Desai T.A. Important Applications of the Behrens-Fisher Statistic and the False Discovery Rate

Cham: Springer, 2022. — 88 p.This book discusses important applications of the Behrens-Fisher statistic and the False Discovery Rate (FDR). Covered applications include ANOVA and MANOVA under potentially non-normal errors and heteroscedasticity; and an intuitive method of analyzing s x r contingency tables when the column variable is ordinal. This book also explores the novel possibility that these applications may be deemed nonparametric.The Behrens-Fisher StatisticOne-Way ANOVA with Possible Heteroscedasticity of Variances and Non-Normality of Errors
The One-Way ANOVA Problem and the Behrens-Fisher Statistic
Our Methodology for One-Way ANOVA When k>3
The Classical ANOVA F Test
The Kruskal-Wallis Test
Comparative Analyses for One-Way ANOVAOne-Way MANOVA with Possible Heteroscedasticity and Non-Normality of Errors
The One-Way MANOVA Problem and Our Methodology For It
The Classical Wilks' Lambda
A Robust Statistic for One-Way MANOVA
Comparative Analyses for One-Way MANOVA
Data Analysis Example: The Oslo Transect DataStatistical Analysis of s r Tables When the Column Variable Is Ordinal
Methodology for a Single 2 r Table
Simulations for a Single 2 r Table
Example of a Behrens-Fisher Analysis of a Single 2 r Table
Sets of 2 r Tables
Methodology
Simulations of Sets of 2 r Tables
Example of an Analysis of a Set of Two 2 r Tables
Behrens-Fisher Analysis of s r Tables, s > 3 and Column Variable Ordinal
A Single s r Table When s > 3 and Column Variable Ordinal
Simulations of a Single Set of s r Table, s > 2 and Column Variable Ordinal
Simulations of More Than One s r Table, s > 2, and Column Variable Ordinal
Example of an Analysis of a 3 3 Table When the Column Variable Is OrdinalConcluding Remarks