Combining Information from Similar Experiments: II. Quantifying Qualitative Results

Suppose that independent experiments each indicate general qualitative results, such as higher than normal incidence rates of tumors for exposed populations. This paper suggests methods for amalgamating the qualitative results from several such experiments into a more quantitative form, such as a dose-response relationship. The methods are designed to be robust both to systematic bias in one of the experiments and also to procedural variability across experiments. Data from four rodent experiments with tolazamide are used to illustrate the methods.     

A Comparative Statistical Analysis of Genetic Distances. I - Estimation of Distances and of their Variances: Distribution of the Estimators

We present a Monte-Carlo simulation analysis of the statistical properties of absolute genetic distance and of Nei's minimum and standard genetic distances. The estimation of distances (bias) and of their variances is analysed as well as the distributions of distance and variance estimators, taking into account both gamete and locus samplings. Both of Nei's statistics are non-linear when distances are small and consequently the distributions of their estimators are extremely asymmetrical. It is difficult to find theoretical laws that fit such asymmetrical distributions. Absolute genetic distance is linear and its distributions are better fit by a normal distribution. When distances are medium or large, minimum distance and absolute distance distributions are close to a normal distribution, but those of the standard distance can never be considered as normal. For large distances the jack-knife estimator of the standard distance variance is bad; another standard distance estimator is suggested. Absolute distance, which has the best mathematical properties, is particularly interesting for small distances if the gamete sample size is large, even when the number of loci is small. When both distance and gamete sample size are small, this statistic is biased.     

The Probability of a Negative Linear Combination of Independent Mean Squares

SATTERTHWAITE'S (1941) approximation of the distribution of a linear combination, of independent mean squares is a commonly used technique in the analysis of variance. Confidence intervals and test statistics based on this approximation require that be positive. In this article, the probability that will be negative is considered in situations in which the mean squares are associated with a general balanced mixed model. Expressions are given for exact and approximate values of this probability in terms of the expected values and degrees of freedom of the mean squares. An example is presented to illustrate the implementation of the proposed methodology.