Machine controls for analysis of variance

Abstract

A major problem in using the analysis of variance, as the number of factors increases, is the exponential rise in the number of interactions;. Even though the experimenter may not be interested in these interactions it is impossible to ignore them in most experimental designs because of the problem of getting error terms.It is natural therefore to look to the computer to handle the bulk of work involved in computing the interactions. A program device to get the computer to do this is described. Garber [2]. We use roughly the same line of reasoning as Garber in developing the basic computational routine. We then construct computer controls to carry out the routine for any number of factors, levels and data within computer limits. Generalized program plans for computing the analysis of variance have been reported by Hartley [1] and byThe data are considered as being on a single dimension, and they are controlled by a single index which runs from one to the total number of data, which we call NTOT. This method inw3lves somewhat different problems from the use of a data matrix of as many dimensions as there are factors, but it; permits an unlimited number of factors.The order of data in the single dimension is critical. In our work factors, or variables, are represented by single letters, which are assigned an arbitrary order in a left-toright list. Each factor can have any number of levels (conditions). The order of the data must be such that the levels for the first factor (leftmost letter) change most rapidly, the levels for the next factor change next most rapidly, etc. For example, let there be three factors, ABC, for which the number of levels are as follows: A-2, B-3, C-2. Then the data must be ordered as follows: 1 = a~b~c~, 2 = a2blcl, 3 = alb2cl, 4 = a2b2cl , 5 = a~b~c~, 6 = a2bacl, * Systems Engineering Department. i The starting value of the loop index is ml , the final value is m2 , and the increment is m3 .

A general purpose program variance for the analysis of variance

“…The control generator executes five relatively simple rules (Weldon, 1964) and in doing so generates a sequence of 14 J values for the seven loops in this program. This is done by the control generator.…”