Three-Way ANOVA

It is used to determine if there is an interaction effect between 3 independent variables on continuous dependent variables.  

These are called between subjects’ factors, and three-way ANOVA is also called factorial ANOVA. There can be other factors that can be split into multiple levels. 

The procedure uses many different types of assumptions about the data to meet the requirement of the method to give you a good outcome. 

It can happen that the data does not meet the assumptions at some point when conducting the evaluations. Certain methods are used in the technique to transform it or use an alternative figure to overcome it.

It is widely used in gathering and analyzing health-related or medical data.

For example - a specific type of physical exercise can be recommended to different groups of people categorized based on gender (male or female), age and body weight, and the method can produce a relationship between the three factors.

There are six assumptions made in such statistical calculations are – 

• Firstly, the dependent variables are measured at a continuous level, specific interval level, or ratio variable. 

• Secondly, the three variables should be consistent and belong to categorically unrelated groups (like male and female). 

• There should be no relationship between the observations related to each group.

• There should be no significant outliner (outliner means the figures that do not follow the usual pattern).

• The dependent data is normally distributed for each group of 3. 

There should be homogeneity with the involved factors for combining the groups of the three independent factors. 

Similar theories can be applied in financial risk management to get commodity substitution bias, to know the best thing to do with savings, etc.