Difference Between ANOVA and MANOVA


ANOVA and MANOVA are two statistical methods used to check for the differences in the two samples or populations.

What is ANOVA (Analysis of Variance)?

Analysis of the variance is a method of investigating the differences between two samples, or populations. ANOVA does not involve the analysis of relation between two or more variables explicitly. Rather it checks whether two or more samples from different populations have the same mean. For example, consider the test results of an exam held for a grade in a school. Even though the tests are different, performance may be alike from class to class. One method of verifying this is by comparing the mean of every class. ANOVA or ANalysis Of Variance allows this hypothesis to be tested. At basics, ANOVA can be considered as an extension of the t-test, where the means of two samples drawn from two populations are compared.

Fundamental idea of ANOVA is to consider the variation within the sample and variation between the samples. The variation within the sample can be attributed to the randomness, whereas the variation among samples can be attributed to both randomness and other external factors. Analysis of variance is based on three models; fixed effects model, random effects model, and mixed effects model.

What is MANOVA?

MANOVA stands for Multivariate ANalysis Of VAriance, and it accounts for more than two samples or populations. It concerns multiple dependent variables and can be considered as a generalization of the ANOVA.

In contrast to ANOVA, MANOVA uses the variance-covariance between random variables when testing the statistical significance of the differences in means. The MANOVA test provides details for the effects of the independent variable on the dependent variable, and the interactions between independent variable and the interaction between independent and dependent variables.

What is the difference between ANOVA and MANOVA?

• ANOVA checks the differences between the means of two samples/ populations while MANOVA checks for the differences between multiple sample/populations.

• ANOVA concerns about two variables, while MANOVA concerns the differences in multiple variables simultaneously.

• MANOVA uses covariance-variance relationship.