Analysis of variance (ANOVA)

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Abstract

Univariate ANOVA is reviewed from a user point-of-view with emphasis on understanding the model building and the assumptions underlying the method. Illustrative examples are taken from organic chemistry and analytical chemistry. The use of graphical techniques to visualize the ANOVA model as well as to analyse residuals is recommended. The main models of ANOVA are developed in some detail including one-factor ANOVA, crossed designs, nested designs, repeated measures ANOVA and variance components estimation. Hypothesis testing by F-tests-and follow up by pairwise comparison methods is shown. The distinction between random effects and fixed effects is explained. Methods to handle non-linearities by transformations or by using response surface methodology are mentioned. Throughout the paper the importance of experimental design is emphasized. References are given to ANOVA methods for more complicated models.

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