Sequential Trials, Sequential Analysis and the Likelihood Principle

1. I shall be concerned in this paper with a single question, the answer to which is of great importance to all those engaged in the sequential collection of data. The question is this: Do the conclusions to be drawn from any set of data depend only on the data or do they depend also on the stopping rule which led to the data? In discussing this question I shall draw heavily upon the theoretical work of others, particularly L. J. Savage, but also F. J. Anscombe, G. A. Barnard, A. Birnbaum, and D. V. Lindley. Biostatisticians have tended to regard the theoretical developments suggested by these names as unduly abstract and perhaps of no great relevance to statistical practice. I shall nevertheless review some of them in the hope that few of us would go so far as to say with Falstaff that because "Honour hath no skill in surgery . . . I'll none of it." These newer developments, abstract or not, are, in my opinion of great relevance to biostatistical practice and their absorption into thinking, teaching and consultation is becoming overdue.