Mathematics of Design and Analysis of Experiments by M. C. Chakrabarti

By M. C. Chakrabarti

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Where P. = 1b Q, + W Q B, = r, [to + w'l ( k - 1) ], A . = (1o w')\ . and set in o addition >. r, r, = 0 S r'r'= 18. In the intrablock analysis, find the expected values of (i) adjusted treatment sum of squares and (ii) adjusted block sum of squares. 19. v = s1 x *2 treatments v^, (t = 1, 2, ... , st) are arran- ged in 6 blocks with A; plots each such that every treatment is replicated r times and vtj and vVy occur together in Xj^ t plots where kt = 0 or 1 according as i = i' or i ^ i' and k2 = 0 or 1 according as j =j' or j ^j'.

No treatment is assigned more than once to a block and the number of times * and s' treatments occur together hi a block is X .. Let nti denote 1 if the s th treatment occurs in the i th block and o therewise. , A;). org/access_use#pd-google standard derivation y-2*. %1. «/<*> ---. 2/wt) I,. ff1 ff1 ('1 " "-aa) ff1 ffi (ffi -r''

24. Show that (0 («) trC + C -N' N' diag"(ft1 , .... kb) W = ktk2 ... kb rtrt ... -, rv} When rx = r2 = ... ) CHAPTER III STANDARD DESIGNS 1. Randomised, Block Design. Here we have bk plots divided into b blocks of k plots each and each of the v = k treatments is assigned at random to one of these plots in each block. 26) is satisfied and the adjusted treatment and block yields are orthogonal. org/access_use#pd-google DfC STANDARD DESIGNS 89 2. Latin Square Design. It is an arrangement of us plots of u rows and u columns in which u treatments are assigned in such a way that each treat- ment occurs once and only once in each row and in each column.

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