** ANALYSIS OF VARIANCE (ANOVA)**

##### INTRODUCTION

**Analysis of variance ( ANOVA)** is a statistical method for making simultaneous comparisons between two or more means of a dependent variable affected by numerous factors of an independent variable. It investigates the causes of differences occurring in the mean values of two or more populations under study. The null hypothesis for such cases is ‘all means are equal’.

The significance of the difference between the means of two samples can be tested by using z-test or the t-test. But, the difficulty arises when we have to examine the significance of the difference amongst more than two sample means at the same time. The ANOVA technique enables us to perform this test and so it is considered as an important tool of analysis. Using this technique, one can draw inferences whether the samples have been drawn from populations having the same mean or not.

The ANOVA technique is important in the situations where the researchers want to compare more than two populations such as:

- Comparing the marks of the students of four different colleges.
- Comparing the life span of electric bulbs of three different brands.
- Comparing the petrol mileage of five automobiles, and so on.

In such circumstances one uses ANOVA technique to investigate the differences among the means of all the populations simultaneously.

**Types of ANOVA :-**