ANOVA aka Analysis of Variance

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What is Anova?

ANOVA aka Analysis Of Variance is a statistical tool created by Ronald Fisher. It is also known as Fisher analysis of variance and is an extension of the z-test and t-test, also a statistical tool. ANOVA is used to understand if there is any statistical difference between the means of three or more independent variables/groups. Analysts use ANOVA to establish if independent variables have any influence on the dependent variable. It breaks down an aggregate variable found in data into two parts – Systematic Factors and Random Factors. Systematic Factor has a statistical influence on the data, unlike Random Factor.

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Formula Used to Calculate ANOVA

F = MST/MSE

F is ANOVA coefficient

MST is the Mean sum of squares due to Treatment

MSE is the Mean sum of squares due to Error

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When to use ANOVA?

You can use ANOVA when you want to test a hypothesis. As a market researcher, using ANOVA can help you understand how different groups respond. For the test, you can begin with a null hypothesis, i.e., assuming that the means of all the observed groups are equal. In case of a statistically significant result, it will indicate that the populations are unequal.

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How can ANOVA help you?

An ANOVA test allows an analyst to compare two or more groups at the same time to establish if there is any relationship between the groups. The result of the test, F-ratio/statistics, allows an analysis of multiple groups of data to determine the variability within samples as well as between samples.

The One-way ANOVA can help you examine if there is any difference between the means of your independent variables. You can understand how the mean differs from one independent variable to another. As a result, you can understand which independent variable has a relationship with your dependent variable and what is motivating that behavior.

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Example of ANOVA test

ANOVA test is used when your data has a categorical independent variable with at least three groups and one quantitative dependent variable.

Your collected data may have Social Media use as the independent variable. The groups may be divided into Low, Medium, and High levels of social media usage. You can compare it with the dependent variable of ‘hours of sleep’ to determine if there is any difference.

In the case of Location as an independent variable, you may have USA, China, and Australia as the levels/ groups of the independent variables. You can compare it with the dependent variable, NPS^® , and find out if it has any relationship to the independent variable.

How does an Analysis of Variance test work?

When analyzing factors of data, ANOVA is the initial step. It determines if the group of the independent variables statistically differs. It does so by calculating if there is any difference between the group means and the overall mean of the dependent variable.

The null hypothesis is rejected if there is any difference between the group means and the overall mean.
In case there is no difference between the tested groups, then the result of the ANOVA F- ratio statistic will be near 1.

ANOVA is an Omnibus Test Statistics. This implies that the test cannot tell you exactly which groups are statistically different from others.

What are One-Way ANOVA and Two-Way ANOVA?

There are mainly two types of ANOVA: One Way and Two Way. Both the ANOVA tests differ from one another by the number of independent variables in the ANOVA test.

One-Way ANOVA implies that it has one independent variable. One-way ANOVA can give you the result that at least two groups were different from one another but cannot reveal which group is different. To find out exactly which group has different means, you can run an ad hoc test

Two-Way ANOVA includes two independent variables. A two-way ANOVA is appropriate for use when you have one measurement variable with two nominal variables.

There is also another variation of ANOVA, which is called MANOVA. MANOVA means Multivariate ANOVA. MANOVA tests for multiple dependent variables all at the same time.

FAQs

What is the difference between t-test and ANOVA?

A t-test is used to figure out if the two populations are statistically different from each other.

ANOVA is used to determine the statistical difference in the mean of three or more populations.

Is F-test the same as ANOVA?

F-test is used in the process of ANOVA to either test the difference between means or the equality of variance. ANOVA separates the variability of within-sample from between-samples. The F-test is the ratio of the mean squared error of these two samples.

Can F-value be less than 1?

If the null hypothesis results false, it is possible to get an F-value that is less than 1. The F-distribution moves to the right as the population effect size increases. As a result, the possibility of getting a value that is less than one decreases.