ANOVA or the Analytics of Variance test is appropriate when the data contains three or more independent group means. ANOVA tests for significant differences between two or more groups.

The value of F statistics is calculated when the variance of the total group is compared with the variances of individual groups.

The formula for it

If there are no observed differences (in other words no actual effect), the value of F is 1. If there are observed differences, the value of F is greater than 1. The F statistic has 1-tailed distribution, with F always being positive.


Assumptions of ANOVA:

  1. Normality of Sample Distribution of Means when sample means are normally distributed.

  2. Independence of errors: the errors between cases are independent of one another.

  3. The absence of outliers.To get meaningful results from ANOVA testing, the outliers need to be removed from the data set prior to performing statistical analysis.

  4. Homogeneity of Variance: the population variances in different levels of each independent variable are equal.


When the statistical significance is found, ANOVA does not identify which two groups means are different.  To find out which two groups means are different, a “post hoc” (“after the fact”) analysis is needed.