The use of analysis of variance procedures in biological studies. (English) Zbl 0636.62077
The analysis of variance (ANOVA) is widely used in biological studies, yet there remains considerable confusion among researchers about the interpretation of hypotheses being tested. Ambiguities arise when statistical designs are unbalanced, and in particular when not all combinations of design factors are represented in the data.
This paper clarifies the relationship among hypothesis testing, statistical modelling and computing procedures in ANOVA for unbalanced data. A simple two-factor fixed effects design is used to illustrate three common parametrizations for ANOVA models, and some associations among these parametrizations are developed. Biologically meaningful hypotheses for main effects and interactions are given in terms of each parametrization, and procedures for testing the hypotheses are described. The standard statistical computing procedures in ANOVA are given along with their corresponding hypotheses. Throughout the development unbalanced designs are assumed and attention is given to problems that arise with missing cells.
This paper clarifies the relationship among hypothesis testing, statistical modelling and computing procedures in ANOVA for unbalanced data. A simple two-factor fixed effects design is used to illustrate three common parametrizations for ANOVA models, and some associations among these parametrizations are developed. Biologically meaningful hypotheses for main effects and interactions are given in terms of each parametrization, and procedures for testing the hypotheses are described. The standard statistical computing procedures in ANOVA are given along with their corresponding hypotheses. Throughout the development unbalanced designs are assumed and attention is given to problems that arise with missing cells.
MSC:
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 65C99 | Probabilistic methods, stochastic differential equations |
Keywords:
hypothesis testing; statistical modelling; computing procedures; ANOVA; unbalanced data; two-factor fixed effects design; parametrizations; unbalanced designs; missing cellsReferences:
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