Excel 2013 for physical sciences statistics a guide to solving practical problems

Excel for Statistics Thomas J Quirk Meghan H Quirk Howard F Horton Excel 2013 for Physical Sciences Statistics A Guide to Solving Practical Problems Excel for Statistics Excel for Statistics is a series of textbooks that explain how to use Excel to solve statistics problems in various fields of study Professors, students, and practitioners will find these books teach how to make Excel work best in their respective field Applications include any discipline that uses data and can benefit from the power and simplicity of Excel Books cover all the steps for running statistical analyses in Excel 2013, Excel 2010 and Excel 2007 The approach also teaches critical statistics skills, making the books particularly applicable for statistics courses taught outside of mathematics or statistics departments Series editor: Thomas J Quirk The following books are in this series: T.J Quirk, J Palmer-Schuyler, Excel 2013 for Human Resource Management Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2016 T.J Quirk, S Cummings, Excel 2013 for Health Services Management Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2016 T.J Quirk, M Quirk, H Horton, Excel 2013 for Physical Sciences Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2016 T.J Quirk, J Palmer-Schuyler, Excel 2010 for Human Resource Management Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2014 T.J Quirk, Excel 2013 for Business Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2015 T.J Quirk, M Quirk, H.F Horton, Excel 2013 for Biological and Life Sciences Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2015 T.J Quirk, Excel 2013 for Social Science Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2015 T.J Quirk, Excel 2013 for Engineering Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2015 T.J Quirk, Excel 2013 for Educational and Psychological Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2015 T.J Quirk, M Quirk, H.F Horton, Excel 2013 for Environmental Sciences Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2015 T.J Quirk, M Quirk, H.F Horton, Excel 2010 for Environmental Sciences Statistics: A Guide to Solving Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2015 Additional Statistics books by Dr Tom Quirk that have been published by Springer T.J Quirk, Excel 2010 for Engineering Statistics: A Guide to Solving Practical Problems, Springer International Publishing Switzerland 2014 T.J Quirk, S Cummings, Excel 2010 for Health Services Management Statistics: A Guide to Solving Practical Problems, Springer International Publishing Switzerland 2014 T.J Quirk, M Quirk, H Horton, Excel 2010 for Physical Sciences Statistics: A Guide to Solving Practical Problems, Springer International Publishing Switzerland 2013 T.J Quirk, M Quirk, H.F Horton, Excel 2010 for Biological and Life Sciences Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media New York 2013 T.J Quirk, M Quirk, H.F Horton, Excel 2007 for Biological and Life Sciences Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media New York 2013 T.J Quirk, Excel 2010 for Social Science Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media New York 2012 T.J Quirk, Excel 2010 for Educational and Psychological Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media New York 2012 T.J Quirk, Excel 2007 for Business Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media New York 2012 T.J Quirk, Excel 2007 for Social Science Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media New York 2012 T.J Quirk, Excel 2007 for Educational and Psychological Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media New York 2012 T.J Quirk, Excel 2010 for Business Statistics: A Guide to Solving Practical Problems, Springer Science+Business Media 2011 More information about this series at http://www.springer.com/series/13491 Thomas J Quirk • Meghan H Quirk Howard F Horton Excel 2013 for Physical Sciences Statistics A Guide to Solving Practical Problems Thomas J Quirk Webster University St Louis, MO, USA Meghan H Quirk Bailey, CO, USA Howard F Horton Bailey, CO, USA Excel for Statistics ISBN 978-3-319-28963-2 ISBN 978-3-319-28964-9 DOI 10.1007/978-3-319-28964-9 (eBook) Library of Congress Control Number: 2016930834 © Springer International Publishing Switzerland 2016 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 The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland This book is dedicated to the more than 3,000 students I have taught at Webster University’s campuses in St Louis, London, and Vienna; the students at Principia College in Elsah, Illinois; and the students at the Cooperative State University of Baden-Wuerttemburg in Heidenheim, Germany These students taught me a great deal about the art of teaching I salute them all, and I thank them for helping me to become a better teacher Thomas J Quirk We dedicate this book to all the newly inspired students emerging into the ranks of the various fields of science Meghan H Quirk and Howard F Horton Preface Excel 2013 for Physical Sciences Statistics: A Guide to Solving Practical Problems is intended for anyone looking to learn the basics of applying Excel’s powerful statistical tools to their science courses or work activities If understanding statistics isn’t your strongest suit, you are not especially mathematically inclined, or if you are wary of computers, then this is the right book for you Here you’ll learn how to use key statistical tests using Excel without being overpowered by the underlying statistical theory This book clearly and methodically shows and explains how to create and use these statistical tests to solve practical problems in physical sciences Excel is an easily available computer program for students, instructors, and managers It is also an effective teaching and learning tool for quantitative analyses in science courses The powerful numerical computational ability and the graphical functions available in Excel make learning statistics much easier than in the past years However, this is the first book to show Excel’s capabilities to more effectively teach science statistics; it also focuses exclusively on this topic in an effort to render the subject matter not only applicable and practical, but also easy to comprehend and apply Unique features of this book: • This book is appropriate for use in any course in the Physical Sciences Statistics (at both undergraduate and graduate levels) as well as for managers who want to improve the usefulness of their Excel skills • Includes 162 color screen shots so that you can be sure you are performing the Excel steps correctly • You will be told each step of the way, not only how to use Excel, but also why you are doing each step so that you can understand what you are doing and not merely learn how to use statistical tests by rote • Includes specific objectives embedded in the text for each concept, so you can know the purpose of the Excel steps vii viii Preface • This book is a tool that can be used either by itself or along with any good statistics book • Statistical theory and formulas are explained in clear language without bogging you down in mathematical fine points • You will learn both how to write statistical formulas using Excel and how to use Excel’s drop-down menus that will create the formulas for you • This book does not come with a CD of Excel files which you can upload to your computer Instead, you’ll be shown how to create each Excel file by yourself In a work situation, your colleagues will not give you an Excel file; you will be expected to create your own This book will give you ample practice in developing this important skill • Each chapter presents the steps needed to solve a practical science problem using Excel In addition, there are three practice problems at the end of each chapter, so you can test your new knowledge of statistics The answers to these problems appear in Appendix A • A “Practice Test” is given in Appendix B to test your knowledge at the end of the book The answers to these practical science problems appear in Appendix C St Louis, MO, USA Bailey, CO, USA Bailey, CO, USA Thomas J Quirk Meghan H Quirk Howard F Horton Acknowledgements Excel 2013 for Physical Sciences Statistics: A Guide to Solving Practical Problems is the result of inspiration from three important people: my two daughters and my wife Jennifer Quirk McLaughlin invited me to visit her M.B.A classes several times at the University of Witwatersrand in Johannesburg, South Africa These visits to a first-rate M.B.A program convinced me there was a need for a book to teach students how to solve practical problems using Excel Meghan QuirkHorton’s dogged dedication to learning the many statistical techniques needed to complete her Ph.D dissertation illustrated the need for a statistics book that would make this daunting task more user-friendly And Lynne Buckley-Quirk was the number one cheerleader for this project from the beginning, always encouraging me and helping me to remain dedicated to completing it Thomas J Quirk We would like to acknowledge the patience of our two little girls, Lila and Elia, as we worked on this book with their TQ We would also like to thank Professors Sarah Perkins, Doug Warren, John Moore, and Lee Dyer for their guidance and support during our college and graduate school careers Meghan H Quirk and Howard F Horton Marc Strauss, our editor at Springer, caught the spirit of this idea in our first phone conversation and shepherded this book through the idea stages until it reached its final form His encouragement and support were vital to this book seeing the light of day And Christine Crigler did her usual great job of helping this book through the editing/production process We thank them both for being such outstanding product champions throughout this process ix 228 Appendix C: Answers to Practice Test Practice Test Answer: Chapter (see Fig C.1) Fig C.1 Practice Test Answer to Chap Problem Appendices Appendices Practice Test Answer: Chapter (see Fig C.2) Fig C.2 Practice Test Answer to Chap Problem 229 230 Practice Test Answer: Chapter (see Fig C.3) Fig C.3 Practice Test Answer to Chap Problem Appendices Appendices Practice Test Answer: Chapter (see Fig C.4) Fig C.4 Practice Test Answer to Chap Problem 231 232 Practice Test Answer: Chapter (see Fig C.5) Fig C.5 Practice Test Answer to Chap Problem Appendices Appendices Practice Test Answer: Chapter (see Fig C.6) Fig C.6 Practice Test Answer to Chap Problem 233 234 Practice Test Answer: Chapter (continued) (d) a ¼ y-intercept ¼ 45.197 b ¼ slope ¼ À6.394 (note the negative sign!) (e) Y ẳ a ỵ b X Y ẳ 45:197 6:394 X (f) r ¼ correlation ¼ À:900 ðnote the negative sign!ị (g) Y ẳ 45:197 6:3942:5ị Y ẳ 45:197 À 15:985 Y ¼ 29:212 mpg (h) About 22 À 23 mpg Practice Test Answer: Chapter (see Fig C.7) Fig C.7 Practice Test Answer to Chap Problem Appendices Appendices 235 Practice Test Answer: Chapter (continued) 10 11 Rxy ¼ 77 a ¼ y-intercept ¼ 0.29 b1 ¼ 1.01 b2 ẳ 0.01 Y ẳ a ỵ b1 X ỵ b2 X Y ẳ 0:29 ỵ 1:01X1 ỵ 0:01X2 Y ẳ 0:29 ỵ 1:013:8ị ỵ 0:01126ị Y ẳ 0:29 ỵ 3:84 ỵ 1:26 Y ẳ 5:39 gallons +.76 +.60 +.65 The better predictor of TOTAL GALLONS USED was WEIGHT with a correlation of +.76 The two predictors combined predict TOTAL GALLONS USED only slightly better (Rxy ¼ 77) than the better single predictor by itself 236 Appendices Practice Test Answer: Chapter (see Fig C.8) Fig C.8 Practice Test Answer to Chap Problem Let STEEL ¼ Group 1, ALLOY A ¼ Group 2, and ALLOY B ¼ Group (b) H0 : μ1 ¼ μ2 ¼ μ3 H1 : μ1 6¼ μ2 6¼ μ3 (f) MSb ¼ 105.25 and MSw ¼ 5.10 (g) F ¼ 20.63 Appendices 237 Practice Test Answer: Chapter (continued) (h) Mean of STEEL ¼ 84.83 and Mean of ALLOY A ¼ 79.38 (j) critical F ¼ 3.28 (k) Result: Since 20.63 is greater than 3.28, we reject the null hypothesis and accept the research hypothesis (l) Conclusion: There was a significant difference in strength between the three types of beams (m) H0 : μ1 ¼ μ2 H1 : μ1 6¼ μ2 (n) df ¼ nTOTAL À k ¼ 36 À ¼ 33 (o) 1/12 + 1/13 ¼ 0.08 + 0.08 ¼ 0.16 s.e ¼ SQRT(5.10 * 0.16) s.e ¼ SQRT(0.82) s.e ¼ 0.90 (p) ANOVA t ¼ (84.83 À 79.38)/0.90 ¼ 6.06 (q) critical t ¼ 2.035 (r) Result: Since the absolute value of 6.06 is greater than the critical t of 2.035, we reject the null hypothesis and accept the research hypothesis (s) Conclusion: ALLOY A had significantly less deflection (i.e., it was stronger) than STEEL (79.4 vs 84.8) 238 Appendices Appendix D: Statistical Formulas Mean  ¼ ΣX X n Standard Deviation STDEV ¼ S ¼ Confidence interval about the mean S s:e: ¼ SX ¼ pffiffiffi n  X ặ t SX S where SX ẳ p n One-group t-test t¼ Standard error of the mean qffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 XX ị n1  X SX S where SX ẳ pffiffiffi n Two-group t-test (a) when both groups have a sample size greater than 30 t¼ where SX ÀX 1 À X 2 X SX ÀX s S1 S2 ẳ ỵ n1 n2 and where df ẳ n1 ỵ n2 (b) when one or both groups have a sample size less than 30 t¼ where SX À X 1 À X 2 X SX ÀX sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi n1 1ịS1 ỵ n2 1ịS2 1 ẳ ỵ n1 n2 n1 ỵ n2 and where df ẳ n1 ỵ n2  Þ ðY À Y Þ Σð X À X Sx Sy where Sx ¼ standard deviation of X and where Sy ¼ standard deviation of Y Correlation r ¼ n1 Appendices 239 Simple linear regression YẳaỵbX where a ẳ y-intercept and b ¼ slope of the line Multiple regression equation Y ẳ a ỵ b1 X1 ỵ b2 X2 þ b3 X3 þ etc where a ¼ y-intercept One-way ANOVA F-test F ¼ MSb =MSw ANOVA t-test 1 À X 2 X s:e:ANOVA sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   1 where s:e:ANOVA ẳ MSw ỵ n1 n2 and where df ẳ nTOTAL k where nTOTAL ẳ n1 ỵ n2 ỵ n3 ỵ etc and where k ẳ the number of groups ANOVA t ¼ 240 Appendices Appendix E: t-Table Critical t-values needed for rejection of the null hypothesis (see Fig E.1) Fig E.1 Critical t-values Needed for Rejection of the Null Hypothesis Index A Absolute value of a number, 64–65 Analysis of Variance ANOVA t-test formula (8.2), 174 degrees of freedom, 175, 179, 181–183 Excel commands, 176–178 formula (8.1), 172 interpreting the summary table, 172 s.e formula for ANOVA t-test (8.3), 175 ANOVA (see Analysis of Variance) ANOVA t-test (see Analysis of Variance) Average function (see Mean) C Centering information within cells, 6–7 Chart adding the regression equation, 136–139 changing the width and height, 111 creating a chart, 115–125 drawing the regression line onto the chart, 115–125 moving the chart, 123 printing the spreadsheet, 125–127 reducing the scale, 126 scatter chart, 117 titles, 117–121 Column width (changing), 111 Confidence interval about the mean 95% confident, 36–39 drawing a picture, 42, 43, 45, 52, 60, 61 formula (3.2), 39, 52 lower limit, 36, 37, 44 upper limit, 36, 37 CORREL function (see correlation) Correlation formula (6.1), 108 negative, 103, 105, 106, 134, 139, 145 positive, 103–105, 110, 114, 139, 145 steps for computing r, 108–110 COUNT function, 52 Critical t-value, 58, 69, 100, 175, 176, 179, 181, 183 D Data Analysis ToolPak, 128–130, 167 Data/Sort commands, 27 Degrees of freedom, 81–82, 87, 175, 179, 181, 182 Duplicate frame numbers, 24–28, 33, 34 F Fill/Series/Columns commands step value/stop value commands, 5, 22 Formatting numbers currency format, 15–16 decimal format, 11–12, 17 H Home/Fill/Series commands, Hypothesis testing decision rule, 52 null hypothesis, 47–51 rating scale hypotheses, 49 research hypothesis, 47–51 stating the conclusion, 53, 54, 57 stating the result, 57 steps for hypothesis testing, 51–57 © Springer International Publishing Switzerland 2016 T.J Quirk et al., Excel 2013 for Physical Sciences Statistics, Excel for Statistics, DOI 10.1007/978-3-319-28964-9 241 242 M Mean formula (1.1), 1–2 Multiple correlation correlation matrix, 157–160 Excel commands, 152, 157–160 predicting Y, 149 Multiple regression correlation matrix, 157–160 equation (7.1) (7.2), 149–160 Excel commands, 152 predicting Y, 149 N Naming a range of cells, 8–9 Null hypothesis (see Hypothesis testing) O One-group t-test for the mean absolute value of a number, 64–65 formula (4.1), 63 hypothesis testing, 64–67 steps for hypothesis testing, 63–71 s.e formula (4.2), 63 P Page Layout/Scale to Fit commands, 44, 125, 171, 177 Population mean, 35–36, 63, 65, 80, 87, 167, 172–174, 176 Printing a spreadsheet entire worksheet, 139–141 part of the worksheet, 139–141 printing a worksheet to fit onto one page, 125–127 R RAND() (see Random number generator) Random number generator (RAND) duplicate frame numbers, 27, 33, 34 Index frame numbers, 21–24, 33, 34 sorting duplicate frame numbers, 26–29, 33, 34 Regression, 103–146 Regression equation adding it to the chart, 136–139 formula (6.3), 135 negative correlation, 139 predicting Y from X, 103, 105, 127, 135–136 slope, b, 134 writing the regression equation using the Summary Output, 137 y-intercept, a, 134 Regression line, 115–125, 134–138, 142, 144–146 Research hypothesis (see Hypothesis testing) S Sample Size COUNT function, Saving a spreadsheet, 60, 61, 179, 181, 182 Scale to Fit commands, 177 s.e (see Standard error of the mean) Standard Deviation formula (1.2), Standard error of the mean formula (1.3), STDEV (see Standard deviation) T t-table (see Appendix E) Two-group t-test basic table, 79 degrees of freedom, 81–82 drawing a picture of the means, 85 formula (5.2), 86 Formula #1 (5.3), 86 Formula #2 (5.5), 95 hypothesis testing, 78–86 steps in hypothesis testing, 78–86 s.e formula (5.3), (5.5), 86, 95 ... Practical Problems, Excel for Statistics Springer International Publishing Switzerland 2014 T.J Quirk, Excel 2013 for Business Statistics: A Guide to Solving Practical Problems, Excel for Statistics. .. #3 (a) Use Excel to create a table for these data, and at the right of the table, use Excel to find the sample size, mean, standard deviation, and standard error of the mean for these data Label... into the ranks of the various fields of science Meghan H Quirk and Howard F Horton Preface Excel 2013 for Physical Sciences Statistics: A Guide to Solving Practical Problems is intended for anyone