By Ian Kitching, Peter Forey, Christopher Humphries, David Williams,
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Extra info for Cladistics: Theory and Practice of Parsimony Analysis (Systematics Association Publications, 11)
If other roots are equal to rk, then the intrablock estimators for the corresponding treatment parameters do not exist. Similarly, if other roots are equal to zero, then the interblock estimators for the corresponding treatment parameters do not exist. The treatment parameters ν1 , ν2 , . . , νt−1 are necessarily treatment contrasts. If the design is connected, then no δi (i = 1, 2, . . , t − 1) will equal rk. 76) are now transformed to r− δi k + bi 1 δi ν i = ai + k(1 + γ k) k(1 + γ k) (i = 1, 2, .
The other alternative is to use the natural blocks and then use the analysis as given in the previous section. Before doing so we mention that its validity will depend on one very important assumption, and that is the constancy of the variance σe2 for all blocks. 4). In fact, this is the reason for reducing the block size since it may also reduce the experimental error. Experience shows that such a reduction in σe2 is not appreciable for only modest reduction in block size. It is therefore quite reasonable to assume that σe2 is constant for blocks of different size if the number of experimental units varies only slightly.
2. 2 is associated with the ordered model y = µI + X τ τ + Xβ β + e and hence shall be referred to as the block-after-treatment ANOVA or B | TANOVA. f. σe2 Difference n−1 yij2 − τ Cτ t −1 G2 n = degrees of freedom. f. 1 n−1 yij2 − ij G2 n INCOMPLETE DESIGNS WITH VARIABLE BLOCK SIZE 13 design, thereby avoiding the commonly used but not always clearly understood terms blocks ignoring treatments for (Xβ | I), treatments eliminating blocks for (X τ | I, Xβ ), and blocks eliminating treatments for (Xβ | I, Xτ ).
Cladistics: Theory and Practice of Parsimony Analysis (Systematics Association Publications, 11) by Ian Kitching, Peter Forey, Christopher Humphries, David Williams,