Token swap test revisited

Area of Science:

• Statistics
• Computational Statistics

Background:

• The token swap test is a valuable statistical method for analyzing associations in 2x2 contingency tables.
• This test operates within sample misclassification space and does not rely on assumptions of repeated or random sampling.
• Standard statistical software packages currently lack implementation for the token swap test.

Purpose of the Study:

• To introduce and describe 'tokenSwaps,' a novel Mathematica program designed to perform the token swap test.
• To enable comparison between the token swap test and the one-tailed Fisher exact test by including both in the program.
• To demonstrate the utility and application of the 'tokenSwaps' program.

Main Methods:

• Development of a Mathematica program named 'tokenSwaps'.
• Implementation of the token swap test within the program.
• Inclusion of a one-tailed Fisher exact test for comparative analysis.
• Utilization of recursive functional programming and local rewrite rules for efficient coding.

Main Results:

• The 'tokenSwaps' program successfully implements the token swap test.
• The program allows for direct comparison of results from the token swap test and the Fisher exact test.
• The program demonstrates substantial coding economy through its functional programming approach.

Conclusions:

• The 'tokenSwaps' program provides a practical implementation of the token swap test, addressing its absence in standard software.
• The program facilitates the comparison of two distinct statistical approaches for analyzing 2x2 tables.
• The described methodology highlights efficient programming techniques for statistical software development.