MANOVA – Multivariate Analysis of Variance


What is MANOVA?

MANOVA is a statistical test that is extension to ANOVA in terms that, in MANOVA we have 2 dependent numeric variables and 1 independent categorical variable. In ANOVA, we have 1 categorical and 1 numeric variable. These 2 numeric variable are combined to form a composite variable and then mean difference is compared.

Why do we use MANOVA?

We use it to check whether there is a significant difference between groups by comparing the means of different groups of 2 or more dependent variables.
Example – We can check whether salary and bonus for male and female are significantly different or same.

If there is a significant difference, we say that we reject null hypothesis.
If there is no significant difference, we do not reject null hypothesis.

There are typically two types of hypothesis:

1. Null Hypothesis – meaning, there is no change/ everything is same.

2. Alternate Hypothesis – meaning, there is a change / there is a difference.

Determining significant value is also in the hands of clients. In this tutorial we will be using significant value as 0.05, meaning, if the results are below 0.05, we will reject null hypothesis and say there is a significant difference between the groups.

When we use 1 independent and 2 dependent variable then we say we are doing One-Way MANOVA.
When we use multiple independent variables and multiple dependent variables, we use n-Way MANOVA.
n is the number depending upon the number of independent variables being used.
If, there are 2 independent variables and 2 dependent variables, we will be doing Two-Way MANOVA.


Example of One-Way MANOVA:

Problem Statement: Is there a significant difference between salaries and bonus of people gender-wise in an organization named ‘Y’?

Here, the dependent variables will be salary and bonus. Salary and Bonus are numeric variables. Independent variable will gender having 2 groups as male and female.

Let’s say, after running the test, our significant value comes as 0.15, we will say there is no significant difference between salaries of males and females. The significant value is above 0.05, so we do not reject null hypothesis.
In other words, we can say the employees are not paid higher salaries and bonus in organization ‘Y’ on the basis of their gender.



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