Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate. We prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses. This condition for positive dependency is general enough to cover many problems of practical interest, including the comparisons of many treatments with a single control, multivariate normal test statistics with positive correlation matrix and multivariate $t$. Furthermore, the test statistics may be discrete, and the tested hypotheses composite without posing special difficulties. For all other forms of dependency, a simple conservative modification of the procedure controls the false discovery rate. Thus the range of problems for which a procedure with proven FDR control can be offered is greatly increased.

/pdf/the-control-of-the-false-discovery-rate-in-multiple-testing-426hrdkyhb.pdf

The control of the false discovery rate in multiple testing under dependency

Linear regression equations have been obtained to directly calculatenutrient requirements of dairy cattle (TDN, DE, ME, NEL,CP, Ca, P, Vitamin A and Vitamin D) on differentphysiological stages: maintenance, pregnancy and milkproduction based on NRC nutrient requirements tables. TheR-square was calculated for each equation to establish thedegree of adjustment.

/pdf/estimacion-lineal-de-los-requerimientos-nutricionales-del-2bgbp8s5al.pdf

Estimación lineal de los requerimientos nutricionales del NRC para ganado de leche

a b s t r a c t The interest in nonparametric statistical analysis has grown recently in the field of computational intelligence. In many experimental studies, the lack of the required properties for a proper application of parametric procedures - independence, normality, and homoscedasticity - yields to nonparametric ones the task of performing a rigorous comparison among algorithms. In this paper, we will discuss the basics and give a survey of a complete set of nonparametric procedures developed to perform both pairwise and multiple comparisons, for multi-problem analysis. The test problems of the CEC'2005 special session on real parameter optimization will help to illustrate the use of the tests throughout this tutorial, analyzing the results of a set of well-known evolutionary and swarm intelligence algorithms. This tutorial is concluded with a compilation of considerations and recommendations, which will guide practitioners when using these tests to contrast their experimental results.

https://sci2s.ugr.es/sites/default/files/ficherosPublicaciones/1374_2011-Derrac-SWEVO.pdf

A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms

http://staff.pubhealth.ku.dk/~tag/Teaching/share/material/dupont-plummer-power-sample-size-1990.pdf

Power and sample size calculations. A review and computer program.

https://sci2s.ugr.es/sites/default/files/files/TematicWebSites/sicidm/2010-Garcia-INS.pdf

Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power

Observations probability sampling from a normal distribution comparisons involving two sample means principles of experimental design analysis of variance I - the one-way classification mutiple comparisons analysis of variance II - multiway classification linear regression linear correlation matrix notation linear regression in matrix notation multiple and partial regression and correlation analysis of variance III - factorial experiments analysis of variance analysis of covariance IV analysis of covariance analysis of variance V - unequal subclass numbers some uses of chi-square enumeration data I - one-way classifications enumeration data II - contingency tables categorical models some discrete distributions nonparametric statistics sampling finite populations.

Principles and Procedures of Statistics: A Biometrical Approach

Principles and Procedures of Statistics: A Biometrical Approach.

Principles and procedures of statistics : a biometrical approach

Bioestadística : principios y procedimientos

Buku ini berisi tentang statistika, bahwa statistika sangat diperlukan, dan telah digunakan ooleh semakin banyak disiplin ilmu pengetahuan. Prinsip-prinsip statistika tidak bergantung pada bidang terapan, dan prosedur yang diterapkan dengan berhasil di bidan pertanian dan ilmu-ilmu biologi, dll

Robert G. D. Steel

Papers

Principles and Procedures of Statistics: A Biometrical Approach

Principles and Procedures of Statistics: A Biometrical Approach.

Principles and procedures of statistics : a biometrical approach

Bioestadística : principios y procedimientos

Prinsip dan Prosedur Statistika : Suatu Pendekatan Biometrik