Randomized and random run order experiments

Abstract

Randomization in industrial and scientific experiments on equipment has meant randomizing the order of application of levels of treatments to units. This definition is inadequate because it does not render independent error terms. Randomization also requires independent resettings of treatment levels when the levels for the preceding run are the same. We review how the literature incorrectly explains how randomization is to be carried out. The need to reset levels of a treatment from one run to the next is never emphasized. Using a simple example we show why statistical tests are biased for all treatments even when levels for just one treatment are not independently reset. Even if the expected mean squares recognize the restrictions on randomization, the usual F test will not give predictable results because its numerator and denominator are correlated. Experimental design on equipment includes experiments from the chemical, automobile, pharmaceutical, and aeronautical industries. The statistical interpretation of data from such experiments will be misleading. Books on experimental design must emphasize the independent resetting of levels just as carefully as they emphasize the random assignment of treatment levels.