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# Difference Between ANOVA and MANOVA

ANOVA vs MANOVA

ANOVA and MANOVA are two different statistical methods used to compare means.

ANOVA
“ANOVA” stands for “Analysis of Variance.” In statistics, when two or more than two means are compared simultaneously, the statistical method used to make the comparison is called ANOVA. It is a method which gives values and results which can be tested in order to determine if a relationship of any significance exists between different variables. It provides a test to determine if the means of two or more groups are equal. This test used is called the “t-test.”

The name ANOVA has been given to the comparison of means because in order to determine any relationship between different means, the variances are actually being compared. ANOVA is especially useful because while carrying out multiple, two-sample tests, there is an increased chance of a Type l error, and ANOVA can compare the means simultaneously. Another characteristic of ANOVA is that it compares scale or interval variables also called “continuous variables.”

ANOVA has three different models:
Fixed-effect models- This model of ANOVA is applied in experiments where the subject is subjected to one or more than one treatment to determine if the value of the response variable changes.
Random-effect models- This model of ANOVA is applied when the treatments applied to the subject are not fixed in a large population where the variables are already random.
Mixed-effect models- As the name suggests, this model of ANOVA is applied to experimental factors which have both random-effect and fixed-effect types.

MANOVA
“MANOVA” stands for “Multivariate Analysis of Variance.” MANOVA methods in statistics contain multiple, dependent variables. They help in determining the differences between either two or more than two dependent variables. It assists in determining this difference simultaneously.

The MANOVA method determines if the dependent variables get significantly affected by changes in the independent variables. It also determines the interactions taking place amongst dependent variables. MANOVA finally determines the interactions taking place amongst independent variables too.

Summary:

1.“ANOVA” stands for “Analysis of Variance” while “MANOVA” stands for “Multivariate Analysis of Variance.”
2.The ANOVA method includes only one dependent variable while the MANOVA method includes multiple, dependent variables.
3.ANOVA uses three different models for experimentations; random-effect, fixed-effect, and multiple-effect methods to determine the differences in means which is its main objective while MANOVA determines if the dependent variables get significantly affected by changes in the independent variables. It also determines the interactions taking place amongst dependent variables and determines the interactions taking place amongst independent variables too.

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### 1 Comment

1. Excelent description of ANOVA and MANOVA and the difference between the two. As a student conducting my PhD research and using MANOVA, i found the write up very useful.

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