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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).
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.

 One-way ANOVA One-way ANOVA description Two-way ANOVA or Three-way ANOVA description GLM ANOVA General Linear Models (GLM) ANOVA procedure description Using Latin Squares for design and analysis of factorial experiments