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One-way MANOVA in Excel tutorial


This tutorial will help you set up and interpret a Multivariate Analysis of Variance (MANOVA) in Excel using the XLSTAT software.
Not sure this is the modeling feature you are looking for? Check out this guide

Dataset for running a one-way MANOVA in XLSTAT

An Excel sheet containing both the data and the results for use in this tutorial can be downloaded by clicking here.
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.

Goal of this one-way MANOVA

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 command, or click on the corresponding button of the Modeling data toolbar (see below).

Once you've clicked on the button, the MANOVA dialog box appears.

Select the data on the Excel sheet in the General tab. The Observations/variables table field should contain the Dependent variables (or variables to model), which are the four morphological variables in our situation.
The Groups 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 Column labels activated.

Then move to the Options tab.

The interactions option is deactivated as we only have one single explanatory variable.
The default confidence level is  5%.
The tests are activated to help us treat the final results.
The computations begin once you have clicked on the OK button. The results are displayed in a new Excel spreadsheet.

Interpreting the results of a one-way MANOVA in XLSTAT

Summary statistics on the variables are displayed followed by the results relative to multivariate tests. 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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