ANOVA and MANOVA are basically two different statistical methods that are used to calculate the mean for a given data. The word ANOVA stands for analysis of variant, while the word MANOVA stands for multivariate analysis of variant.

The ANOVA method used for calculating mean includes only one dependent variable, while the MANOVA method used for calculating mean includes multiple dependent variables. It is basically used to determine if there is any difference in the variant groups or if there is more than one dependent variable present. And this is how it is different from ANOVA in one way, which requires only one variable.

Table of Contents

**ANOVA vs MANOVA**

**The main difference between ANOVA and MANOVA is that there is only one variable while calculating for mean through the ANOVA method, but in the MANOVA method, there are two or more than two different variables. Both methods are used in the study of statistics for determining the mean of a given equation. ANOVA uses three different models for the calculation, while there are no such models used in the method of MANOVA.**

ANOVA stands for analysis of variant while Manova stands for multivariate analysis variant. They are both used as a statistical method for calculating mean but in a different way as ANOVA is used when there is only one dependent variant present, but MANOVA is used when there is more than one dependent variant present. When studying statistics, when there are two or more than two means are compared to one another, the method that is used to find the mean is called ANOVA that is an analysis of variants.

The MANOVA method that is a multivariate analysis variant, as the name says, is used when there are multiple dependent variables. These multiple variables help in calculating two or more than that dependent variable. MANOVA uses no particular model for calculating the mean of a given equation as the ANOVA does. In MANOVA, the Wilk’s Lamba is determined as multiple variables are used at a single time in one calculation and also helps in determining the difference between them.

**Comparison Table Between ANOVA and MANOVA **

Parameters of Comparison | ANOVA | MANOVA |

Abbreviation | Analysis of variant | Multivariate analysis of variants. |

Uses | When there is only one dependent variable for calculating the mean. | When there are multiple variables for the calculation of the mean. |

Number of Models | ANOVA uses three different models for the calculation. | There is no such number of models used in MANOVA for calculating the mean. |

Determination | In ANOVA, the F-test is used in order to determine the significance of the factor. | In MANOVA, the multivariate F-test is used, which is called Wilk’s Lambda. |

Value of F | The comparison of the factor variance to the error variance decides the value of F in the ANOVA. | The factor variance-covariance matrix is compared to the error variance-covariance matrix in order to obtain Wilk’s Lambda. |

**What is ANOVA? **

ANOVA stands for analysis variant. When studying statistics, when there are two or more than two means are compared to one another, but simultaneously the method that is used to find the mean is called ANOVA that is an analysis of variants. In order to learn and establish relationships between significant variables, the method is ANOVA is used. To determine if the mean calculated of two or more groups is equal or not, it lays a test. And this test thus used is called the t-test.

For the comparison of means, the name ANOVA has been given because, in order to determine or establish a relationship between means, those variances are actually being compared to set the establishment.

ANOVA has three different models that are used in different aspects to calculate the mean. A fixed-effect model is applied when the object is subjected to be having one or even more than one treatment. The random effect model is applied when the treatment that is applied is not fixed before for the subject in the large population. A mixed-effect model is applied when the treatment has both the previous methods, the fixed one and the mixed one too.

**What is MANOVA? **

MANOVA stands for multivariate analysis variance. The method of MANOVA in statistics is used when there are two or more than two variables for calculating the mean. It helps in establishing and determining the difference between two or even more than two different dependent variables. The assistance provided by this method is simultaneously between the two different variables.

The MANOVA method that is a multivariate analysis variant, as the name says, is used when there are multiple dependent variables. These multiple variables help in calculating two or more than that dependent variable. In MANOVA, the multivariate F-test is used, which is called Wilk’s Lambda. The factor variance-covariance matrix is compared to the error variance-covariance matrix in order to obtain Wilk’s Lambda.

**Main Differences Between ANOVA and MANOVA **

- The main difference between ANOVA and MANOVA is that ANOVA is used when there is only one variable present to calculate the mean, while MANOVA is used when there are two or more than two variables present.
- ANOVA stands for analysis variant, while MANOVA stands for multivariate analysis variant.
- ANOVA uses three different models for the calculation, while in MANOVA, there are no such models.
- In ANOVA, the F-test is used to determine the significance of the factor, but in MANOVA, the multivariate F-test is used, which is called Wilk’s Lambda.
- There is only one dependent variable in ANOVA, but in MANOVA, there are two or even more than two dependent variables.

## ** Conclusion **

From the discussion so far, it is to be concluded that ANOVA and MANOVA are basically two different statistical methods that are used to calculate the mean for a given data. The word ANOVA stands for analysis of variant, while the word MANOVA stands for multivariate analysis of variant.

The ANOVA method used for calculating mean includes only one dependent variable, while the MANOVA method used for calculating mean includes multiple dependent variables. It is basically used to determine if there is any difference in the variant groups or if there is more than one dependent variable present. And this is how it is different from ANOVA in one way, which requires only one variable.

ANOVA has three different models that are used in different aspects to calculate the mean. A fixed-effect model is applied when the object is subjected to be having one or even more than one treatment. The random effect model is applied when the treatment that is applied is not fixed before for the subject in the large population. A mixed-effect model is applied when the treatment has both the previous methods, the fixed one and the mixed one too.

**References **

- https://books.google.com/books?hl=en&lr=&id=nz241IjmSGgC&oi=fnd&pg=PR13&dq=anova&ots=SkgpPsjjgl&sig=vkGrX8KBtqN1_bS-ls9TczrlF-o
- https://books.google.com/books?hl=en&lr=&id=Cy_IoTEKkngC&oi=fnd&pg=PR7&dq=manova&ots=jwnZi3tISr&sig=h5RfPg_0qSxrxlctyny5r6VDbFw

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