What is the ANOVA test?

The ANOVA defines as one way analysis of variance or one-factor analysis variance that is used to determine if there are any statically significant differences between the means of three or more unrelated groups. The ANOVA method is used to test the null hypothesis.

ANOVA test

Where ยต= mean of the group

K = number of groups

If, the one way ANOVA produces a significant result, the alternative Hypothesis gets accepted i.e. Ha. The alternative hypothesis explains that there is a minimum of two group means that are significantly unrelated to each other. However, the ANOVA test cannot determine which two statistically groups from the whole data set are significantly different from each other. To find these particular groups other methods are implemented later.

The Formula for ANOVA is:

F =MST/MSE

Where: F= ANOVA Coefficient

MST= Mean sum of squares due to treatment

MSE= Mean sum of squares due to error.

In simple terms, the ANOVA test helps you to compare three or more groups at the same time to know if a relationship exists between the groups. The test helps to determine if any variance exists in groups of a given data set.

An example to explain where you can apply ANOVA method:

Say a researcher is working on a new drug and wants to determine its maximum efficacy on a group of sick people. To experiment a group of volunteers was selected divided into 3 groups named a b and c. group a is supplied with drug empty stomach, group b is supplied with the drug while eating food, and group c are supplied with the drug after 1 hour. The result of drug efficacy on 3 groups is the dependent variable.

Assumption of ANOVA:

There are three assumptions for ANOVA Test-

  1. Normally distribution of variables
  2. Variable of the population are equal
  3. Independence of variance.

To seek more detail or conduct one way ANOVA test for your data set you can look for some of the free online one way ANOVA calculators. StatsJournal is one of the most simple and efficient free online calculators that solve your statistical problems real quickly and seamlessly.