On Testing Equality of Means of Correlated Variates with Incomplete Data

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. Expressions for the second and fourth central moments of the statistic are obtained. These moments are used to approximate the distribution of the statistic by a Student's t distribution under the null hypothesis. The powers of the test are computed and compared with those of the conventional paired t and the other known statistics.     

On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

Construction of Partially Balanced Incomplete Block Designs with Nested Rows and Columns

A number of methods of construction of partially balanced incomplete block designs with nested rows and columns are developed and new balanced incomplete block designs with nested rows and columns are obtained as a by-product.     

Conditional Maximum Likelihood Estimation Following a Group Sequential Test

We consider estimation after a group sequential test. An estimator that is unbiased or has small bias may have substantial conditional bias (Troendle and Yu, 1999, Coburger and Wassmer, 2001). In this paper we derive the conditional maximum likelihood estimators of both the primary parameter and a secondary parameter, and investigate their properties within a conditional inference framework. The method applies to both the usual and adaptive group sequential test designs. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian Estimation of the Distribution Function of the Poisson Model

This paper presents the Bayes estimators of the Poisson distribution function based on complete and truncated data under a natural conjugate prior. Laplace transform of the incomplete gamma function and the Gauss hypergeometric function have been employed in order to overcome the intractability of the integrals. Numerical examples from biosciences are given to illustrate the results. A Monte Carlo study has been carried out to compare Bayes estimators under complete data with the corresponding maximum liklihood estimators.     

Magnetite biomineralization and geomagnetic sensitivity in higher animals: an update and recommendations for future study

Magnetite, the only known biogenic material with ferromagnetic properties, has been identified as a biochemical precipitate in three of the five kingdoms of living organisms, with a fossil record that now extends back nearly 2 billion years. In the magnetotactic bacteria, protoctists, and fish, single-domain crystals of magnetite are arranged in membrane-bound linear structures called magnetosomes, which function as biological bar magnets. Magnetosomes in all three of these groups bear an overall structural similarity to each other, which includes alignment of the individual crystallographic [111] directions parallel to the long axis. Although the magnetosomes represent only a small volume fraction in higher organisms, enough of these highly energetic structures are present to provide sensitivity to extremely small fluctuations and gradients in the background geomagnetic field. Previous experiments with elasmobranch fish are reexamined to test the hypothesis that gradients played a role in their successful geomagnetic conditioning, and a variety of four-turn coil designs are considered that could be used to test the various hypotheses proposed for them.     

A design criterion for symmetric model discrimination based on flexible nominal sets

Experimental design applications for discriminating between models have been hampered by the assumption to know beforehand which model is the true one, which is counter to the very aim of the experiment. Previous approaches to alleviate this requirement were either symmetrizations of asymmetric techniques, or Bayesian, minimax, and sequential approaches. Here we present a genuinely symmetric criterion based on a linearized distance between mean-value surfaces and the newly introduced tool of flexible nominal sets. We demonstrate the computational efficiency of the approach using the proposed criterion and provide a Monte-Carlo evaluation of its discrimination performance on the basis of the likelihood ratio. An application for a pair of competing models in enzyme kinetics is given.