Analysis of Variance (ANOVA): An Introduction

Analysis of Variance is applied to compare population means across 2 or more samples/groups using variance of the samples/groups.

In common applications of ANOVA, the dependent variable is continuous and independent variable is categorical (Nominal or Ordinal) variable. The mean of dependent variables is compared across categorical variable values.

Typically, Null hypothesis is that means value is same across the groups.  If the number of groups across which mean values are compared are 2, the result of ANOVA analysis is similar or same to that of t test.

ANOVA analysis compares variance between samples/groups with variance within sample for testing the null hypothesis.  Variance in overall population is broken into two parts – one due to groups (variance between groups) and second due to randomness (implicit in the population, residual/error).

Total Variance = Variability between groups + Variability within groups


  • Populations across groups follow a normal distribution
  • Populations across groups have the same variance (or standard deviation)
  • Populations across groups are randomly selected and independent of one another

Since, ANOVA analysis involves assumption of normality; it is categorized as parametric test. If normality assumption is not satisfied, non-parametric test such as Kruskal-Wallis ANOVA and Mood’s Median Test

Analysis of Variance (ANOVA) Statistics: Formulations

Illustrative Example:ANOVA

Illustrative Example: ANOVA

ANOVA calc details













ANOVA Statistics: Claim Example

ANOVA using R