Sach excel 2013 for social sciences statistics a guide to solving practical problems by thomas j quirk english

Excel for Statistics

Thomas J. Quirk

Excel 2013 for
Social 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 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.

In addition, the following books are scheduled to be published in this series in 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 (expected).
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 (expected).
T.J. Quirk. Excel 2013 for Engineering Statistics: A Guide to Solving Problems, Excel for Statistics.
Springer International Publishing Switzerland 2015 (expected).
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 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 Science 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: />

Thomas J. Quirk

Excel 2013 for Social
Sciences Statistics
A Guide to Solving Practical Problems


Thomas J. Quirk
Webster University
St. Louis, MO, USA

Excel for Statistics
ISBN 978-3-319-19176-8
ISBN 978-3-319-19177-5
DOI 10.1007/978-3-319-19177-5

(eBook)

Library of Congress Control Number: 2015940881
Springer Cham Heidelberg New York Dordrecht London
© Springer International Publishing Switzerland 2015
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
Springer International Publishing AG Switzerland is part of Springer Science+Business Media
(www.springer.com)


This book is dedicated to more than three
thousand 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 BadenWuerttemburg 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.



Preface

Excel 2013 for Social Science 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 social 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 the social 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 social science courses. The powerful numerical computational ability and the
graphical functions available in Excel make learning statistics much easier than in
years past. However, this is the first book to show Excel’s capabilities to more
effectively teach social 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:
• 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.
• Includes 167 color screenshots so that you can be sure you are performing the
Excel steps correctly.
• This book is a tool that can be used either by itself or along with any good
statistics book.

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viii

Preface

• Practical examples and problems are taken from the social sciences, including
political science, sociology, anthropology, education, and psychology.
• 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 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 social 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 social science problems appear in Appendix C.
This book is appropriate for use in any course in Social Science Statistics
(at both undergraduate and graduate levels) as well as for managers who want to
improve the usefulness of their Excel skills.
This book has a single author, Dr. Tom Quirk, a current Professor of Marketing
at the George Herbert Walker School of Business & Technology at Webster
University in St. Louis, Missouri (USA), where he teaches Marketing Statistics,
Marketing Research, and Pricing Strategies. The ideas in this book have been
thoroughly tested in Professor Quirk’s Marketing Statistics and Marketing
Research courses. At the beginning of his academic career, Prof. Quirk spent
6 years in educational research at The American Institutes for Research and
Educational Testing Service. He then taught Social Psychology, Educational
Psychology, and General Psychology at Principia College in Elsah, Illinois (USA).

He has published articles in The Journal of Educational Psychology, Journal of
Educational Research, Review of Educational Research, Journal of Educational
Measurement, Educational Technology, The Elementary School Journal, Journal of
Secondary Education, Educational Horizons, and Phi Delta Kappan. In addition,
Professor Quirk has written more than 60 textbook supplements in Management and
Marketing, published more than 20 articles in professional journals, and presented
more than 20 papers at professional meetings, including annual meetings of The
American Educational Research Association, The American Psychological Association, and the National Council on Measurement in Education. He holds a B.S. in
Mathematics from John Carroll University, both an M.A. in Education and a Ph.D.
in Educational Psychology from Stanford University, and an M.B.A. from the
University of Missouri-St. Louis.
St. Louis, MO, USA

Thomas J. Quirk


Acknowledgements

Excel 2013 for Social Science 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 social science problems using Excel. Meghan
Quirk-Horton’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 remain dedicated to completing it.
Marc Strauss, my 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. I thank him for being such an outstanding product champion
throughout this process. And Hannah Bracken at Springer did her usual first-rate job
in coordinating the editing and production of this book; she is always a pleasure to
work with.

ix



Contents

1

Sample Size, Mean, Standard Deviation, and Standard
Error of the Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Standard Error of the Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Sample Size, Mean, Standard Deviation, and Standard
Error of the Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Using the Fill/Series/Columns Commands . . . . . . . . . . . .
1.4.2 Changing the Width of a Column . . . . . . . . . . . . . . . . . .
1.4.3 Centering Information in a Range of Cells . . . . . . . . . . .
1.4.4 Naming a Range of Cells . . . . . . . . . . . . . . . . . . . . . . . .
1.4.5 Finding the Sample Size Using
the ¼COUNT Function . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.6 Finding the Mean Score Using
the ¼AVERAGE Function . . . . . . . . . . . . . . . . . . . . . . .

1.4.7 Finding the Standard Deviation Using
the ¼STDEV Function . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.8 Finding the Standard Error of the Mean . . . . . . . . . . . . .
1.5 Saving a Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Printing a Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7 Formatting Numbers in Currency Format
(Two Decimal Places) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8 Formatting Numbers in Number Format
(Three Decimal Places) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.9 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4

Contents

Random Number Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Creating Frame Numbers for Generating
Random Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Creating Random Numbers in an Excel Worksheet . . . . . . . . . .
2.3 Sorting Frame Numbers into a Random Sequence . . . . . . . . . .
2.4 Printing an Excel File So That All of the Information
Fits onto One Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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37

Confidence Interval About the Mean Using the TINV Function
and Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Confidence Interval About the Mean . . . . . . . . . . . . . . . . . . . . .
3.1.1 How to Estimate the Population Mean . . . . . . . . . . . . . .
3.1.2 Estimating the Lower Limit and the Upper Limit
of the 95 % Confidence Interval About the Mean . . . . . .
3.1.3 Estimating the Confidence Interval the Chevy Impala
in Miles Per Gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 Where Did the Number “1.96” Come From? . . . . . . . . . .
3.1.5 Finding the Value for t in the Confidence
Interval Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.6 Using Excel’s TINV Function to Find the Confidence
Interval About the Mean . . . . . . . . . . . . . . . . . . . . . . . .
3.1.7 Using Excel to Find the 95 % Confidence Interval
for a Car’s mpg Claim . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Hypotheses Always Refer to the Population of People
or Events That You Are Studying . . . . . . . . . . . . . . . . . .
3.2.2 The Null Hypothesis and the Research (Alternative)
Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 The 7 Steps for Hypothesis-Testing Using the Confidence
Interval About the Mean . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Alternative Ways to Summarize the Result
of a Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Different Ways to Accept the Null Hypothesis . . . . . . . .
3.3.2 Different Ways to Reject the Null Hypothesis . . . . . . . . .
3.4 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
One-Group t-Test for the Mean . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 The 7 STEPS for Hypothesis-Testing Using
the One-Group t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 STEP 1: State the Null Hypothesis and the Research
Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 STEP 2: Select the Appropriate Statistical Test . . . . . . .

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4.1.3

STEP 3: Decide on a Decision Rule
for the One-Group t-Test . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 STEP 4: Calculate the Formula
for the One-Group t-Test . . . . . . . . . . . . . . . . . . . . . . . .
4.1.5 STEP 5: Find the Critical Value of t in the t-Table
in Appendix E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.6 STEP 6: State the Result of Your Statistical Test . . . . . . .
4.1.7 STEP 7: State the Conclusion of Your Statistical
Test in Plain English! . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 One-Group t-Test for the Mean . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Can You Use Either the 95 % Confidence Interval About
the Mean OR the One-Group t-Test When Testing Hypotheses? .
4.4 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5

Two-Group t-Test of the Difference of the Means
for Independent Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 The 9 STEPS for Hypothesis-Testing Using
the Two-Group t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 STEP 1: Name One Group, Group 1, and the Other
Group, Group 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 STEP 2: Create a Table That Summarizes
the Sample Size, Mean Score, and Standard Deviation
of Each Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 STEP 3: State the Null Hypothesis and the Research
Hypothesis for the Two-Group t-Test . . . . . . . . . . . . . .
5.1.4 STEP 4: Select the Appropriate Statistical Test . . . . . . .
5.1.5 STEP 5: Decide on a Decision Rule for the Two-Group
t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1.6 STEP 6: Calculate the Formula for the Two-Group
t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.7 STEP 7: Find the Critical Value of t in the t-Table
in Appendix E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.8 STEP 8: State the Result of Your Statistical Test . . . . . .
5.1.9 STEP 9: State the Conclusion of Your Statistical
Test in Plain English! . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Formula #1: Both Groups Have More than 30 People
in Them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 An Example of Formula #1 for the Two-Group
t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Formula #2: One or Both Groups Have Less than 30 People
in Them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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xiv

6

7

Contents

Correlation and Simple Linear Regression . . . . . . . . . . . . . . . . . . .
6.1 What Is a “Correlation?” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Understanding the Formula for Computing

a Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Understanding the Nine Steps for Computing
a Correlation, r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Using Excel to Compute a Correlation Between
Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Creating a Chart and Drawing the Regression Line
onto the Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Using Excel to Create a Chart and the Regression
Line Through the Data Points . . . . . . . . . . . . . . . . . . . . .
6.4 Printing a Spreadsheet So That the Table and Chart Fit
onto One Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Finding the Regression Equation . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1 Installing the Data Analysis ToolPak into Excel . . . . . . .
6.5.2 Using Excel to Find the SUMMARY
OUTPUT of Regression . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.3 Finding the Equation for the Regression Line . . . . . . . . .
6.5.4 Using the Regression Line to Predict
the y-Value for a Given x-Value . . . . . . . . . . . . . . . . . . .
6.6 Adding the Regression Equation to the Chart . . . . . . . . . . . . . . .
6.7 How to Recognize Negative Correlations
in the SUMMARY OUTPUT Table . . . . . . . . . . . . . . . . . . . . . .
6.8 Printing Only Part of a Spreadsheet Instead
of the Entire Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.1 Printing Only the Table and the Chart
on a Separate Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.2 Printing Only the Chart on a Separate Page . . . . . . . . . . .
6.8.3 Printing Only the SUMMARY OUTPUT
of the Regression Analysis on a Separate Page . . . . . . . .
6.9 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Multiple Correlation and Multiple Regression . . . . . . . . . . . . . . .
7.1 Multiple Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Finding the Multiple Correlation and the Multiple
Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Using the Regression Equation to Predict FROSH GPA . . . . . .
7.4 Using Excel to Create a Correlation Matrix in Multiple
Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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One-Way Analysis of Variance (ANOVA) . . . . . . . . . . . . . . . . . . . .
8.1 Using Excel to Perform a One-Way Analysis
of Variance (ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 How to Interpret the ANOVA Table Correctly . . . . . . . . . . . . . .
8.3 Using the Decision Rule for the ANOVA F-Test . . . . . . . . . . . .
8.4 Testing the Difference Between Two Groups Using
the ANOVA t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.1 Comparing Republicans vs. Democrats in Their
Attitude Toward U.S. Military Spending Using
the ANOVA t-Test . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5 End-of-Chapter Practice Problems . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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196

Appendix A:

Answers to End-of-Chapter Practice Problems . . . . . . . 197

Appendix B:

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

Appendix C:

Answers to Practice Test . . . . . . . . . . . . . . . . . . . . . . . . 242

Appendix D:

Statistical Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

Appendix E:

t-Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255


Chapter 1

Sample Size, Mean, Standard Deviation,
and Standard Error of the Mean

This chapter deals with how you can use Excel to find the average (i.e., “mean”) of
a set of scores, the standard deviation of these scores (STDEV), and the standard
error of the mean (s.e.) of these scores. All three of these statistics are used
frequently and form the basis for additional statistical tests.

1.1

Mean

The mean is the “arithmetic average” of a set of scores. When my daughter was in
the fifth grade, she came home from school with a sad face and said that she didn’t
get “averages.” The book she was using described how to find the mean of a set of
scores, and so I said to her:
“Jennifer, you add up all the scores and divide by the number of numbers that you have.”
She gave me “that look,” and said: “Dad, this is serious!” She thought I was teasing her.
So I said:
“See these numbers in your book; add them up. What is the answer?” (She did that).
“Now, how many numbers do you have?” (She answered that question).
“Then, take the number you got when you added up the numbers, and divide that number by
the number of numbers that you have.”

She did that, and found the correct answer. You will use that same reasoning
now, but it will be much easier for you because Excel will do all of the steps for you.
We will call this average of the scores the “mean” which we will symbolize as: X,
and we will pronounce it as: “Xbar.”

© Springer International Publishing Switzerland 2015
T.J. Quirk, Excel 2013 for Social Sciences Statistics, Excel for Statistics,
DOI 10.1007/978-3-319-19177-5_1

1


2

1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

The formula for finding the mean with you calculator looks like this:
Xẳ

X
n

1:1ị

The symbol is the Greek letter sigma, which stands for “sum.” It tells you to
add up all the scores that are indicated by the letter X, and then to divide your
answer by n (the number of numbers that you have).
Let’s give a simple example:
Suppose that a political scientist developed a survey measuring the attitudes of
registered voters on a variety of issues and that one of the items on this survey was

the following: “Wealthy people should pay taxes at a much higher rate than poor
people.” Suppose, further, that a 7-point rating scale was used for this item such that
1 ¼ strongly disagree, and 7 ¼ strongly agree.
Suppose that you had these six ratings on this one item:
6
4
5
3
2
5
To find the mean of these scores, you add them up, and then divide by the
number of scores. So, the mean is: 25/6 ¼ 4.17 (close to the middle of the 7-point
scale).

1.2

Standard Deviation

The standard deviation tells you “how close the scores are to the mean.” If the
standard deviation is a small number, this tells you that the scores are “bunched
together” close to the mean. If the standard deviation is a large number, this tells
you that the scores are “spread out” a greater distance from the mean. The formula
for the standard deviation (which we will call STDEV) and use the letter, S, to
symbolize is:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Á2
XÀ
XÀX
STDEV ¼ S ¼
nÀ1

The formula look complicated, but what it asks you to do is this:
À
Á
1. Subtract the mean from each score X À X .
2. Then, square the resulting number to make it a positive number.
3. Then, add up these squared numbers to get a total score.

ð1:2Þ


1.3 Standard Error of the Mean

3

4. Then, take this total score and divide it by n À 1 (where n stands for the number
of numbers that you have).
5. The final step is to take the square root of the number you found in step 4.
You will not be asked to compute the standard deviation using your calculator in
this book, but you could see examples of how it is computed in any basic statistics
book. Instead, we will use Excel to find the standard deviation of a set of scores.
When we use Excel on the six numbers we gave in the description of the mean
above, you will find that the STDEV of these numbers, S, is 1.47.

1.3

Standard Error of the Mean

The formula for the standard error of the mean (s.e., which we will use SX to
symbolize) is:
S

s:e: ẳ SX ẳ p
n

1:3ị

To find s.e., all you need to do is to take the standard deviation, STDEV, and
divide it by the square root of n, where n stands for the “number of numbers” that
you have in your data set. In the example under the standard deviation description
above, the s.e. ¼ 0.60. (You can check this on your calculator).
If you want to learn more about the standard deviation and the standard error of
the mean, see Weiers (2011) and Neuman (2000).
Now, let’s learn how to use Excel to find the sample size, the mean, the standard
deviation, and the standard error or the mean using a geometry test given to a class
of 9th graders at the end of the first term of the school year (50 points possible). The
hypothetical data appear in Fig. 1.1.

Fig. 1.1 Worksheet Data
for a Geometry Test
(Practical Example)


4

1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

1.4

Sample Size, Mean, Standard Deviation, and Standard
Error of the Mean

Objective: To find the sample size (n), mean, standard deviation (STDEV), and
standard error of the mean (s.e.) for these data
Start your computer, and click on the Excel 2013 icon to open a blank Excel
spreadsheet.
Enter the data in this way:
A3: Student
B3: Geometry Test Score
A4: 1

1.4.1

Using the Fill/Series/Columns Commands

Objective: To add the student numbers 2–8 in a column underneath student #1
Put pointer in A4
Home (top left of screen)
Fill (top right of screen: click on the down arrow; see Fig. 1.2)

Fig. 1.2 Home/Fill/Series commands

Series
Columns
Step value: 1
Stop value: 8 (see Fig. 1.3)


1.4 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

5

Fig. 1.3 Example of Dialogue Box for Fill/Series/Columns/Step Value/Stop Value commands

OK
The student numbers should be identified as 1–8, with 8 in cell A11.
Now, enter the Geometry Test Scores in cells B4:B11.
Since your computer screen shows the information in a format that does not look
professional, you need to learn how to “widen the column width” and how to
“center the information” in a group of cells. Here is how you can do those two steps:

1.4.2

Changing the Width of a Column

Objective: To make a column width wider so that all of the information fits
inside that column
If you look at your computer screen, you can see that Column B is not wide
enough so that all of the information fits inside this column. To make Column
B wider:
Click on the letter, B, at the top of your computer screen
Place your mouse pointer at the far right corner of B until you create a “cross sign”
on that corner
Left-click on your mouse, hold it down, and move this corner to the right until it is
“wide enough to fit all of the data”
Take your finger off the mouse to set the new column width (see Fig. 1.4)


6

1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

Fig. 1.4 Example of How
to Widen the Column Width

Then, click on any empty cell (i.e., any blank cell) to “deselect” column B so that
it is no longer a darker color on your screen.
When you widen a column, you will make all of the cells in all of the rows of this
column that same width.
Now, let’s go through the steps to center the information in both Column A and
Column B.

1.4.3

Centering Information in a Range of Cells

Objective: To center the information in a group of cells
In order to make the information in the cells look “more professional,” you can
center the information using the following steps:
Left-click your mouse on A3 and drag it to the right and down to highlight cells A3:
B11 so that these cells appear in a darker color
At the top of your computer screen, you will see a set of “lines” in which all of the
lines are “centered” to the same width under “Alignment” (it is the second icon
at the bottom left of the Alignment box; see Fig. 1.5)


1.4 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

Fig. 1.5 Example of How to Center Information Within Cells

Click on this icon to center the information in the selected cells (see Fig. 1.6)

Fig. 1.6 Final Result of
Centering Information in
the Cells

7


8

1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

Since you will need to refer to the Geometry Test Scores in your formulas, it will
be much easier to do this if you “name the range of data” with a name instead of
having to remember the exact cells (B4:B11) in which these figures are located.
Let’s call that group of cells: Geometry, but we could give them any name that you
want to use.

1.4.4

Naming a Range of Cells

Objective: To name the range of data for the test scores with the name:
Geometry
Highlight cells B4:B11 by left-clicking your mouse on B4 and dragging it down to
B11
Formulas (top left of your screen)
Define Name (top center of your screen)
Geometry (type this name in the top box; see Fig. 1.7)

Fig. 1.7 Dialogue box for “naming a range of cells” with the name: Geometry

OK
Then, click on any cell of your spreadsheet that does not have any information in it
(i.e., it is an “empty cell”) to deselect cells B4:B11


1.4 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

9

Now, add the following terms to your spreadsheet:
E6:
E9:
E12:
E15:

n
Mean
STDEV
s.e. (see Fig. 1.8)

Fig. 1.8 Example of Entering the Sample Size, Mean, STDEV, and s.e. Labels

Note: Whenever you use a formula, you must add an equal sign (¼) at the beginning
of the name of the function so that Excel knows that you intend to use a
formula.

1.4.5

Finding the Sample Size Using the ¼COUNT Function

Objective: To find the sample size (n) for these data using the ¼COUNT
function
F6:

¼COUNT(Geometry)

This command should insert the number 8 into cell F6 since there are eight students
in this class.