# Contributions to Statistics by P. C. Mahalanobis, C. R. Rao

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

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2-í>}2> β = ή2+ή2. = 0. A = y2+2yí+l, θ^ = r+\[(X^-X^)(V^+y)-{X^+X^)l ... 14) ... 15) ... (616) = ^-έ[(λι-λ2)(ΝΔ-γ)+(λι+λ2)]. 10) tr 7 = l+a^-\-a^ = v, tr NN' = rk+oc^ θ^+α^θ^ = vr, ... 17) ... e. parameters of the first kind. φ^-θ)"", ... , are independent of c^, c^, c^. 2). Hence the multiplicity of the roots of NN' is independent of r, Aj, Ag, A^. Since the multiplicities are expressible in terms of the parameters of the asso ciation scheme, we cannot have a set of parameters leading to nonintegral values ol^ This fact can be used to prove the impossibihty of certain association schemes.

A . (1954) : Y A T E S , F . (1936a) : Ann. Math. , 30, 781-798. Contributions to Sankhyä, 23, Series A , 115-116. On the ratio of variances in the mixed incomplete block model. Doctoral University Thesis. A note on P B I B design matrices. Ann. Math. , 29, 919-922. A new method of arranging variety trials involving a large number of varieties. Agri. , 26, 424-455. (1936b): Probability Stanford University Press. Incomplete randomised blocks. Ann. , 7, 121-140. J. LATTICE SAMPLING BY MEANS OF LAHIRI'S SAMPLING SCHEME By TORE DALENIUS University of Stockholm and The Swedish Oouncil for Social Science Re8earch 1.

BOSE We are now in a position to see how Fisher's inequahty should be modified for the ease when Π and therefore Π* has a zero characteristic root. Let α be the multiphcity of the root zero of Β = NN'. Then 6 > rank Ν > rank NN' = v—oc. Hence Fisher's inequality is replaced by b > v-a. 22) This result is due to Connor and Clatworthy (1954). ,θ^ of NN' are the roots of Π, the ö's are functions of parameters of the design. Since NN' is symmetric the ö's are all real and positive. This fact yields interesting inequalities among the parameters of the design.