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Testing transition rates in generalized binomial models
Author(s) -
Stucky W.,
Unkelbach H. D.
Publication year - 1980
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710220807
Subject(s) - mathematics , binomial distribution , negative binomial distribution , binomial (polynomial) , statistics , sample size determination , basis (linear algebra) , set (abstract data type) , statistical physics , computer science , physics , geometry , poisson distribution , programming language
In toxicological experiments the type II error is of important interest, but it is seldom discussed. For certain experiments like those in reproduction toxicology this paper gives some ideas to calculate it analytically. The basis is a generalized binomial model describing transition processes in experimental units. Each experimental unit contains a set of × members which develop from one to another specified state with some probability P. This transition probability P is allowed to vary from one experimental unit to the other; there is no restriction on the distribution of P and X, nor is P assumed to be independent of the total number × in contrast to the commonly used models. The model is extended to describe the treatment of an experimental unit, which permits to separate the treatment effect from the spontaneous development. This allows to investigate the power of some statistical tests for calculating sample sizes and for comparing different experimental designs.