O'Reilly logo

Statistical Hypothesis Testing with SAS and R by Dirk Taeger, Sonja Kuhnt

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 17

Tests in variance analysis

Analysis of variance (ANOVA) in its simplest form analyzes if the mean of a Gaussian random variable differs in a number of groups. Often the factor which determines each group is given by applying different treatments to subjects, for example, in designed experiments in technical applications or in clinical studies. The problem can thereby be seen as comparing group means, which extends the t-test to more than two groups. The underlying statistical model may also be presented as a special case of a linear model. In Section 17.1 we handle the one- and two-way cases of ANOVA. The two-way case extends the treated problem to groups characterized by two factors. In this case it is also of interest if the two factors influence each other in their effect on the measured variable, and hence show an interaction effect. One of the crucial assumptions of an ANOVA is the homogeneity of variance within all groups. Section 17.2 deals with tests to check this assumption.

17.1 Analysis of variance

17.1.1 One-way ANOVA

Description: Tests if the mean of a Gaussian random variable is the same in c17-math-0001 groups.
Assumptions:
  • Let c17-math-0002, c17-math-0003, be independent samples of independent ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required