Analysis of Variance

Reference work entry

The analysis of variance is a technique that consists of separating the total variation of data set into logical components associated with specific sources of variation in order to compare the mean of several populations. This analysis also helps us to test certain hypotheses concerning the parameters of the model, or to estimate the components of the variance. The sources of variation are globally summarized in a component called error variance, sometime called within-treatment mean square and another component that is termed “effect” or treatment, sometime called between-treatment mean square.


Analysis of variance dates back to Fisher, R.A. (1925). He established the first fundamental principles in this field. Analysis of variance was first applied in the fields of biology and agriculture.


The analysis of variance compares the means of three or more random samples and determines whether there is a significant difference between the populationsfrom...

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  1. 1.
    Fisher, R.A.: Statistical Methods for Research Workers. Oliver & Boyd, Edinburgh (1925)Google Scholar
  2. 2.
    Rao, C.R.: Advanced Statistical Methods in Biometric Research. Wiley, New York (1952)zbMATHGoogle Scholar
  3. 3.
    Scheffé, H.: The Analysis of Variance. Wiley, New York (1959)zbMATHGoogle Scholar

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