# Sequential Analysis

Courier Corporation, Jun 10, 2004 - Mathematics - 212 pages

In 1943, while in charge of Columbia University's Statistical Research Group, Abraham Wald devised Sequential Design, an innovative statistical inference system. Because the decision to terminate an experiment is not predetermined, sequential analysis can arrive at a decision much sooner and with substantially fewer observations than equally reliable test procedures based on a predetermined number of observations. The system's immense value was immediately recognized, and its use was restricted to wartime research and procedures. In 1945, it was released to the public and has since revolutionized many aspects of statistical practice.
This book is Professor Wald's own description of the system. Part I contains a discussion of the general theory of the sequential probability ratio test, with comparisons to traditional statistical inference systems. Part II discusses applications that illustrate the general theory and raise points of theoretical interest specific to these applications. Part III outlines a possible approach to the problem of sequential multi-valued decisions and estimation. All three sections can be understood by readers with only a background in college algebra and a first course in calculus. Mathematical derivations of somewhat intricate nature appear in the appendix.
Sequential Analysis offers statistical researchers a time- and money-saving approach, introduces students to one of the major systems in contemporary use, and presents those already acquainted with the system with valuable background information.

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### Contents

 INTRODUCTION 1 SEQUENTIAL TEST OF A STATISTICAL 22 Chapter S THE SEQUENTIAL PROBABILITY RATIO TEST 37 OUTLINE OF A THEORY OF SEQUENTIAL 70 APPLICATION OF THE GENERAL THEORY 88 TESTING THE DIFFERENCE BETWEEN 106 DISTRIBUTION WITH KNOWN STANDARD DEVIATION 117 Chapter S TESTING THAT THE STANDARD DEVIATION 125
 THE PROBLEM OF SEQUENTIAL ESTIMATION 151 APPENDIX 157 Upper and Lower Limits for the ASN Function of a Sequential 170 Derivation of Exact Formulas for the OC and ASN Functions 181 Approximate Distribution of n When z Is Normally Distributed 191 EFFICIENCY or THE SEQUENTIAL PROBABILITY RATIO TEST 196 DETERMINATION OF OPTIMUM WEIGHT FUNCTIONS wa6 AND wr6 203 INDEX 209

 TESTING THAT THE MEAN OF A NORMAL 134