Data analysis with crossed and nested treatment structures based on example of experiment with lupine
Katarzyna Ambroży
katarzyna.ambrozy-deregowska@up.poznan.plKatedra Metod Matematycznych i Statystycznych, Uniwersytet Przyrodniczy w Poznaniu (Poland)
Iwona Mejza
Katedra Metod Matematycznych i Statystycznych, Uniwersytet Przyrodniczy w Poznaniu (Poland)
Abstract
To illustrate the proposed in this paper method of a statistical analysis of non-orthogonal data with nested and crossed treatment structures, some results from a complete factorial experiment with lupine were used. The observations have been collected keeping up relations occurring in the original experiment. It means that our conclusions should be treated only in terms of the methodology of a design and analysis of this type of data. The experiment has been designed to test the effects of dates of sowing (A) and spacing (C) on the yield of some lupine varieties (B). In the paper is assumed that the experiment was designed with block sizes less than the number of treatment combinations. For comparing the effectiveness of some experiment designs which are commonly used in such study, the statistical analyses have been performed twice, once using the mixed model for observations from the split-block-plot (strip-split-plot) type experiment and then the mixed model for observations from split-plot × split-block type experiment. Both designs presented in this paper are incomplete with respect to the treatments of the third factor (C) and complete with respect to the treatments of the remaining two factors. It was assumed that all comparisons among C treatments effects are equally important, so a balanced incomplete block (BIB) design was chosen as the generating design. Since the both three factorial designs are non-orthogonal and have got different structures of the experimental units, the conclusions considering relative efficiency of them have been limited to the intra-stratum analyses appropriated for the type of comparisons of treatment combinations effects.
Keywords:
incomplete split-block-plot design (strip-split-plot design), incomplete split-plot × split-block design, mixed model, relative efficiencyReferences
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Authors
Katarzyna Ambrożykatarzyna.ambrozy-deregowska@up.poznan.pl
Katedra Metod Matematycznych i Statystycznych, Uniwersytet Przyrodniczy w Poznaniu Poland
Authors
Iwona MejzaKatedra Metod Matematycznych i Statystycznych, Uniwersytet Przyrodniczy w Poznaniu Poland
Statistics
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