Modeling data from three-factor experiments with split units set up in designs with different block structures
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
In agricultural research, particularly in field experiments, many experimental designs with different block structures can be used. Selecting a design when setting up the experiment is important primarily from the standpoint of practice, but it also entails statistical consequences. In many-factor experiments where there is a different degree of interest in the factors, the literature describes experimental designs with split units, such as split-plot design, split-block design or various combinations of these arrangements. Multi-stage randomization schemes used in the designs lead to different so-called randomization linear models. In this paper we consider the multistratum models of observations for three-factor experiments set up in so-called mixed designs, which are different combinations of split-plot and split-block layouts. The different division of the total variability between the individual effects generates a number of errors in the analysis of variance in these designs. This entails a different precision of estimation of comparisons among the particular and interaction effects of the treatments. Knowing this fact enables the conscious modeling of data and an optimal statistical analysis using the experimental material structure given. The empirical relative efficiency of these designs will be illustrated on the example of simulated data from experiments with winter wheat.
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Keywords:
designs with split units, mixed linear 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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