The Relative Size of the Inter- and Intra-Block Error in an Incomplete Block Design
William A. Thompson · Biometrics · 1955
Results of scientific experiments are frequently classified according to the factors contributing to the observed data. Thus, several technicians may test a property of a certain type of shoe on several different walking courses, and yi is the score given to the shoe by the ith technician on the jth course. The shoe to shoe factor for a given type shoe is assumed negligible. The two factors considered in this example are then (i) different technicians and (ii) different courses. An individual technician's gradings will not be completely reproducible, i.e., if he repeatedly grades the same type shoe on the same course he will not always give it the same score. He will tend to give scores which fall in a regular manner about the actual value for the particular shoe and course. This variation is then the error contribution to the score. If, as is usually the case, we wish to draw inferences about locations other than those where we perform our experiments, it may be more reasonable to assume that the course effect is composed of a large number of effects which have a tendency to counterbalance each other. This suggests to the author that we should also assume the course effects to be random ones, and we will then have two sources of variability with which to deal: (i) the variability in performance due to the different courses and (ii) the variability due to all other factors which we have called the error variability.