Learn One way Anova and Two way Anova in simple language with easy to understand examples. Anova is used when X is categorical and Y is continuous data type.

Definition : ANOVA is an analysis of the variation present in an experiment. It is used for examining the differences in the mean values of the dependent variable associated with the effect of independent variables. Essentially , ANOVA is used as a test of means for two or more populations.

The tests in an ANOVA are based on the F-ratio: the variation due to an experimental treatment or effect divided by the variation due to experimental error.

Before we move ahead, we need to understand following four terms very clearly:

Dependent Variable – Analysis of variance must have a dependent variable that is continuous. This is our “Y-Total sales”, its value will depend on different levels of “X” or “Xs” in our experiment or analysis.

Independent Variable – ANOVA must have one or more categorical independent variable like Sales promotion. These variables are also called Factors.

Null hypothesis – All means are equal.

Factor level – Each Factor can have multiple levels like Heavy, Medium and Low are three levels of Sales promotion.

ANOVA is used as a test of means for two or more populations. The null hypothesis, typically is that all means are equal as you can see in the above example.

In its simplest form, ANOVA must have a dependent variable that is metric/continuous. There must also be one or more independent variables, all categorical like different levels of sales promotion.

Categorical independent variables are called factors and different levels of factor is called a treatment. One way ANOVA involves only one categorical independent variable that why it is called one way ANOVA.