Types of factor in experiments

Abstract Much statistical writing and practice is based on the notion that all factors in comparative experimentation are of one or other of two types, but there is conflict between the different dichotomies produced by different authors. The present paper argues that all such dichotomies (fixed versus random, treatment versus block, randomised versus unrandomised, etc.) are inadequate for categorising the factors that can be present in a single experiment. At the very least, a trichotomy is needed as a logical basis for designing and analysing individual experiments, the three basic types of factor being (A) treatment factors whose levels can be assigned at random to plots; (B) classification factors whose effects (and perhaps interactions with other factors) are to be studied; and (C) block factors. This trichotomy is a special case of one described by Cox (Int. Statist. Rev. 52 (1984) 1–31). Before a factor can be identified as belonging to a particular type, unaccustomed care may be needed in identifying and characterising the plot or experimental unit used in the experiment. A factor involving time may be of type (A) or (B), or may be of a further type that must be distinguished separately. The paper illustrates its arguments with examples from agricultural, industrial, medical and behavioural experimentation.