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Applying the permutation test to factorial designs.

D J K Mewhort¹, Brendan T Johns, Mary Alexandria Kelly

¹Queen's University, Kingston, Ontario, Canada. mewhortd@queensu.ca

Behavior Research Methods

|May 19, 2010

Summary

Permutation tests offer advantages over parametric tests but are computationally intensive for factorial designs. New methods using orthogonal contrasts and Gill

Area of Science:

Statistics
Experimental Design
Psychological Research Methods

Background:

Permutation tests are valuable for comparative experiments due to their non-reliance on error distributions and potential for higher sensitivity.
However, their application to factorial designs is limited by significant computational demands.

Purpose of the Study:

To address the computational challenges of applying permutation tests to factorial designs.
To propose and validate efficient methods for conducting factorial permutation tests.

Main Methods:

Implementing orthogonal contrasts to reduce computational load in factorial permutation tests.
Integrating Gill's (2007) algorithm to enhance the practicality and efficiency of these tests.
Comparing factorial permutation tests with Analysis of Variance (ANOVA) for within- and between-subjects designs.

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Main Results:

Orthogonal contrasts effectively limit the computational requirements for factorial permutation tests.
The combination of orthogonal contrasts and Gill's algorithm makes factorial permutation tests practical and efficient.
For within-subjects designs, the factorial permutation test aligns with ANOVA results when assumptions are met.
For between-subjects designs, the factorial permutation test demonstrates a conservative approach.

Conclusions:

Factorial permutation tests are now computationally feasible and efficient for researchers.
These methods provide a robust alternative to traditional parametric tests, especially when distributional assumptions are uncertain.
The developed techniques enhance the utility of permutation testing in complex experimental designs.