Student and the Lanarkshire milk experiment

A detailed examination of the 1930 Lanarkshire Milk Experiment (LME) by the famous statistician William Sealy Gossett (“Student”), which appeared in Biometrika in 1931, is re-examined from a more modern perspective. The LME had a complicated design whereby 67 schools in Lanarkshire were allocated to receive either raw or pasteurised milk but pupils within the schools were allocated to either receive milk or to act as controls. Student’s criticisms are considered in detail and examined in terms of subsequent developments on the design and analysis of experiments, in particular as regards appropriate estimation of standard errors of treatment estimates when an incomplete blocks structure has been used. An analogy with a more modern trial in osteoarthritis is made. Suggestions are made as to how analysis might proceed if the original data were available. Some lessons for observational studies in epidemiology are drawn and it is speculated that hidden clustering structures might be an explanation as to why results may vary from observational study to observational study by more than conventionally calculated standard errors might suggest.