# Difference between MANOVA and ANOVA

## Introduction

The researchers utilise both the ANOVA and MANOVA test in statistics in order to conduct in depth research and analyse the data efficiently. For performing the ANOVA tests, the SPSS-Tutor utilise excel and SPSS to develop in depth analysis about the variance by measuring the mean values in the datasets. The article provides a scope to understand the use of ANOVA and MANOVA and discuss the differences between these two statistical measures.

## ANOVA

Analysis of variance or ANOVA is a collection of statistical models and their associated estimation procedures that is mainly utilised to analyse the existing differences among the values of means. ANOVA was developed by the statistician Ronald Fisher, with the assumption that the data is normally distributed. Additionally, the **ANOVA** also assumes homogeneity of the variance, which further means that, the variance among the different groups should be approximately equal. ANOVA also assumes that, the observations are independent of each other. It is helpful for finding out whether the differences between groups of data are statistically significant. Analysing the levels of variance within the groups through samples taken from each of them is effective tow test ANOVA and performs the statistical program to analyse its significance. A one-way ANOVA is utilised for three or more groups of data, to gain adequate information about the relationship between the dependent and independent variables. Hence, the researchers try to utilise one way ANOVA test for examining interlink between the dependent and independent variables. The researchers utilise Microsoft excel and also SPSS software for performing ANOVA efficiently. One-way has one independent variable and two ways ANOVA means that there are two independent variables for analysing interlink between the independent variables and its dependent one. Differences among the mean values can also be identified through the ANOVA test and additionally, the researchers analyse the normal distribution and predict future data trend.

## MANOVA

In statistics, multivariate analysis of variance or MANOVA is another crucial procedure for comparing the multivariate sample means. As a multivariate procedure, it is utilised by the researchers when there are two or more dependent variables, and it is often followed by the significance tests involving individual dependent variables separately. Hence, the numbers of dependent variables is more than one and there multiple variables in which different mean values must be evaluated. The one-way multivariate analysis of variance **(one-way MANOVA) ** is mainly utilised in order to determine whether there are any differences between the independent groups on more than one continuous dependent variable. In this regard, it differs from a one-way ANOVA, which only measures one dependent variable. The numbers of dependent variables is more than one, where in ANOVA test, the number of dependent variables is one with different independent variables. The researchers utilise MANOVA widely as MANOVA determines if the dependent variables get significantly affected by changes in the independent variables. The MANOVA uses the covariance-variance between the existing variables to test for the difference between vectors of means. For example, the researchers can measure how men and women did in life in multiple ways such as income, number of promotions gained, and a test of overall job happiness of each individual.

## Differences between ANOVA and MANOVA

ANOVA and MANOVA are two of the most extensively used statistical measures that are helpful for analysing relationship between the variables in a data set. There are several differences between the ANOVA and MANOV test for which the researchers try to sort the gathered data and choose the best method for conducting the statistical test. ANOVA mainly checks the differences between the means of two samples/ populations while MANOVA checks for the differences between multiple sample/populations. MANOVA uses covariance-variance relationship of considering more than one dependent variable. Where the ANOVA test can be conducted, where there is only on dependent variables, but the numbers of independent variables may vary as per the data set. The MANOVA test is helpful where there is more than one dependent variables, and the researchers can analyse and assess the differences but the independent variables an analyse its impacts on dependent variables in the data set.

Hence, ANOVA concerns about two variables, while MANOVA concerns the differences in multiple variables simultaneously. ANOVA hereby helps to compare two means at the same time, but can only include one dependent variable in the analysis. On the other hand, MANOVA can determine the relationship between multiple variables concurrently. ANOVA decomposes the total sum of squares T into different group sum of squares B ad within the Group sum of squares W, so that T= B + W. it calculates F= B/ W ration, which main follows the F distribution. The result indicates that; vary small P value of F statistics leads to rejection of Null hypothesis. on the other hand, MANOVA decomposes the total scatter matrix T into between group scatter matrix B and within group scatter matrix W, so that T= B + W. if the P value of the matrix insignificant, the null hypothesis will be rejected and alternative hypothesis being accepted. As per the data set, the researchers can chose the statistical measure to evaluate the significance of the data and analyse variance and internal means.

## Summary

Through this article, it is possible to demonstrate the ANOVA and MANOVA test, where the researchers must identify the dependent and independent variables in the data set after data sorting and management. If there is one dependent variable and two or more independent variables, the one or two way ANOVA test can be implemented for analysing the means of variance and valuate its significance. However, if there is more than one dependent variable with different independent variable, the researchers can choose MANOVA test for considering all the data sets of the independent variables and analyse different means and their variances for evaluating the impacts of the independent variables on the dependent variables. Hereby, **ANOVA and MANOVA**** tests are different from each other as per the numbers of the dependent and independent variables for considering all the matrixes in the statistical analysis and analysing the significance of the data critically.
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