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Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data

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Published on: May 16, 2022

Discriminant analysis.

Peter H Bartels¹, Hubert G Bartels

¹College of Optical Sciences and Arizona Cancer Center, University of Arizona, Tucson, Arizona 85724, USA. hubertbartels@msn.com

Analytical and Quantitative Cytology and Histology

|August 13, 2010

Summary

This tutorial provides a detailed, step-by-step numerical example for deriving discriminant functions and their coefficients, essential for understanding karyometric data analysis.

Area of Science:

Biostatistics
Quantitative Biology
Karyometry

Background:

Discriminant analysis is a widely used statistical technique in karyometry.
The detailed derivation of discriminant functions and their coefficients has not been presented with a numerical example for over 50 years.

Purpose of the Study:

To offer a fully worked numerical example for discriminant function derivation.
To provide insight into the processing steps and the origin of function coefficients.

Main Methods:

The example details raw data reduction for variance/covariance matrix calculation.
It demonstrates covariance matrix inversion using pivotal condensation.
Coefficient calculation is shown, with all steps performed manually.

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Quantification of Orofacial Phenotypes in Xenopus

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Main Results:

A comprehensive numerical example for discriminant function derivation is presented.
The process clarifies the origin and calculation of discriminant function coefficients.

Conclusions:

Manual discriminant analysis is impractical for large karyometric datasets.
This tutorial aims to demystify the process, addressing the limitations of using computer algorithms without full understanding.