XLSTAT: Friedman-Rafsky Test in Excel

Background

The Friedman-Rafsky test is a nonparametric test commonly used in multivariate analysis to compare the distribution of multiple variables between two groups, without requiring any assumptions about the distribution of the data. 

Dataset for Example

This attached data contains a simple dataset that contains two samples. The first sample gives the height and weight of basketball players, and the second sample gives the height and weight of football players.

Setting Up

• Open XLSTAT.
• Click on the Nonparametric test menu and select the Friedman-Rafsky test feature:

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

In the General tab:

• Select the basketball players' sample in Sample 1.
• Select the football players' sample in Sample 2.
• Select the Euclidean distance as the distance measure.
• Choose the Chazelle algorithm to compute the minimum spanning tree more efficiently.

• Click on the OK button to launch the computations.
• The results are displayed on a new Excel sheet.

Interpret the Results

The p-value is lower than 0.05, so we reject the null hypothesis, which means that the two samples do not follow the same distribution. The result makes sense, as we know that the heights and weights of football players and basketball players are on average different.

The following table gives a view of the minimum spanning tree computed using the Chazelle algorithm. In the first line, we can see that the first edge connects nodes 1 and 17. The Euclidean distance between these nodes is 0.08. The last column indicates that both nodes come from the same sample.