Ssb

= 67.5

q-

1 = 1

Figure 1.13 Schematic partition of the total sum of squares and degrees of freedom for CRF-32 and SPF-3 -2 designs. The shaded rectangles indicate the sums of squares that are used to compute the error variance for each design. The SPF-3-2 design has two error variances: MSBL(A) = SSBL(A)/p(n - 1) is used to test treatment A; MSRES = SSRES/p(n — 1)(q — 1) is used to test treatment B and the A x B interaction. The within-blocks error variance, MSRES, is usually much smaller than the between-blocks error variance, MSBL(A). As a result, tests of treatment B and the A x B interaction are more powerful than the test of treatment A.

Groupj

Group2

Blockj

Block2n

Treatment Treatment Combination Combination ajhk «A

axbx

<hb2

a\b\

<hb2

axb2

a2bl

axb2

Figure 1.14 Layout for a two-treatment randomized block confounded factorial design (RBCF-22 design). A score in the ith block, jth level of treatment A, kth level of treatment B, and zth group is denoted by Yjjkz.

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