Some Constructions of Semi-Regular Group Divisible Designs

Using affine α-resolvable BIB designs, some constructions of semi-regular group divisible designs are given here.     

A New Quantitative Method for Analysing Unreplicated Factorial Designs

The paper proposes a new method for the analysis of unreplicated factorial designs. The new method does not use an estimate of the error variance and has the potential to identify up to m – 1 active contrasts, where m is the number of contrasts in the study. It can be shown that the proposed test statistic, called MaxU_r, is a function of the generalized likelihood ratio test statistic under normality, which was also used by Al‐Shiha and Yang (1999). Our strategy to identify active contrasts using MaxU_r, however, is different from the multistage procedure proposed by Al‐Shiha and Yang (1999). Additionally, our simulation study seems to show that the new method is superior to Al‐Shiha and Yang's (1999) method. In order to test the performance of the new method, we did an extensive simulation study based on 10,000 samples to compare the new method with 12 other methods from the literature. To reasonably compare these methods, some of the 12 existing methods had to be slightly modified, such that the probability of falsely rejecting the global null hypothesis of no active factors was 0.05 for all methods. Two types of evaluation standard were used, the empirical power and the loss of decision. The results show that the new method performs very well, especially for large number of active contrasts (say more than 3 out of 15). A second purpose of the simulation study was to compare the performance of two well‐known estimates for the variance. One is the PSE introduced by Lenth (1989), the other the ASE introduced by Dong (1993). The simulation study confirmed the approximations of Kunert (1997) which indicate that Dong's (1993) estimate should perform better for small numbers of active factors. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Class of Matrices with Application in Experimental Designs

A very general class of balanced matrices is defined in this paper. These matrices are generalisations of the balanced orthogonal designs of Rao (1970) and generalised balanced matrices of Dey and Midha (1976). Some methods of construction of these balanced matrices are discussed. An application of these matrices in experimental designs is also given.     

Analysis of Diallel Table for Experiments Carried Out in BIB Designs-Mixed Model

In this paper the analysis of genotypes obtained in a diallel crossing system, including parents, one set of F₁′s and reciprocal F₁′s, is given. This analysis is presented for data obtained from the experiments carried out in a block design in which block effects are random. The analysis of variance, estimators of reciprocal effects, estimators of general and specific combining abilities are considered. Also statistics for testing hypotheses concerning some genetical parameters are given.     

New Structures in Binding Designs of Freshwater Ectoprocta Dormant Bodies (Statoblasts)

With the critical point drying method a scanning electron microscopic study of freshwater Ectoproct dormant structures was made. The suture zones of major phylactolaemate genera were described suggesting methods of their classification. The new structures revealed, throw light on the binding mechanism and early kinetics of germination of these dormant bodies. Median ribs and lateral ribs were described in the suture zones of Plumatella fruticosa, P. casmiana and Pectinatella magnifica. Dormant bodies of Fredericella sultana lack a medial or lateral rib in their suture zone. The fine structure of the polymorphic statoblasts of P. casmiana revealed different binding mechanisms as suited to different seasons. During germination, the internal pressure increases within the statoblast and the well cemented medial rib unfolds, letting its two valves separate. The mechanics of valve separations and subsequent germination were related to their respective environmental conditions favouring their domination.