, I wish to highlight the value in generating plausible, simple, and coherent models for observed data.