According to wikipedia, “In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. ANOVA facilitates the statistical test of the means of many groups in case all are equal and further generalizes t-test to two or more groups.” ANOVA helps to possess advantage over a two sample t-test. It is used to eliminate the type error occurred from multiple two sample t-tests. ANOVA was first time used in 1800s with least squares, but Sir Ronald Fisher was the first person to publish it as a different function in an article entitled “The Correlation between Relatives on the Supposition of Mendelian Inheritance” in 1918. He also made it popular by including in his book Statistical Methods for Research Workers in 1925.
ANOVA can be categorized in three classes—
Fixed effects model are models of ANOVA, in which the data comes from normal population and may be differed in their means. Fixed effects model allows the researcher to calculate the ranges of various response variables values generated in the population.
Random effects models are used to assuming that data describes a hierarchy of different population while their differences are applied by their hierarchy. These are applied in case when treatments are not fixed.
Mixed effect models are used to describing the situation while the above both fixed and random effects are present.
ANOVA is used in various forms of ANOVA such as one-way ANOVA (to test differences among two or more groups), Factorial ANOVA (to study the interaction effects), Repeated measures ANOVA (when same subjects are applied in each treatment) and Multivariate analysis of variance (aka MANOVA and is used in more than one response variables).