# Statistics in Spectroscopy

Academic Press, Dec 2, 2012 - Science - 313 pages
This tutorial offers a basic hands-on approach to statistical analysis for chemists and spectroscopists. Without involving complicated mathematics, this book is designed to provide the reader with the basic principles underlying the use of common mathematical and statistical tools. Particular emphasis has been given to problem-solving applications and the proper use and interpretation of spectroscopic data. With exercises throughout, this book is also suitable for use as a textbook in analytical chemistry, instrumental analysis, and statistics in chemistry courses.

Key Features
* Serves as a primer for all chemists who need to know more about statistical analysis
* Explains the effect of error on data and how to make the correct interpretation
* Written in a readable style with minimal mathematics
* Developed from the popular series of the same name first published in Spectroscropy magazine

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### Contents

 Chapter 1 INTRODUCTION WHY THIS BOOK? 1 Chapter 2 IMPORTANT CONCEPTS FROM PROBABILITY THEORY 7 THE MEANING OF STATISTICS 17 Chapter 4 DEGREES OF FREEDOM 25 Chapter 5 INTRODUCTION TO DISTRIBUTIONS AND PROBABILITY SAMPLING 35 Chapter 6 THE NORMAL DISTRIBUTION 45 Chapter 7 ALTERNATIVE WAYS TO CALCULATE STANDARD DEVIATION 57 Chapter 8 THE CENTRAL LIMIT THEOREM 69
 Chapter 21 HOW TO COUNT 169 Chapter 22 AND STILL COUNTING 175 Chapter 23 CONTINGENCY TABLES 181 Chapter 24 WHAT DO YOU MEAN RANDOM? 189 Chapter 25 THE F STATISTIC 199 INTRODUCTION TO ANALYSIS OF VARIANCE 207 Chapter 27 ANALYSIS OF VARIANCE AND STATISTICAL DESIGN OF EXPERIMENTS 217 Chapter 28 CROSSED AND NESTED EXPERIMENTS 229

 Chapter 9 SYNTHESIS OF VARIANCE 79 Chapter 10 WHERE ARE WE AND WHERE ARE WE GOING? 87 Chapter 11 MORE AND DIFFERENT STATISTICS 93 Chapter 12 THE T STATISTIC 103 Chapter 13 DISTRIBUTION OF MEANS 113 Chapter 14 ONE AND TWOTAILED TESTS 121 Chapter 15 PHILOSOPHICAL INTERLUDE 131 Chapter 16 BIASED AND UNBIASED ESTIMATORS 135 Chapter 17 THE VARIANCE OF VARIANCE 141 Chapter 18 HYPOTHESIS TESTING OF CHISQUARE 149 Chapter 19 MORE HYPOTHESIS TESTING 155 Chapter 20 STATISTICAL INFERENCES 161
 Chapter 29 MISCELLANEOUS CONSIDERATIONS REGARDING ANALYSIS OF VARIANCE 239 Chapter 30 PITFALLS OF STATISTICS 247 Chapter 31 PITFALLS OF STATISTICS CONTINUED 255 Chapter 32 CALIBRATION IN SPECTROSCOPY 263 LINEAR REGRESSION AS A STATISTICAL TECHNIQUE 271 ERROR SOURCES IN CALIBRATION 277 SELECTING THE CALIBRATION SAMPLES 283 DEVELOPING THE CALIBRATION MODEL 287 AUXILIARY STATISTICS FOR THE CALIBRATION MODEL 293 Chapter 38 THE BEGINNING 303 Index 309 Copyright

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Howard Mark is President of Mark Electronics, Suffern, New York. He was previously affiliated as a Senior Scientist at Technicon Instrument Corp. in Tarry town, New York. He holds a B.S. degree from City College of New York, an M.A. from City University of New York, and a PhD from New York University. His professional interests include instrument development, especially for spectroscopy; statistical and chemometric data analysis; and Custom software development, especially for implementation of data analysis algorithms. He received the 2003 Eastern Analytical Symposium Award for Achievement in Near Infrared Spectroscopy. He holds 6 U.S patents and has published 2 books and numerous book chapters. He has acted as Associate editor for the Handbook of Vibrational Spectroscopy, Wiley (2001). He has served as Past president of Council for Near-Infrared Spectroscopy (CNIRS), Treasurer of the New York section of the Society for Applied Spectroscopy, and as Past Chair of the New York section of the Society for Applied Spectroscopy. In addition he acts as Contributing editor and member of the Editorial Advisory Board of Spectroscopy. He has published over 150 peer-reviewed papers dealing with design and development of scientific instrumentation, new concepts in computerized instrumentation and data analysis.

Jerry Workman, Jr. is Chief Technical Officer and Vice President of Research

& Engineering at Argose Inc., Waltham, MA. In his career, Workman has

focused on molecular and electronic spectroscopy and chemometrics. He has

published over 200 scientific papers, 7 text volumes, and over 20 patents,

patents pending, and trade secrets. He received the B. A. degree in natural

sciences and M. A. degree in biological sciences and genetics from Saint

Mary's University of Minnesota, and the Ph.D. degree in biological chemistry

from Columbia Pacific University. He has completed technical management

certificates from Columbia University and MIT. He is a Fellow of the

American Institute of Chemists, the American Society for Testing and

Materials International, and the Royal Society of Chemistry. In 2002 he was

the recipient of the ASTM International Award of Merit; IBC International

Scientist of the Year; and the Eastern Analytical Symposium Award for

Outstanding Achievements in the Field of Near Infrared Spectroscopy.