Analysis of Variance – A Statistical Method

Do you know about the Analysis of Variance (ANOVA)?

If you are a statistics student, maybe you know about the ANOVA, but some people maybe are not aware of the ANOVA.

Don’t worry because we will help you understand this concept through this blog.

Analysis of Variance is also known as Fisher Analysis of variance and is a statistical method that an analyst uses to determine the relationship between independent variables and dependent variables in a regression experiment. It evaluates the impacts of the independent variable on the dependent variable.

The ANOVA method was developed by Ronald Fisher in 1918 but became widely accepted in 1925. Before this invention, analysts worked on t and z-test methods, and later they adopted the ANOVA as a reliable method for the statistics calculations.

If you want to know about analysis of variance in detain, be with us through this blog, here we will discuss the ANOVA deeply with other useful information.

ANOVA- Analysis of Variance

 In statistics, we use a method to find out the relationship between independent and dependent variables. When an analyst obtains variability inside a dataset, ANOVA divides this aggregated variability into two parts to study it.

The one part is systematic factors, and random factors is the other part. Unlike random factors, systematic factors have a statistical impact on the given data set. The random factors do not affect the given data in any way.

How does ANOVA work?

In order to acquire a perfect relationship between the independent and dependent variable, ANOVA is the first and foremost test step to analyze factors that affect a given data set. An analyst uses the ANOVA test findings or results in an f-test to establish additional data that line up with the regression models.

Once the analysts are done with this test, additional testing is performed on the methodical factors that play a role in the inconsistency of the data set.

The ANOVA test enables an analyst to compare two or more than two groups meanwhile to identify the relationship between them if it exists. This comparison is known as F-ratio or F statistics and helps the analysts reveal the variability within or between the samples.

In the case of the null hypothesis( when no difference exists between the tested groups), the ANOVA’s F-ratio statistics result going to nearby 1.  The F distribution(distribution of all possible F Statistics values) is a group of distribution functions having two characteristic numbers: numerator and denominator degrees of freedom.

Types of ANOVA Test

Analysts mainly use two types of ANOVA tests. One is a One-way test, and the second is a Two-way test. Two-way test is the extension of one-way ANOVA test and is used to reduce the limitations of one-way test and provide better results than the one-way analysis of variance test.

One-way test: This ANOVA test is used to determine the difference between two groups.It uses F-distribution for the comparison of two means from two independent or unrelated groups. In the null hypothesis situation it implies that two means are equal. Hence a significant conclusion implies that two means are not equal.

The disadvantage of the One-way ANOVA

Despite various benefits, Analysis of variance by One-way test possesses some disadvantages that make it less relevant to use.

One way ANOVA system determines the difference between the two groups, but it fails to identify which groups are different. To recognize which groups are different, you need to perform an ad hoc test such as the least significant difference.

So, this is the major disadvantage of this test that makes it difficult for the analysts to identify which groups are different from each other, consequently they need to perform other tests to get the same.

Two-way test: This test can be done with or without replication. Suppose you test the responses of one set of individuals before and after any event, activity, effect, etc. A two-way test without replication is used to single or double test the one group.

Two-way test with replication: It is used when you have two groups, and the members of these two groups are participating in more than one activity. For example- Two groups of customers in a shop are trying different products.

Some compulsory criterias for Two-way ANOVA(analysis of variance)

  • The population should be near to a normal distribution
  • Population variance need to be equal
  • Independent samples are needed for the experiment.
  • The sample size of the groups should be equal.


In this blog we have discussed the analysis of variance and its types with examples. Now you know what is ANOVA, how it works and what are the types of ANOVA tests.

 This is a statistical method used in various calculator processes including getting the difference between two groups and the relationship between independent and dependent variables. I hope this blog is helpful for you in order to evaluate the impacts of one variable on the other variables.

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