# Multivariate Analysis of Variance (MANOVA) in Excel tutorial

This tutorial shows how to set up and interpret a Multivariate Analysis of Variance (MANOVA) in Excel using the XLSTAT software.

A MANOVA is a method to determine the significant effects of qualitative variables considered in interaction or not on a set of dependent quantitative variables.

## Dataset for running a one-way MANOVA in XLSTAT

The data are from [Fisher M. (1936). The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics, 7, 179 -188] and correspond to 150 Iris flowers, described by four variables (sepal length, sepal width, petal length, petal width) and their species. Three different species have been included in this study: setosa, versicolor and virginica.

The goal of this MANOVA is to see if three iris species differ with respect to their flower morphology represented by a combination of 4 dependent variables (sepal length, sepal width, petal length, petal width).

## Setting up a one-way MANOVA in XLSTAT

After opening XLSTAT, select the **XLSTAT** / **Modeling data** / **MANOVA** function.
Once you have clicked on the button, the MANOVA dialog box appears.
Select the data on the Excel sheet in the **General** tab. The **Y / dependant variables** table field should contain the Dependent variables (or variables to model), which are the four morphological variables in our situation.

The **X / Explanatory variables** field should contain the explanatory variables – the Species column in our case.
As we selected the column title for the variables, we left the option **Variables labels** activated.

On the **Options** tab, disable the Interactions option, since the issue involves only one explanatory variable. The default significance level is 5%.
In the **Outputs** tab, check the options as proposed in the picture below. In the **Charts** tab, select the means chart.

Once you have clicked on the **OK** button, the computations begin and then the results are displayed.

## Interpreting the results of a one-way MANOVA in XLSTAT

**Summary statistics** on the variables are first displayed followed by **the table grouping the means by factor level (explanatory variable) and the associated histogram.**
**Multivariate test results** are then displayed. All of those tests are built around the same null hypothesis, which excludes any effect of the explanatory variable on the combination of dependent variables. We will focus on the interpretation of the **Wilks Lambda test.**
In Wilks Lambda test, the lower the Lambda associated to an explanatory variable, the more important the effect of this variable is on the dependent variables combination.
Here we see that Lambda (0.023) is associated to a p-value that is much lower than the significance level alpha (0.05). We can thus reject the null hypothesis that there is no effect of species on flower morphology with a very small risk of being wrong.

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