 # Analysis Of Variance (ANOVA)

## What is Analysis of Variance (ANOVA)?

Analysis of Variance is an analysis tool used in statistics to find out if a survey or experiment results are significant. It was developed by Ronald Fisher. This test gives you the idea if you need to reject the null hypothesis or accept the alternate hypothesis. In a multiple regression study, this test also provides the observation regarding the influence that independent variables have on the dependent variable. There are two kinds of independent variables in the Analysis of Variance:-

### One Way ANOVA

This test is used to compare two means from two independent groups using the F-distribution. While these two means are equal, the null hypothesis occurs. If two means are unequal, this means a significant result.

### Two Way ANOVA

It is an extended form of One-Way ANOVA with one independent variable affecting a dependant variable. For example brand of cereal, calories.

## When to use ANOVA?

When you wanted to find out how your different groups respond to a test performed by you, Analysis of variance is used. If the response is with a null hypothesis to the test, this signifies that the means of the different groups are equal. If the two populations are unequal, there is a statistically significant result.

## How does ANOVA work?

ANOVA works by comparing the means of different groups and represents the statistical difference if there is any. This test is also known as the omnibus test statistic.

1. F=MSE
2. MST

## where:

1. F=ANOVA coefficient
2. MST=Mean sum of squares due to treatment
3. MSE=Mean sum of squares due to error

In SPSS, ANOVA is performed in many ways, In the “compare option” click on the option “one way ANOVA”.While performing two ways or more than two ways analysis of variance (ANOVA), click on the “univariate” option available in the GLM menu. A post hoc test is performed to further check the significant difference between groups and to know exactly which group has means that are significantly different from other groups.

### Assumptions

1. The sampled population should be normally distributed.
2. The sampled population has a common variance of s2.
3. Each group should have a common variance.

### Limitations of ANOVA

ANOVA helps in analysing the difference in means between two independent variables but won’t be able to tell you about which statistical analysis were different from each other. You may need to run a post hoc test to tell you exactly which groups had a difference in means.

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