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A two-dimensional Kolmorogov-Smirnov test for binned data

R H Smallwood¹

¹Department of Medical Physics and Clinical Engineering, University of Sheffield, Royal Hallamshire Hospital, UK.

Physics in Medicine and Biology

|January 1, 1996

Summary

A novel two-dimensional Kolmogorov-Smirnov test was developed for analyzing binned data. This statistical method was validated using Monte Carlo simulations and applied to electrical impedance imaging data.

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Area of Science:

Statistics
Biomedical Engineering
Data Analysis

Background:

The Kolmogorov-Smirnov test is a widely used non-parametric test for comparing probability distributions.
Existing Kolmogorov-Smirnov tests are primarily one-dimensional, limiting their application to multi-dimensional data.
Analyzing two-dimensional data, such as that from imaging techniques, requires specialized statistical tools.

Purpose of the Study:

To develop and validate a new two-dimensional Kolmogorov-Smirnov test.
To provide a statistical method for analyzing data organized in two-dimensional arrays.
To apply the new test to movement vector data from electrical impedance imaging of the stomach.

Main Methods:

Development of a two-dimensional Kolmogorov-Smirnov test statistic.
Utilization of Monte Carlo simulations to derive test statistics for various array sizes (8x8, 16x16, 32x32).
Comparison of predicted probabilities with Monte Carlo results for non-square and intermediate-sized arrays.

Main Results:

The new two-dimensional Kolmogorov-Smirnov test was successfully developed.
Test statistics were accurately derived for multiple array dimensions via Monte Carlo simulations.
The test demonstrated applicability to real-world data, specifically movement vectors in electrical impedance stomach imaging.

Conclusions:

The developed two-dimensional Kolmogorov-Smirnov test offers a robust method for analyzing binned two-dimensional data.
The test is validated for various array configurations, enhancing its practical utility.
This statistical advancement has potential applications in analyzing complex datasets from biomedical imaging and other fields.

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