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

By M. C. Chakrabarti

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Additional info for Mathematics of Design and Analysis of Experiments

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How many times will a particular treatment B belonging to the /associate class of A occur in the above set? How many times will A itself occur? , Aix. Then Aix A{t ... e. p\j,. , A cannot occur unless / = i, in which case it will occur r1i times. Let Si ( t, ) denote summation over the f-associates of t,. Then the above result is equivalent to S,, =St ( T, ) - £Pj, S, ( T, ) if/ ± i i-1 m and -«it. ) if / - i.

Some of the X's may be equal. (iv) if the treatment A is t-associate of B, then treatments is t-associate of A. If A and B are t-associates, then the number of treatments common to the j-associates of A and j'-associates of B is p^, and is independent of the pair of treatments we start with. Also p^, = Pj-j. Let N be the incidence matrix of the design. 2) The matrix N N' consists of r in the principal diagonal and nt times X1, nt times Xt nm times X in each row and column. -. , X n n2 nm are known as primary parameters.

A? ) The variance of the best estimate of t, t,/ is estimated by %E. [l+(0_ft)»] 7. Lattice Design. Let us have &2 treatments arranged in k rows and ft columns. Then if we assign the treatments occurring in rows and columns to different blocks, we have 2k blocks of k plots each. Again if m - 2, (m 2