Biometric Colloquium

STEPHEN SENN
University of Sheffield, UK,
University of St Andrews, UK
Medical University of Vienna, Austria

STANDARD ERRORS IN REPRESENTING FISHER’S VIEWS ON
RANDOMISATION

April 28th, 2026 at 02:00 pm
Spitalgasse 23, Jugendstilhörsaal
Medical University of Vienna, 1090 Wien

Host: Martin Posch

Abstract:
One hundred years ago, RA Fisher proposed randomisation as a solution to a problem in
designing trials in agriculture[1]. However, if curiosity impels a modern statistician to look up
Fisher’s anniversary paper, they may be in for a shock. Randomisation is usually presented as
a device for eliminating bias in treatment estimates. Fisher does not start his paper by addressing
this but opens as follows with another concern:
“The present position of the art of field experimentation is one of rather special interest. For
more than fifteen years the attention of agriculturalists has been turned to the errors of field
experiments…much ingenuity has been expended in devising plans for the proper arrangement
of the plots; and not without result, for there can be no little doubt that the standard of accuracy
has been materially, though very irregularly, raised…an estimate of field errors derived from
any particular experiment may or may not be a valid estimate, and in actual field practice is
usually not a valid estimate, of the averages or differences of averages of which it is required
to estimate the error.” (p503)
The units in agricultural experiments are plots in a field and yields from such plots cannot be
regarded as independent but instead have a complex but poorly estimable spatial correlation.
Medical statisticians such as myself, who are used to dealing with patients as the unit of
experimentation may underestimate the formidable difficulties that such correlation structures
present for the calculation of valid standard errors. It is the valid calculation of such standard
errors that form the central concern of Fisher’s 1926 paper and randomisation was proposed by
him as a way of finessing the issue of the correlation structure.