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By J.C.W. Rayner

"The equipment complex during this publication have their genesis in conventional nonparametrics. They contain the ability of recent pcs to make the method extra entire and extra legitimate than formerly attainable. The authors' unified remedy and readable type make the topic effortless to keep on with and the ideas simply applied, no matter if you're a fledgling or a pro researcher."--BOOK JACKET.

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**Extra info for A contingency table approach to nonparametric testing**

**Example text**

In later chapters we will also note how similar parametric and nonparametric tests can be. Sprent (1998, p. 144) applies S2 to the voting intention data. He uses the exact binomial distribution associated with S rather than the asymptotic χ12 distribution associated with S2. At commonly used levels he accepts the null hypothesis that switches are equally likely to be either way. Our presentation of data for McNemar’s test, and the usual one, both interpret the diagonal terms as uninformative ties.

N .. - 1) n .. - 1 Since the {Nij} are such that the row and column totals are known constants, cov(Ni, N1 + ... + Nr) = 0 for i = 1, ... , r. The covariance matrix of Ni is cov(Ni) = - ∑ cov (N i, Nj) = ∑ fifj R = fi (1 - fi) R, i≠j i≠j which agrees with direct calculation. Now write NT = (N1T , ... 4), the covariance matrix of N is cov(N) = {diag(fj) - (fifj)} ⊗ R, and define the standardised cell counts Zij by Z ij = (Nij - E[Nij])/√E[N ij], i = 1, ... , r and j = 1, ... , c, and Z = (Z11, ...

J n .. - n i. , i = 1, ... , r and j = 1, ... , c. n .. n .. n .. - 1 Similarly cov(N ij, Nik) = - ni. c. k n .. - n i. , i = 1, ... , r and j ≠ k = 1, ... , n .. n .. n .. - 1 By symmetry n .. j , i = 1, ... , r and j ≠ k = 1, ... j nr. ns. n .. n .. n .. - 1 and by the expectation argument again , c. s 1 , i ≠ j = 1, ... , r, and r ≠ s = 1, ... r n .. n .. n .. - 1 Thus, as required, the joint covariance matrix of Ni and Nj is, for i ≠ j, n cov(Ni, Nj) = - n i. j. r n .. s . n .. n .. (n .. - 1) n ..