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The Skillings-Mack test (Friedman test when there are missing data).

Mark Chatfield¹, Adrian Mander

¹Medical Research Council, Human Nutrition Research, Cambridge, UK, mdc_england@hotmail.com.

The Stata Journal

|October 16, 2009

Summary

This summary is machine-generated.

The Skillings-Mack test offers a versatile non-parametric approach for analyzing block designs, effectively handling missing data and ties. This statistical method provides robust results, particularly for small samples, by simulating test statistic distributions.

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Area of Science:

Statistics
Non-parametric methods
Experimental design

Background:

The Friedman test is a common non-parametric test for analyzing data in block designs.
Existing methods may not adequately handle missing data or ties within block designs.
Previous implementations of the Friedman test exist in statistical software.

Purpose of the Study:

Introduce the Skillings-Mack test and its associated `skilmack` command.
Provide a flexible statistical tool for block designs with missing data.
Address limitations of the Friedman test regarding ties and small sample sizes.

Main Methods:

The Skillings-Mack statistic is a generalization of the Friedman test.
It accommodates arbitrary missing-data structures (missing by design or at random).
The `skilmack` command implements the Skillings-Mack test, including simulation for accurate null hypothesis distributions.

Main Results:

The Skillings-Mack test is equivalent to the Friedman test in complete block designs without missing data.
It aligns with Durbin's test for balanced incomplete block designs.
The `skilmack` command provides accurate results for datasets with ties and small sample sizes through simulation.

Conclusions:

The Skillings-Mack test is a powerful and adaptable non-parametric method for block designs.
The `skilmack` command enhances statistical analysis capabilities in software.
This approach improves the reliability of statistical inference in complex experimental designs.