History and Definition
ANOVA or Analysis of Variance is a group of statistical models to test for significant difference between means. It tests whether the means of various groups are equal or not. A Multivariate analysis of Variance is called MANOVA. This is similar to ANOVA which is a one-way Analysis of Variance, except that there are more than one variable or factors involved. This is used in studies where more than one factors affect the dependant variable. When the various factors affecting the dependant variable including all their combinations at different levels are studied and tested, these are called Factorial experiments in MANOVA. No matter which type of MANOVA is being used, the dependant variables are always linearly combined.
Various methods related to Analysis of Variance like hypothesis testing, partitioning of sum of squares, additive models and experimental techniques have been around since the beginning of the 19th century. However, ANOVA and MANOVA as we know today were 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.
Illustration
Say, a retail chain wants a better understanding of its customers’ purchase behavior to increase footfalls. It can use a questionnaire among mall visitors and also conduct focus groups interviews at a few top malls. Data from these will help create a profile of the customers and MANOVA 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.
Benefits and Practical Usage of MANOVA
There are various advantages of MANOVA over one-way ANOVA. Firstly, we can study any interaction between the factors. Secondly, studying two or more factors simultaneously increases the model’s efficiency. And thirdly, the residual variation in the model is reduced when more factors are included in the study.
MANOVA is extremely useful in experimental studies where manipulation of independent factors is seen. Further, since various factors are studied together, it is easier to determine which factors are really important. Also, MANOVA reduces the chances of Type 1 error that would result if multiple ANOVA were used and also aids in the discovery of differences that might remain hidden with ANOVA.
On the other hand MANOVA is more complicated than ANOVA and can lead to problems in interpretation and analysis when substantial interaction between factors is observed. Further, for each additional factor being studied, one Degree of Freedom is reduced.
MANOVA is widely used in the fields of biological research, ecology and medical entomology. Other areas of application of MANOVA are in the fields of experimental design and research. It is often used on production floor to manage the quality settings and decide upon the best combination that can provide the desired quality of output.