XLSTAT: Durbin, Skillings-Mack Test in Excel

 

Background

The Durbin-Skillings-Mack test assesses whether a product is significantly different from others, similar to Friedman’s test but applicable to incomplete data.

It tests if treatments are significantly different (H0: no difference) or if at least one treatment differs (Ha).

Dataset for Example

The data contain the ratings of 5 products (in columns) by 10 judges (in lines). Here, we have chosen a Durbin test because the judges’ ratings are reliable only for three products so we have incomplete data, and we cannot run a Friedman test.

Setting Up

• Open XLSTAT.
• Click on the Nonparametric tests menu and select the Durbin, Skillings-Mack test feature:

• Once the analysis is launched, the dialog box appears.

In the General tab:

• Select the data on the Excel sheet.
• Check the Treatment labels box if product names are included.
• Choose to run Multiple pairwise comparisons if you want to identify specific differences between treatments.

In the Options tab:

• Choose to calculate asymptotical p-values, aligning with the approach used by most software.
• Alternatively, you may select the exact p-values or Monte-Carlo method, depending on your analysis needs.

  

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

Interpreting the Results

A Block design studies the effect of factors like judges and products on a phenomenon, here product similarity. Incomplete block design occurs when not all levels are tested within each block. The design is balanced because each product was evaluated by 6 judges, and each judge evaluated 3 products. The analysis provides a summary statistics table.

For each product, the table shows the name, number of observations (including missing data), and the minimum, maximum, and mean grades with standard deviation. It also presents the results of the Balanced Incomplete Block design Durbin test.

We get a p-value lower than 0.05 so we can reject the null hypothesis H0 and conclude that at least one of the products is different from another.

The Durbin-Cabilio-Alvo test leads us to the same conclusion.

The Conover procedure enables us to make product groups based on their evaluations. For instance, group A contains products 4, 1 and 5 while group B contains products 1, 5 and 3 and group C contains products 5, 3 and 2.

A significant differences table is also displayed. For instance, product 1 has been evaluated to be significantly different from product 2.

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