Confounding in mixed factorial experiments through isomorphisms

The derivation of a simpie mexhoa for confounding in mixed factorial experiments from an isomorphism of finite abelian groups is presented. The theoretical bases of confounding procedures that use modular arithmetic for such experiments are compared.     

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.     

On the existence of linear trend free block designs

We present a class of counerexamples for a conjecture on the existence or linear trend free block designs we will also prove a considerably weakened version of this conjecture which will determine all combinations of designs parmetres for which the class of linear trend free block designs is non empty.     

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.     

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.     

Taguchi methods: linear graphs of high resolution

An important reason behind the success of the Taguchi methodology in qual- ity assurance has been the use of statistical methods, presented in a way that is accessible to the nonexpert user. Among the tools used to simplify the sta- tistical design of experiments has been the linear graph, apparently introduced by Taguchi. However, he did not consider the resolution of the corresponding designs (the higher the resolution, the more accurate the conclusions). For example, it will be shown that half of the linear graphs given by Taguchi for the L₁₆(2¹⁵) orthogonal array correspond to designs of resolution III, when designs of resolution IV are available (with the same lines in the linear graphs but with different assignments to the columns of the orthogonal array). A nontraditional but very straightforward method is presented for obtaining the alias chains and the linear graphs corresponding to an orthogonal array. The procedure can be easily understood and employed by nonstatisticians to find an experimental design of the highest possible resolution. The design can be used to obtain products or processes that are robust to variation.     

Three-stage designs for monitoring clinical trials

Optimal three-stage designs with equal sample sizes at each stage are presented and compared to fixed sample designs, fully sequential designs, designs restricted to use the fixed sample critical value at the final stage, and to modifications of other group sequential designs previously proposed in the literature. Typically, the greatest savings realized with interim analyses are obtained by the first interim look. More than 50% of the savings possible with a fully sequential design can be realized with a simple two-stage design. Three-stage designs can realize as much as 75% of the possible savings. Without much loss in efficiency, the designs can be modified so that the critical value at the final stage equals the usual fixed sample value while maintaining the overall level of significance, alleviating some potential confusion should a final stage be necessary. Some common group sequential designs, modified to allow early acceptance of the null hypothesis, are shown to be nearly optimal in some settings while performing poorly in others. An example is given to illustrate the use of several three-stage plans in the design of clinical trials.     

Admissible minimum bias estimation of response surfaces

The minimum bias estimator was introduced as an alternative to the least squares estimator for approximating response functions by low-order polynomials. Here we show how to obtain an admissible estimator with smaller squared bias.     

A formula for a missing plot in a general incomplete block design,when recovery of interblock information is used

In this paper, Yate's missing plot technique is used to derive the formula for substitution in a missing plot in a general incomplete block design, where blocks are assumed to be independent normal. The use of penalized normal equations, using BLUPS, makes this task simpler.