By M. C. Chakrabarti
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Additional info for Mathematics of Design and Analysis of Experiments
Example text
When, however, the B IB D is resolvable, for estimating to and to' we make use of the error sum of squares and adjusted blocks within replications sum of squares and denoting these mean squares by Et and Eb(a) respectively, we get easily Eh (a) Est. (to E. to') = ^-- - r- (8 5 20) k 'Ee[rEb(a)-Ee] ( M) Est. ti) When the B I B D is symmetrical, the adjusted block sum of squares can be calculated directly. -. 24). 22) Adjusted Block SS = 'v\(v 1) (v . V3 W? f. f. 26). Hence D wv\ + w' (r - X) »(* - i^ + (v ~ k) W' g (T.
St [ a- e st r oj £ st o? 5. Total and Partial Confounding: Let there be m k treatments and let us divide them into wi sets os A; each. We assign to a block all the treatments of a set and there are r replications. 14) C=diag frl- L-Ekk, fh- L Ekk, ... 1) L' - is estimable if rank G rank (C, L). Rank C = m (k 1) and every intraset contrast is estimable. All interset contrasts are not estimable and they are said to be confounded with the blocks. In the notation of Section I, the adjusted treatment sum of squares is T' T B'N'NB .
The number of varieties common between /-associates of variety of the 1st group and the varieties of the second group is p^,. Hence the number of/-associates that can be formed by taking a variety of the group and a variety of the second group is on the one hand ni pjj, and on the other n^p^,. 6) Thus" the m symmetric matrices pi = [PiA > P. = [Pil ] . ] (8-»-7) 771 (771^ 1^ contain only independent elements. Consider the /-associate classes of the rtj 1-associates of a treatment A. How many times will a particular treatment B belonging to the /associate class of A occur in the above set?
Mathematics of Design and Analysis of Experiments by M. C. Chakrabarti
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