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Fisher's Exact Test

Fisher's Exact Test

Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of the...

Behrens–Fisher Test

Behrens–Fisher Test

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The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of freedom; one for the numerator and one for the denominator. The F distribution is derived from the Student's t distribution. The values of the F distribution are squares of the corresponding values of the t distribution. One-Way ANOVA expands the t test for comparing more than two groups. The scope of that derivation is beyond the level of this...

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On Extensions to Fisher's Linear Discriminant Function.

I D Longstaff¹

¹Royal Signals and Radar Establishment (RSRE), Malvern WR14 3PS, England; Western Australia Institute of Technology, Perth, Western Australia.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This study enhances Fisher

Area of Science:

Pattern Recognition
Machine Learning
Statistical Classification

Background:

Fisher's linear discriminant is a foundational technique for classification.
Existing methods may not fully account for class covariance differences.
Feature reduction is crucial for high-dimensional data analysis.

Purpose of the Study:

To extend Fisher's linear discriminant function.
To incorporate both class mean and covariance differences for feature reduction.
To improve classification performance over existing methods.

Main Methods:

Combining the Fukunaga-Koontz transform with Fisher's method.
Systematic inclusion of class mean and covariance differences.
Developing new radius vectors for enhanced discrimination.

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Main Results:

Feature space reduction from high dimensions to two dimensions.
Demonstrated superior performance compared to the Foley-Sammon method.
Achieved effective discrimination even with significant class overlap in projections.

Conclusions:

The extended Fisher's method offers powerful feature reduction and classification.
The Fukunaga-Koontz transform integration enhances discriminatory power.
The technique provides robust classification performance in challenging scenarios.