[For Vol. VII (1981) see Zbl 0481.62090.]
This volume contains three papers containing tables as follows:
(i) ”Expected sizes of a selected subset in paired comparison experiments” by B. J. Trawinski: For a balanced paired comparison experiment intended for selecting from a set T of treatments a subset S containing the best treatment, the principal criteria for designing the experiment are a restriction on the expected sizes of S and a specified probability of including in S the best treatment of T.
The tables of this paper are based on both the exact and asymptotic developments of expected sizes of a selected subset; these tables are applicable in the design of experiments and supportive of data analysis requiring the inclusion, with probability not smaller than a given number, of the best unit of a set in a subset whose size can be controlled. The tables can also be used in screening of units from a fixed set.
(ii) ”Tables of admissible and optimal balanced treatment incomplete block (BTIB) designs for comparing treatments with a control” by R. E. Bechhofer and A. C. Tamhane: For the problem of comparing simultaneously \(p\geq 2\) test treatments with a control treatment in blocks of common size \(k<p+1\), the authors [Technometrics 23, 45-57 (1981; Zbl 0472.62080)] proposed a new class of incomplete block designs called BTIB designs. In this paper tables of admissible BTIB designs and optimal BTIB designs for one-sided and two-sided comparisons for the cases \(p=2(1)6\), \(k=2\) and \(p=3(1)6\), \(k=3.\)
The authors restrict consideration to blocks of size 2 and 3 because in their view these are the ones of greatest practical interest. The tables are to be used for given (p,k) and specified allowance to design experiments which achieve a specified joint confidence for one-sided and two-sided comparisons; the optimal designs provided here accomplish this objective with a minimum total number of blocks.
(iii) ”Expected values and variances and covariances of order statistics for a family of symmetric distributions (Student’s t)” by M. L. Tiku and S. Kumra: In this paper, the authors have considered the family of symmetric distributions \(C\{1+(x-\mu)^ 2/k\sigma^ 2\}^{- p},\) \(-\infty <x<\infty,\) \(p\geq 2\), \(k=2p-3\), and have tabulated the expected values (Table I) and the variances and covariances (Table II) of order statistics of random samples of size \(n=2(1)20\) from this family; \(p=2(.5)10\). These values are reducible to Student’s t through a linear transformation. The tables are extensive and cover almost half the book.