# Statistics Analysis of Variance - Statistics

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## What is analysis of variance?

Analysis of Variance is also known as ANOVA. It is a process proceeds by statisticians to know the major difference between scale-level dependent variable by a nominal-level variable across two or more categories. Initially it introduced by Ronald Fisher in 1918 and it extends t-test and z-test which compares only nominal level variable to make only two categories.

## What are the types of ANOVA?

There are three of ANOVA are there :

• One-way ANOVA - One-way ANOVA will have only one independent variable and it includes numbers in this variable. For example, to assess differences in IQ by country, you can have 1, 2, and more countries data to compare.
• Two-way ANOVA - Two way ANOVA includes two independent variables. For example, to access differences in IQ by country (variable 1) and gender(variable 2). Here you can examine the interaction between two independent variables. Such Interactions may indicate that differences in IQ are not uniform across a independent variable. For examples females may have higher IQ score over males and have very high score over males in Europe than in America.

Two-way ANOVAs are also named as factorial ANOVA and can be balanced as well as unbalanced. Balanced ANOVA refers to include the same number of participants across the group where as unbalanced ANOVA means which will include various participants in each group. Below mentioned kind of ANOVAs can be used to manage the unbalanced groups.

• Hierarchical approach(Type 1) -If data was not intentionaly unbalanced and has some type of hierarchy between the factors.
• Classical experimental approach(Type 2) - If data was not intentionaly unbalanced and has no hierarchy between the factors.
• Full Regression approach(Type 3) - If data was intentionaly unbalanced because of population.

N-way or Multivariate ANOVA - N-way ANOVA have more than two independent variables. For example, to assess differences in IQ by country, gender, age etc. simultaneously, N-way ANOVA is to be deployed.

## What is ANOVA test procedure?

Below are the common steps to carry out ANOVA.

• Setup null and alternative hypothesis where null hypothesis states that there is no significant difference among the groups. And alternative hypothesis assumes that there is a significant difference among the groups.
• Calculate F-ratio and probability of F.
• Compare p-value of the F-ratio with the established alpha or significance level.
• If p-value of F is less than 0.5 then reject the null hypothesis.
• If null hypothesis is rejected, conclude that mean of groups are not equal.
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