Applications of binary numbers in computer routines

Weldon, Roger J.; Baker, Robert L.

doi:10.1145/364914.364950

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“…The flowchart of one such routine is shown in This routine, together with the nest of loops and other routines, is set in a do loop with index K. K is transformed from decimal to I~ binary number, KBIN and this binary number is the input to the routine using the methods described by Weldon and Baker [4]. It represents (in reverse order) the source for which IP(J)'s are being computed.…”

Section: Loop IImentioning

confidence: 99%

“…Using this routine and other routines reported by Weldon and Baker [4], we have developed a program that will handle factorial designs from 1 to 10 factors. For a fiveway analysis of variance, colnputing time on the IBM 7072 is between 2 and 3 minutes; for a ten-way analysis the computing time is approximately a half hour.…”

Section: Loop IImentioning

confidence: 99%

“…IN(3) is the product of the number of levels in the first two factors. IN(4) is the product of the number of levels in the first three factors, etc. The highest IN(J) value is the total number of data, when J = NFACS -4-1, the number of factors plus one.…”

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confidence: 99%

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Machine controls for analysis of variance

Weldon

1964

Commun. ACM

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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 .

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Section: Loop IImentioning

confidence: 99%

Section: Loop IImentioning

confidence: 99%