The Purpose of Analysis of Variance. In general, the purpose of analysis of variance (ANOVA) is to test for significant differences between means. Elementary Concepts provides a brief introduction into the basics of statistical significance testing. If we are only comparing two means, then ANOVA will give the same results as the t-test for independent samples (if we are comparing two different groups of cases or observations), or the t-test for dependent samples (if we are comparing two variables in one set of cases or observations). If you are not familiar with those tests you may at this point want to "brush up" on your knowledge about those tests by reading Basic Statistics and Tables - Introductory Overview.

Why the name analysis of variance? It may seem odd to you that a procedure that compares means is called analysis of variance. However, this name is derived from the fact that in order to test for statistical significance between means, we are actually comparing (i.e., analyzing) variances.

The Partitioning of Sums of Squares

See also ANOVA/MANOVA notes, Methods for analysis of variance, General Linear Models (GLM), General Regression Models (GRM), Variance Components and Mixed Model ANOVA/ANCOVA, and Experimental Design (DOE); to analyze nonlinear models, see Generalized Linear/Nonlinear Models (GLZ).