XLSTAT: Multivariate Analysis of Variance (MANOVA) in Excel

 

Background

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 Example

The (attached) 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 morphology 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 is to see if three iris species differ with respect to their flower morphology.

 

Setting Up

• Open XLSTAT.

• Select the Modeling data menu and the MANOVA feature: 

• Once you have clicked on the button, the MANOVA dialog box appears.

In the General tab:

• Select the data on the Excel sheet.

• In the Y / Dependent variables field, select the four morphological variables.

• In the X / Explanatory variables field, select the Species column.

• Leave the Variable labels option activated, since column headers are included.

In the Options tab:

• Disable the Interactions option, as there is only one explanatory variable.

• Keep the default significance level at 5%.

 

• In the Outputs tab: check the options as shown in the provided reference (e.g., estimated means, ANOVA table, etc.).

• In the Charts tab: select the means chart to visualize group averages.

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

 

Interpreting the Results

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 where:

• the lower the Lambda associated to an explanatory variable, the more important the effect of this variable is on the dependent variables combination.

  

Lambda (0.023) has a p-value below 0.05, so we reject the null hypothesis that species do not affect flower morphology, with high confidence.