ANCOVA – Analysis of Co-variance

What is ANCOVA?

It is a statistical test used to check the significant mean difference between 2 or more groups, but the mean is adjusted by a confounding variable (co-variate). Basically, ANCOVA is same as ANOVA, we have one more variable introduced here as co-variate. That makes total 3 number variables used. Co-variate will divide the mean of the groups into separate results based on the variable we give in co-variate.

There are 3 types of variables used in this test.

1. Independent – will always be a categorical variable with groups. Example – gender is a categorical variable with 2 groups Male & Female

2. Dependent – will always be a numeric variable. Example – Salary of an employee

3. Covariate – will always be numeric. Example – Hours worked in a week

Why do we use ANCOVA?

We use it to check if there is significant difference between 2 or more groups, if you introduce co-variate in your analysis.
Example – We can check whether salary for male and female are significantly different as per the hours worked 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.

Example of One-Way ANCOVA:

Problem Statement: Does hours spent on work has a significant difference between the salaries of males and females in an organization ‘Y’?

Here, the dependent variable will be salary where salary is our numeric variable. Independent variable will gender having 2 groups as male and female. Covariate will be hours spent on work, another numeric variable.

Let’s say, after running the test, our significant value comes as 0.02, we will say there is significant difference between salaries of males and females on the basis of hours spent. The significant value is below 0.05, so we reject null hypothesis.
In other words, we can say the males and females who are working for more hours, seems to have more salary.