Difference Between ANOVA and MANOVA

ANOVA and MANOVA are two different statistical methods used to calculate the mean for a given data.

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The ANOVA method used for calculating the mean includes only one dependent variable, while the MANOVA method used for calculating the mean includes multiple dependent variables.

Key Takeaways

  1. ANOVA (Analysis of Variance) compares means between two or more groups. MANOVA (Multivariate Analysis of Variance) compares means between groups on two or more dependent variables.
  2. ANOVA is used when the dependent variable is continuous and normally distributed, while MANOVA is used when there are multiple dependent variables.
  3. ANOVA provides information about whether there is a significant difference between groups, while MANOVA provides information about which dependent variables are significantly different.

ANOVA vs. MANOVA

The difference between ANOVA and MANOVA is that there is only one variable while calculating for mean through the ANOVA method. Still, in the MANOVA method, there are two or more two different variables. Both ways are used in the statistics study to determine the mean of a given equation. ANOVA uses three other models for the calculation, while no such models are used in the method of MANOVA.

ANOVA vs MANOVA

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They are both used as a statistical methods for calculating the mean but in different ways, as ANOVA is used when only one dependent variant is present. Still, MANOVA is used when there is more than one dependent variant.

The MANOVA method, a multivariate analysis variant, as the name says, is used when there are multiple dependent variables.

Comparison Table

Parameters of ComparisonANOVA  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 to determine the significance of the factor. In MANOVA, the multivariate F-test is used, which is called Wilk’s Lambda.  
Value of F Comparing 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 to obtain Wilk’s Lambda.  

What is ANOVA? 

ANOVA stands for analysis variant. When studying statistics, when there are two or more two means that are compared to one another simultaneously, the method used to find the mean is called ANOVA, which is an analysis of variants.

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

ANOVA has three different models used in other aspects to calculate the mean. A fixed-effect model is applied when the object has one or more than one treatments.

anova

What is MANOVA? 

MANOVA stands for multivariate analysis variance. The method of MANOVA in statistics is used when there are two or more two variables for calculating the mean.

The MANOVA method, a multivariate analysis variant, as the name says, is used when there are multiple dependent variables.

manova

Main Differences Between ANOVA and MANOVA 

  1. In ANOVA, the F-test is used to determine the significance of the factor, but in MANOVA, the multivariate F-test is used, called Wilk’s Lambda.
  2. There is only one dependent variable in ANOVA, but in MANOVA, there are two or even more than two dependent variables.
References
  1. https://books.google.com/books?hl=en&lr=&id=nz241IjmSGgC&oi=fnd&pg=PR13&dq=anova&ots=SkgpPsjjgl&sig=vkGrX8KBtqN1_bS-ls9TczrlF-o
  2. 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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