Practical Statistics for Pharmaceutical Analysis: With Minitab Applications PDF
Preview Practical Statistics for Pharmaceutical Analysis: With Minitab Applications
AAPS Advances in the Pharmaceutical Sciences Series 40 James E. De Muth Practical Statistics for Pharmaceutical Analysis With Minitab Applications AAPS Advances in the Pharmaceutical Sciences Series Volume 40 Series Editor Yvonne Perrie, Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, Glasgow, UK The AAPS Advances in the Pharmaceutical Sciences Series, published in partnership with the American Association of Pharmaceutical Scientists, is designed to deliver volumes authored by opinion leaders and authorities from around the globe, addressing innovations in drug research and development, and best practice for scientists and industry professionals in the pharma and biotech industries. More information about this series at http://www.springer.com/series/8825 James E. De Muth Practical Statistics for Pharmaceutical Analysis With Minitab Applications James E. De Muth School of Pharmacy University of Wisconsin-Madison Madison, WI, USA ISSN 2210-7371 ISSN 2210-738X (electronic) AAPS Advances in the Pharmaceutical Sciences Series ISBN 978-3-030-33988-3 ISBN 978-3-030-33989-0 (eBook) https://doi.org/10.1007/978-3-030-33989-0 © American Association of Pharmaceutical Scientists 2019 Jointly published with American Association of Pharmaceutical Scientists. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. 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This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Dedicated to Grayson and Korra Preface The purpose of this book is to present a brief and organized approach to statistics for scientists working in the pharmaceutical industry, as well as an introduction to sta- tistics for undergraduate and graduate students in the pharmaceutical sciences. It is designed for individuals desiring a brief introduction to the field of statistics, as well as a quick reference for statistical problem-solving. It can serve as a guide and a reference for researchers in need of methods to statistically analyze data. Unlike other texts, which are heavy with mathematical formulas, this book emphasizes the selection of the correct statistical test to address specific types of data and the interpretation of those statistical results. The primary objective is to help researchers identify the most appropriate test given the type of variables pres- ent in a study. To assist with this process, Appendix A provides a flow chart to help determine the best test for any given situation. A Book for Non-statisticians Statistics provide useful methods to analyze data commonly seen in the laboratory. Evaluating these findings helps in making correct and beneficial decisions. These tests provide a means for answering questions faced by analytical scientists working in the pharmaceutical industry. With an organized approach to evaluating observed data, it helps researchers avoid jumping to conclusions and making choices that may be unwise or even dangerous to the quality of the product or application being tested. During the 2004 Land O’Lakes Bioanalytical Conference at the University of Wisconsin, Wendell Smith spoke on the topic of statistical issues with developing and validating methods. He made two interesting observations: (1) statistics “pro- vides methods and tools for decision making in the face of uncertainty,” and (2) successful applications of statistics “requires collaboration among participating sci- entists.” Regarding the first statement, data will vary (the uncertainty), and statistics are useful tools that can help control and interpret this variability. This book deals with that uncertainty. Possibly of greater importance is the second statement. By vii viii Preface participating scientists, Smith was referring to the “analytical” scientist and the “statistical” scientists, both of whom are required to accomplish a successful statis- tical analysis. Some questions and decisions are clearly in the analytical domain and need to be addressed by the scientist designing the study and collecting the data. Other questions and applications need to be the focus for professional statisticians. Working together in collaboration, a successful evaluation of sample data can be accomplished using statistics. At certain points in this book, the appropriate delega- tion of these responsibilities will be noted. Contents of This Book The book is still divided into two major sections: (1) the underpinnings required to understand the basic elements of statistical tests (terminology, descriptive statistics, statistical inference, and hypothesis testing) and (2) inferential statistics to help in problem-solving (test identifying differences, relationships, similarities, and poten- tial outliers). Additional supportive materials are provided in the Appendices with flow charts, tables, software commands, and proofs for statistical calculations. Chapter 1 focuses on the terminology and essential elements of statistical testing. Statistics is often complicated by synonyms, and this chapter establishes the terms used in the book and how rudiments interact to create statistical tests. Chapter 2 presents descriptive statistics that are used to organize and summarize sample results. Chapter 3 introduces the basic concepts of probability, the characteristics of a normal distribution, the alternative approaches for non-normal distributions, and the topic of making inferences about a larger population based on a small sample taken from that population. Chapter 4 discusses hypothesis testing where computer output is interpreted and decisions are made regarding statistical significance. This chapter also deals with the determination of appropriate sample sizes. The next four chapters focus on tests that make decisions about a population based on a small subset of that population. Chapter 5 looks at statistical tests that evaluate whether a significant difference exists in a population based on the results of sample data. In Chap. 6, the tests try to determine the extent and importance of relationships between variables being compared. In contrast to Chap. 5, Chap. 7 presents tests that evaluate the equivalence or similarity among samples, instead of the difference between the samples (how close samples are to being the same). The last chapter deals with potential outlier or aberrant values and how to statistically determine if they should be removed from the sample data. Each statistical test presented includes at least one example problem with the resultant software output and how to interpret the results. Minimal time will be spent on the mathematical calculations or theory. For those interested in the mechan- ics of the associated equations, supplemental figures will be presented for tests with their respective formulas. In addition, Appendix D presents the equations and math- ematical proofs for the output result for many of the various examples. Preface ix Minitab Software Examples and results from the appropriate statistical results will be displayed using Minitab1. In addition to the results, the required steps to set up and analyze data using Minitab will be presented with the examples for those having access to this software. Numerous other software packages are available, including basic statistical pro- grams available on Excel. Minitab was selected by the author because of the ease of use, extent of available statistical tests, and quality of output reports. It is a relatively simple point-and-click technology to help scientists with a variety of data analysis problems including design of experiment, system analysis, quality tools, graphic analysis, and process analytical control. This book only focuses on the Minitab applications for descriptive and inferential statistics. Guidelines for the Use of This Book The goals for this book are twofold: (1) to serve as a useful resource for selecting and interpreting inferential statistics and (2) to provide a practical guide for using Minitab software to evaluate sample data. If the reader is interested in learning more about statistics and not interested in Minitab, simply read the text covering the importance of these tests, the required variables, and the critical assumptions. Look at the example problems, the computer output results (which will be similar to most commercial statistical packages), and how to interpret these results. Ignore the sections covering Minitab. However, if the reader has access to Minitab, procedures are described for the individual descriptive and inferential statistics. As mentioned previously, this book is designed to minimize the time spent on mathematical formulas. The main text describes when each test should be used, the type of variables required, and any special rules or conditions for the use of each test. For those interested, the mathematical formulas are presented as figures, but their derivation is not discussed. Have faith, the equations work! Examples illustrate the results seen with the computer software evaluation of the data and how to inter- pret the results of the various tests. Proofs that the software and hand calculation are the same (worked out for most examples) are presented in Appendix D for those interested in the mathematical manipulations. 1 Portions of information contained in this publication/book are printed with permission of Minitab, LLC. All such material remains the exclusive property and copyright of Minitab, LLC. All rights reserved. MINITAB® and all other trademarks and logos for the Company’s products and services are the exclusive property of Minitab, LLC. All other marks referenced remain the property of their respective owners. See minitab.com for more information. x Preface Acknowledgments The author has been fortunate to have taught over 200 statistics short courses throughout the United States and internationally. The input from the learners attend- ing these classes and examples of data they shared has helped create examples used in this book. In addition, the author has had the opportunity to work closely with a variety of excellent statisticians especially while serving as Chair of the USP Biostatistics Expert Committee. Both these students and colleagues have helped contribute to the author’s understanding of statistics and to the development of the contents of this book. Thanks to Taylor & Francis Group for releasing the intellectual property rights to the previous statistics book Basic Statistics and Pharmaceutical Statistical Applications. Very little material is duplicated in this book, but for those sections that are duplicated, Taylor & Francis Group’s support of this effort is greatly appre- ciated. Various references in this book refer to sections in the aforementioned text, and if required by the reader, it covers selected topics in much greater detail. The completion of this text is directly attributable to the love and support of my family. A very special thanks to my wife, Judy, and to our daughters, Jenny and Betsy, for their continued encouragement and patience during my reported “retirement.” Madison, WI, USA James E. De Muth December 2019
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