Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among means. It is a statistical method that separates observed variance data into different components to use for additional tests. ANOVA is used to test the difference between two or more means. It is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means.

ANOVA is used in the analysis of comparative experiments, those in which only the difference in outcomes is of interest. The statistical significance of the experiment is determined by a ratio of two variances. ANOVA is helpful for testing three or more variables. It is similar to multiple two-sample t-tests. However, it results in fewer type I errors and is appropriate for a range of issues.

ANOVA can only tell if there is a significant difference between the means of at least two groups, but it can’t explain which pair differs in their means. If there is a requirement for granular data, deploying further follow-up statistical processes will assist in finding out which groups differ in mean value. ANOVA relies on three main assumptions that must be met for the test results to be valid, including normality, homogeneity of variance, and independence.

There are different types of ANOVA, including one-way ANOVA and two-way ANOVA. A one-way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables. A two-way ANOVA has two or more categorical independent variables and a normally distributed continuous dependent variable.

In summary, ANOVA is a statistical method used to analyze the differences among means. It is used to test the difference between two or more means and provides a statistical test of whether two or more population means are equal. ANOVA is helpful for testing three or more variables and is similar to multiple two-sample t-tests. There are different types of ANOVA, including one-way ANOVA and two-way ANOVA.