An R Introduction to Statistics

Analysis of Variance

  In an experiment study, various treatments are applied to test subjects and the response data is gathered for analysis. A critical tool for carrying out the analysis is the Analysis of Variance (ANOVA). It enables a researcher to differentiate treatment results based on easily computed statistical quantities from the treatment outcome.

The statistical process is derived from estimates of the population variances via two separate approaches. The first approach is based on the variance of the sample means, and the second one is based on the mean of the sample variances. Under the ANOVA assumptions as stated below, the ratio of the two statistical estimates follows the F distribution. Hence we can test the null hypothesis on the equality of various response data from different treatments via estimates of critical regions.

  • The treatment responses are independent of each other.
  • The response data follow the normal distribution.
  • The variances of the response data are identical.

In the following tutorials, we demonstrate how to perform ANOVA on a few basic experimental designs.