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analysis of variance, ANOVA, mathematics, repeated measures


Applied Mathematics | Mathematics | Physical Sciences and Mathematics


Analysis of variance, referred to as ANOVA, is a test for the equality of means of several different treatment groups. It is based on the partitioning of sums of squares of errors. In an experiment that requires the use of ANOVA, subjects are randomly assigned to one of several treatment groups. These treatment groups can be random, where there are more treatment possibilities than just the ones being tested, or they can be fixed, where all the possible treatments are being tested. In order to test whether or not the means of the multiple treatment groups are statistically different from one another the following hypotheses are developed:

H0 : µ1 = µ2 = … = µa

H1 : µiµj for at least one ij

where a is the number of treatment groups and µi is the ith treatment mean (i = 1,2,...,a). Instead of performing multiple t-tests to test whether rejecting the null hypothesis, H0, is warranted, ANOVA allows us to perform a single F-test to compare two or more means.

ANOVA can be adjusted to take repeated measures and unbalanced data into account. However, before we address these special cases an understanding of the basic form of ANOVA must be developed.

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