What is ANOVA?

History and Definition

ANOVA or Analysis of Variance is a group of statistical models to test if there exists a significant difference between means. It tests whether the means of various groups are equal or not. In ANOVA, the variance observed in a particular variable is partitioned into different components based on the sources of variation. An important fact to note is that while we use ANOVA to find out whether the means differ significantly, we actually compare the variances (hence the name – ANalysis Of VAriance).

While various related methods like hypothesis testing, partitioning of sum of squares, additive models and experimental techniques have been around since the beginning of the 19th century, ANOVA as we know today was first used by Sir Ronald Fisher in 1925 in his book ‘Statistical Methods for Research Workers’. Randomization models were first published in 1923 by Neyman. ANOVA is easy to compute and can be manually computed using simple algebra rather than complex matrix calculations. This was one of the reasons for its early popularity.

Benefits and Practical Usage of ANOVA

When we have only two samples, t-test and ANOVA give the same results, but using a t-test would not be reliable in cases where there are more than two samples to be compared (as the chances of Type 1 error would increase). In such cases, ANOVA is most effective to compare the means. Hence, ANOVA is the preferred model used in industries like pharmaceuticals and medical research because of its ability to test more than two samples simultaneously. Another advantage of ANOVA is that it can be used effectively even when the number of observations is different in each group. In medical research, ANOVA can help us compare various treatments and decide which one is most effective over time and hence most cost effective. Agricultural research is another field where ANOVA is used widely to test the effectiveness of different fertilizers, seeds or other factors.


Say, a retail chain wants a better understanding of its customers’ buying behavior to increase footfalls. It can construct a questionnaire to be administered among mall visitors and also conduct focus groups interviews among select few top malls. Data from these will help create a profile of the customers and ANOVA will help determine which mall is considered best for factors like prices, recreational activities, fashion, value for money and so on. This information can then be used to create better and more effective marketing campaigns to increase footfalls.

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