t-Latinized Designs

A variety trial sometimes requires a resolvable block design in which the replicates are set out next to each other. The long blocks running through the replicates are then of interest. A t -latinized design is one in which groups of these t long blocks are binary. In this paper examples of such designs are given. It is shown that the algorithm described by John & Whitaker (1993) can be used to construct designs with high average efficiency factors. Upper bounds on these efficiency factors are also derived.     

A general method of constructing E(s2)-optimal supersaturated designs

There has been much recent interest in supersaturated designs and their application in factor screening experiments. Supersaturated designs have mainly been constructed by using the E ( s ²)-optimality criterion originally proposed by Booth and Cox in 1962. However, until now E ( s ²)-optimal designs have only been established with certainty for n experimental runs when the number of factors m is a multiple of n-1 , and in adjacent cases where m = q ( n -1) + r (| r | 2, q an integer). A method of constructing E ( s ²)-optimal designs is presented which allows a reasonably complete solution to be found for various numbers of runs n including n ,=8 12, 16, 20, 24, 32, 40, 48, 64.     

Book Reviews

Books reviewed:
David Griffiths, W. Douglas Stirling, and K. Laurence Weldon, Understanding Data: Principles and Practice of Statistics
Ingwer Borg and Patrick Groenen, Modern Multidimensional Scaling: Theory and Applications
Jeffrey H. Dorfman, Bayesian Economics Through Numerical Methods: A Guide to Econometrics and Decision-making with Prior Information
Marek Musiela and Marek Rutkowski, Martingale Methods in Financial Modelling: Theory and Applications
Aad W. van der Vaart and Jon A. Wellner, Weak Convergence and Empirical Processes     

Serial unblocked designs balanced for correlation between neighbours,II

The theory in Part I contained an error that was inferred from the output of a program, written in SAS by Eric P. Smith and David D. Morris. The program produces random BUS designs in accordance with the algorithm of Part I. The theory is here corrected by using a combinatorial argument that involves elementary number theory. The algorithm needs no change but its interpretation is now adjusted.     

Optimal repeated measurements designs for comparing test treatments with a control

A-optimal and mv optimal repeated measurments designs for comparing serveral test treatments with a control are considered. the models considered are basically of two types: without preperides and the cirular model. It is shown known that some known strongly balanced uniform repeated measurements designs can be modified to obtain optimal designs for this problem. Some other methods of finding optimal designs are also given.     

A simpler way of obtaining non-sIngularity conditions of rotatability

In response surface designs, it is not usually easy to handle the moment matrix X'X, especially for higher orders. This paper presents a method in which the moment matrix of a response surface of any order can be standardized, i.e., X'X splits into a diagonal matrix consisting of sub-matrices of lower order. This eases the calculation of the determinant and the inverse of X'X. The method has been illustrated with applications to second, third and fourth order response surfaces.     

Cutting Experimental Designs into Blocks

Most experimental material in agriculture and industry is heterogeneous in nature and therefore its statistical analysis benefits from blocking. Many experiments are restricted in time or space, and again blocking is useful. This paper adopts the idea of orthogonal blocking of Box & Hunter (1957) and applies it to optimal blocking designs. This approach is then compared with the determinant-based approach described in the literature for constructing block designs.     

Is regression adjustment supported by the Neyman model for causal inference?

This paper examines both theoretically and empirically whether the common practice of using OLS multivariate regression models to estimate average treatment effects (ATEs) under experimental designs is justified by the Neyman model for causal inference. Using data from eight large U.S. social policy experiments, the paper finds that estimated standard errors and significance levels for ATE estimators are similar under the OLS and Neyman models when baseline covariates are included in the models, even though theory suggests that this may not have been the case. This occurs primarily because treatment effects do not appear to vary substantially across study subjects.     

Rejoinder to 'Ahmed, M.S. (1998). A note on regression-type estimators using multiple auxiliary information.'

In the estimators t ₃ , t ₄ , t ₅ of Mukerjee, Rao & Vijayan (1987), b _{y x} and b _{y z} are partial regression coefficients of y on x and z , respectively, based on the smaller sample. With the above interpretation of b _{y x} and b _{y z} in t ₃ , t ₄ , t ₅ , all the calculations in Mukerjee at al. (1987) are correct. In this connection, we also wish to make it explicit that b _{x z} in t ₅ is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t ₃ , t ₄ , t ₅ , as given in Ahmed (1998 Section 3) are computed assuming that our b _{y x} and b _{y z} are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t ₀ , quoted also in Ahmed (1998), is no better than t ₅ of Mukerjee at al. (1987).     

UPPER BOUNDS FOR LATINIZED DESIGNS

Upper bounds axe derived for the efficiency factor of a class of resolvable incomplete block designs known as latinized designs. These designs are particularly useful in glasshouse and field trials, and can be readily extended to two-dimensional blocking structures. Existing bounds for resolvable designs axe also reviewed and a comparison is made between the third moment bounds discussed by Jarrett (1989) and the second moment bounds of Tjur (1990).