New PDF release: Contributions to Statistics

By P. C. Mahalanobis, C. R. Rao

ISBN-10: 1483231607

ISBN-13: 9781483231600

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Extra info for Contributions to Statistics

Sample text

3. Here we will relax the rather unreaUstic assumption where η is an integer. The fact that Ν Φ means that we have q^

In particular if r ... 5) 2, jo(r, t) = 4. 29) is an scheme provided that k> \{r-\)[r^-r^+r+2). 29) exists, then we can arrange the k'^ treatments in a ¿ X A : square scheme, and find a corresponding set of r—2 mutually orthogonal Latin squares, such that two treatments are first associates if they occur together in the same row or column of the square scheme, or correspond to the same symbol of one of the Latin squares, and are second associates otherwise. 6) holds. In the case r > 2, it is necessary to add the words unique up to type because in general there will exist many non-isomorphic sets of r—2 mutually orthogonal Latin squares.

In this case = ag = 6, Δ = 12. 25) takmg Ä: = 3, we have ai = ag = 4, (ii) Δ = 9. / / a i = ag {which is necessarily the case when Δ is not an integral square) ί>Ϊ2=ί>ΐ2 = ^, aj = ag = Til = T i 2 = ( t ; - l ) / 2 = 2ί, v = A = át+l. 32) ... 33) ... 34) 38 R. C. BOSE Since « 1 = «2, we have η = 0 or whence γ = 0, ^3 = n^, and (iii) = j^fg = ^ (say). The other results easily follow. 30), must be a non-zero integer divisible by V A . 31) by noting that ^ / V A must be an odd integer. 34) hold) or η is a non-zero even integer, and Δ is an integral square.