ch09 - Chapter 9 Supplemental Text Material S9-1 Yates's...

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Chapter 9. Supplemental Text Material S9-1. Yates's Algorithm for the 3 k Design Computer methods are used almost exclusively for the analysis of factorial and fractional designs. However, Yates's algorithm can be modified for use in the 3 k factorial design. We will illustrate the procedure using the data in Example 5-1. The data for this example are originally given in Table 5-1. This is a 3 2 design used to investigate the effect of material type ( A ) and temperature ( B ) on the life of a battery. There are n = 4 replicates. The Yates’ procedure is displayed in Table 1 below. The treatment combinations are written down in standard order; that is, the factors are introduced one at a time, each level being combined successively with every set of factor levels above it in the table. (The standard order for a 3 3 design would be 000, 100, 200, 010, 110, 210, 020, 120, 220, 001, . . . ). The Response column contains the total of all observations taken under the corresponding treatment combination. The entries in column (1) are computed as follows. The first third of the column consists of the sums of each of the three sets of three values in the Response column. The second third of the column is the third minus the first observation in the same set of three. This operation computes the linear component of the effect. The last third of the column is obtained by taking the sum of the first and third value minus twice the second in each set of three observations. This computes the quadratic component. For example, in column (1), the second, fifth, and eighth entries are 229 + 479 + 583 = 1291, -229 + 583 = 354, and 229 - (2)(479) + 583 = -146, respectively. Column (2) is obtained similarly from column (1). In general, k columns must be constructed. The Effects column is determined by converting the treatment combinations at the left of the row into corresponding effects. That is, 10 represents the linear effect of A , A L , and 11 represents the AB LXL component of the AB interaction. The entries in the Divisor column are found from 2 r 3 t n where r is the number of factors in the effect considered, t is the number of factors in the experiment minus the number of linear terms in this effect, and n is the number of replicates. For example, B L
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ch09 - Chapter 9 Supplemental Text Material S9-1 Yates's...

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