Complete Details on What is ANOVA in Statistics?

Statistics itself is a complicated subject that is used to calculate the mean, median, mode, variance, and other factors of a large collected data. ANOVA (Analysis of Variance) is used to test the hypothesis equality of two or more values of the population. There are several students who do not have any idea about what is ANOVA, its types, and much more. Therefore, this blog will help you to know all this information about what is ANOVA. So let’s get information on it.

What is ANOVA and its history?

It is a type of analytical tool which is used for statistical data that divides an observed value found within the data set in two different parts: systematic factors and random factors. To represent the statistical influence on the provided data sets, the systematic factors are used, whereas the random factors do not have any statistical influence on the data. Various analysts are using ANOVA to determine the statistics influence, which can show for independent variables on the dependent variables for the regression period. Now, you have an idea about what is ANOVA, so let’s know some history of ANOVA.

The z-test and T-test methods were implemented in the 20th century and were used until 1918 for statistical analysis. Initially, ANOVA is known as the Fisher analysis of variance as it is created by Ronald Fisher; this has the extension of z-test and t-test. The terminology ANOVA was renowned in the year 1925 when it was written in Fisher’s book known as “statistical methods for research workers”. Initially, it was included in experimental psychology, but later, it was expanded to more complicated subjects.

The formula of Analysis of Variance:



F = ANOVA Coefficient.

MST = Mean sum of squares due to treatment.

MSE = Mean sum of squares due to error.

How to use ANOVA?

When one has the knowledge of what is ANOVA, then one can easily use ANOVA for various purposes that also depend on the design of the research. Usually, there are three different ways to use ANOVA that are one-way, two-way, and N-way ANOVA. Let’s get details of each of them.


It has one independent variable. Let’s take an example of it, and the IQ difference can be evaluated by a nation, and a nation can have 2,20, even more categories to compare the values. 


The two-way ANOVA is also known as factorial ANOVA, which is used for two independent variables. Let’s take an example of it; the two-way ANOVA is used to examine the difference between IQ scores by gender (independent variable 2), and country (independent variable 1). This two-way ANOVA is used to check the interaction in the two independent variables. Let’s take an example, females might have a higher IQ score as compared to males, but the difference might vary as greater or less for the European countries as compared to other North American countries.


When a researcher uses more than two variables, or we can say that if the research is done with n as the number of independent variables, then it is termed as N-Way ANOVA. An example of it is the potential difference in IQ scores can be tested by Gender, Ethnicity, Country, Age group, and much more simultaneously. 

What is the purpose of ANOVA?

For omnibus ANOVA test

There is no major difference between the groups for the null hypothesis value. The other hypothesis supposes that there must be one particular difference between the groups. The researcher can test the estimated value of ANOVA that are generated after cleaning the data. Then they measure the F-ratio and the p-value, which is the associated probability value. If the associate p-value is 0.5 smaller than the F, then the value of the null hypothesis can be rejected; therefore, one can conclude that the mean value of a group is not equal. To check the differences of the group, the researcher uses the Post-hoc testing method.

What if one finds statistical significance? Method for multiple comparisons test

When you use an ANOVA test, one is trying to determine the significant difference of the statistical data among the groups. If one successfully finds the differences, then you are required to analyze where the difference of the group lay.  

This is the correct place where you can use Post-hoc tests that use t-tests methods to check the mean difference in the groups. There are various multiple tests that are used to control the type I error rate, that includes the Scheffe, Tukey, Bonferroni, and Dunnet test.

What are the assumptions and data levels?

Besides the understanding of what is ANOVA, the level of calculation of the assumptions and variables of the test plays an essential role in ANOVA. For the testing of ANOVA, the dependent variables should be continuous (ratio or interval) level of measurement. In ANOVA, the independent variables should be categorical (ordinal or nominal) variables. Just as a t-test, it is used for some assumptions and a parametric test. It is also used to distribute the data normally. It is also used as homogeneity of variance, which means the variance must be equal among the groups. ANOVA also has the observed value that is independent of each other. To make sure, researchers are planning to study out the confounding or extraneous variables. It has various ways to control confounding variables. 

Testing of the assumptions

  1. The population must be normally distributed for the drawn samples.
  2. In the case of independent variables: the model cases must be independent of each other.
  3. Homogeneity of variance: here, the homogeneity means that the variance of a group sets must be equal.

These assumptions are tested using statistical software (such as Intellectus Statistics). The homogeneity of variance’s assumption is tested using a test like the Brown-Forsythe or Levene test. The normality distribution of the scores is tested using the values of kurtosis and skewness, histograms, or using a test like Kolmogorov-Smirnov or Shapiro-Wilk. The assumption of independence is determined from the design of the study.

It is essential to notice that ANOVA is not used for violation of the assumed independence value. If you have to violate the assumed value of normality or homogeneity, one can easily get the test and trust the outcomes. If any of the independent assumptions are violated, then the output of ANOVA is considered as invalid. But, with the homogeneity violations, the other analysis can be considered as robust for the equal-sized groups. If you have a large sample size, the violations of normality are considered to be ok.

Relative Analyses term: ANCOVA and MANOVA

As per the requirement, the researchers have expended the use of ANOVA in ANCOVA and MANOVA, where ANCOVA stands for Analysis Of Covariance, which is used if the researchers need to include one or more covariate variables values in the analysis whereas MANOVA is the term for the multivariance analysis of variance, which is used for two or more dependent variable values.


This blog has all the details on what is ANOVA, its history, formula, ways to use ANOVA, and much more. We hope that this blog helps you to understand the meaning of ANOVA. One can easily use this to check the hypothesis value for the large population data. This can be used in three different ways, like a one-way test, a two-way test, and an n-way test, and all of them are used for different purposes. 

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