A study of BIB designs through support matrices

This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given.     

Complete designs with blocks of maximal multiplicity

The set of distinct blocks of a block design is known as its support. We construct complete designs with parameters v(?7), k=3, λ=v ? 2 which contain a block of maximal multiplicity and with support size $\text{b}{}^1\text{= (}{}^{\mathrm{v}}{}_3\text{) ? 4(v ? 2)}$. Any complete design which contains such a block, and has parameters v, k, λ as above, must be supported on at most (^v₃) ? 4(v ? 2) blocks. Attention is given to complete designs because of their direct relationship to simple random sampling.     

The family of t-designs—part I

The family of t-designs is, without any doubt, the most important family of statistical designs. Their importance is due to their statistical optimalities, desirable symmetries for analyses and interpretations, and uses for constructing other important designs and structures such as Youden designs, generalized Youden designs, optimal fractional factorial designs, error defecting and correcting binary codes, balanced arrays, combinatorial filing systems, Hadamard matrices, finite projective and affine planes, strongly regular graphs, and so on. Research in the area of t-designs has been steadily and rapidly growing, especially during the last three decades. The number of publications in this area is in the several hundreds. Since papers on t-designs are published in a variety of journals, and because of the extensive role of these designs in design of experiments and other areas we believe it is imperative to gather these results and present them in varied form to suit diverse interests. This paper is an instance of such an attempt.     

An introduction to designh optimality with an overview of the literature

A brief introduction to oprimal design theorv is given for those who are not familiar with the subject. A list of 312 selected articles on the theory of optimal design is provided. The bibliography should be sufficiently thorough to be of use to researchers in the field.     

On integrals of dirichlet distributions and their applications

The purpose of this paper is to extend results obtained by Sahai and Anderson (1973) and Hurlburt and Spiegel (1976) computationally as well as theoretically. We apply results given in Yassaee (1974), (1976) and apply our computer program to show that one can evaluate the probability of type one error for conditional tests in linear model, in general. We show that one can compute the probability integral of Dirichlet distribution by the use of our program which computes the probability integral of inverted Dirichlet distribution.     

A characterization of a universally optimal design within a class of block designs

It is shown that within the class of connected binary designs with arbitrary block sizes and arbitrary replications only a symmetic balanced incomplete block design produces a completely symmetric information matrix for the treatment effects whenever the number of blocks is equal to the number of treatments and the number of experimental units is an integer multiple of the number of treatments. Such a design is known to be universally optimal.     

Crossover designs based on type I orthogonal arrays for a self and simple mixed carryover effects model with correlated errors

We investigate the performance of crossover designs based on type I orthogonal arrays for a self and simple mixed carryover effects model in the presence of correlated errors. Assuming that between-subject errors are independent while within-subject errors behave according to the stationary first-order autoregressive and moving average processes, analytical optimality results for 3-period designs are established and, as an illustration, numerical details for a number of 4-period cases are tabulated.     

A construction of repeated measurements designs with balance for residual effects

Families of Repeated Measurements Designs balanced for residual effects are constructed (whenever the divisibility conditions allow), under the assumption that the number of periods is less than the number of treatments and that each treatment precedes each other treatment once. These designs are then shown to be connected for both residual and direct treatment effects.     

Statistical scoring procedures applicable to laboratory performance evaluation

Two statistical scoring procedures based on p$p$-values have been developed to evaluate the overall performance of analytical laboratories performing environmental measurements. The overall scores of bias and standing are used to determine how consistently a laboratory is able to measure the true (unknown) value correctly over time. The overall scores of precision and standing are used to determine how well a laboratory is able to reproduce its measurements in the long run. Criteria are established for qualitatively labeling measurements as Acceptable, Warning, and Not Acceptable and for identifying areas where laboratories should re-evaluate their measurement procedures. These statistical scoring procedures are applied to two real environmental data sets.     

Examination and analysis of residuals: A test for detecting a monotonic relation between mean and variance in regression through the origin

This paper presents a simple and exact test for detecting a monotonic relation between the mean and variance in linear regression through the origin. This test resulted from utilizing uncorrelated Theil-residuals and the Goldfeld-Quandt peak test. A numerical example is provided to elucidate the method. A simulation experiment was performed to compare the empirical power of this test with those of the existing tests.