Vol: 37 Page: 95

Authors:
Joanna Olejnik
Zofia Hanusz

Title:
 Relative potency of preparations based on principal components analysis of multivariate responses

Language: English

Keywords:
relative potency
multivariate bioassays
principal components analysis
parallel-line assay
completely randomized block design
multivariate observations
testing hypotheses

Summary:
Estimation of a test preparation efficiency in relation to a standard preparation in multivariate bioassays is presented in this paper. This estimation is provided if null hypotheses about parallelism and the relative potency fail to reject. However, when many traits in the response for dosages of preparation are considered, both hypotheses can be rejected. Then we cannot estimate the relative potency or we can choose the traits in the response which are the most important for the experimenter responsible for acceptation of the hypotheses. In order to reduce dimensionality of the responses, using principal components analysis is proposed in this paper. Principal components related to the greatest eigenvalues of a sample correlation matrix are taken into account. Test functions for the transformed responses are given. Theoretical results presented in the paper are applied to estimate the efficiency of two forms of nitrogen fertilizer in tobacco and winter wheat experiments.

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