SPSS Data Analysis for Univariate, Bivariate, and Multivariate Statistics Daniel J. Denis This edition first published 2019 © 2019 John Wiley & Sons, Inc. Library of Congress Cataloging‐in‐Publication Data Names: Denis, Daniel J. Title: SPSS data analysis for univariate, bivariate, and multivariate statistics / Daniel J.
Description: Hoboken, NJ : Wiley, 2019. | Includes bibliographical references and index. | Identifiers: LCCN 2018025509 (print) | LCCN 2018029180 (ebook) | ISBN 9781119465805 (Adobe PDF) | ISBN 9781119465782 (ePub) | ISBN 9781119465812 (hardcover) Subjects: LCSH: Analysis of variance–Data processing. | Multivariate analysis–Data processing.
| Mathematical statistics–Data processing. | SPSS (Computer file) Classification: LCC QA279 (ebook) | LCC QA279 .5/3–dc23 LC record available at https://lccn.gov/2018025509 Set in 10/12pt Warnock by SPi Global, Pondicherry, India Printed in the United States of America Contents Preface ix 1 Review of Essential Statistical Principles 1 1.1 Variables and Types of Data 2 1.2 Significance Tests and Hypothesis Testing 3 1.3 Significance Levels and Type I and Type II Errors 4 1.4 Sample Size and Power 5 1.5 Model Assumptions 6 2 Introduction to SPSS 9 2.1 How to Communicate with SPSS 9 2.2 Data View vs.3 Missing Data in SPSS: Think Twice Before Replacing Data! 12 3 Exploratory Data Analysis, Basic Statistics, and Visual Displays 19 3.1 Frequencies and Descriptives 19 3.2 The Explore Function 23 3.3 What Should I Do with Outliers? Delete or Keep Them? 28 3.4 Data Transformations 29 4 Data Management in SPSS 33 4.1 Computing a New Variable 33 4.3 Recoding Variables into Same or Different Variables 36 4.5 Transposing Data 38 5 Inferential Tests on Correlations, Counts, and Means 41 5.1 Computing z‐Scores in SPSS 41 5.3 A Measure of Reliability: Cohen’s Kappa 52 5.5 Chi‐square Goodness‐of‐fit Test 54 5.6 One‐sample t‐Test for a Mean 57 5.7 Two‐sample t‐Test for Means 59 6 Power Analysis and Estimating Sample Size 63 6.1 Example Using G*Power: Estimating Required Sample Size for Detecting Population Correlation 64 6.2 Power for Chi‐square Goodness of Fit 66 6.3 Power for Independent‐samples t‐Test 66 6.4 Power for Paired‐samples t‐Test 67 7 Analysis of Variance: Fixed and Random Effects 69 7.1 Performing the ANOVA in SPSS 70 7.2 The F‐Test for ANOVA 73 7.4 Contrasts and Post Hoc Tests on Teacher 75 7.5 Alternative Post Hoc Tests and Comparisons 78 7.6 Random Effects ANOVA 80 7.7 Fixed Effects Factorial ANOVA and Interactions 82 7.8 What Would the Absence of an Interaction Look Like? 86 7.9 Simple Main Effects 86 7.10 Analysis of Covariance (ANCOVA) 88 7.11 Power for Analysis of Variance 90 8 Repeated Measures ANOVA 91 8.1 One‐way Repeated Measures 91 8.2 Two‐way Repeated Measures: One Between and One Within Factor 99 9 Simple and Multiple Linear Regression 103 9.1 Example of Simple Linear Regression 103 9.2 Interpreting a Simple Linear Regression: Overview of Output 105 9.3 Multiple Regression Analysis 107 9.5 Running the Multiple Regression 112 9.6 Approaches to Model Building in Regression 118 9.7 Forward, Backward, and Stepwise Regression 120 9.8 Interactions in Multiple Regression 121 9.9 Residuals and Residual Plots: Evaluating Assumptions 123 9.10 Homoscedasticity Assumption and Patterns of Residuals 125 9.11 Detecting Multivariate Outliers and Influential Observations 126 9.13 Power for Regression 129 10 Logistic Regression 131 10.1 Example of Logistic Regression 132 10.2 Multiple Logistic Regression 138 10.3 Power for Logistic Regression 139 11 Multivariate Analysis of Variance (MANOVA) and Discriminant Analysis 141 11.1 Example of MANOVA 142 11.4 Discriminant Function Analysis 148 11.5 Equality of Covariance Matrices Assumption 152 11.6 MANOVA and Discriminant Analysis on Three Populations 153 11.9 Power Analysis for MANOVA 162 12 Principal Components Analysis 163 12.1 Example of PCA 163 12.4 Visualizing Principal Components 167 12.5 PCA of Correlation Matrix 170 13 Exploratory Factor Analysis 175 13.1 The Common Factor Analysis Model 175 13.2 The Problem with Exploratory Factor Analysis 176 13.3 Factor Analysis of the PCA Data 176 13.4 What Do We Conclude from the Factor Analysis? 179 13.6 Rotating the Factor Solution 181 13.7 Is There Sufficient Correlation to Do the Factor Analysis? 182 13.8 Reproducing the Correlation Matrix 183 13.10 How to Validate Clusters? 187 13.11 Hierarchical Cluster Analysis 188 14 Nonparametric Tests 191 14.1 Independent‐samples: Mann–Whitney U 192 14.2 Multiple Independent‐samples: Kruskal–Wallis Test 193 14.3 Repeated Measures Data: The Wilcoxon Signed‐rank Test and Friedman Test 194 14.4 The Sign Test 196 Closing Remarks and Next Steps 199 References 201 Index 203 Preface The goals of this book are to present a very concise, easy‐to‐use introductory primer of a host of computational tools useful for making sense out of data, whether that data come from the social, behavioral, or natural sciences, and to get you started doing data analysis fast. The emphasis on the book is data analysis and drawing conclusions from empirical observations. The emphasis of the book is not on theory.
Formulas are given where needed in many places, but the focus of the book is on concepts rather than on mathematical abstraction. We emphasize computational tools used in the discovery of empirical patterns and feature a variety of popular statistical analyses and data management tasks that you can immediately apply as needed to your own research. The book features analyses and demonstrations using SPSS. Most of the data sets analyzed are very small and convenient, so entering them into SPSS should be easy.
If desired, however, one can also download them from www. Many of the data sets were also first used in a more theoretical text written by the same author (see Denis, 2016), which should be consulted for a more in‐depth treatment of the topics presented in this book. Additional references for readings are also given throughout the book. Target Audience and Level This is a “how‐to” book and will be of use to undergraduate and graduate students along with researchers and professionals who require a quick go‐to source, to help them perform essential statistical analyses and data management tasks.
The book only assumes minimal prior knowledge of statistics, providing you with the tools you need right now to help you understand and interpret your data analyses. A prior introductory course in statistics at the undergraduate level would be helpful, but is not required for this book. Instructors may choose to use the book either as a primary text for an undergraduate or graduate course or as a supplement to a more technical text, referring to this book primarily for the “how to’s” of data analysis in SPSS. The book can also be used for self‐study.
It is suitable for use as a general reference in all social and natural science fields and may also be of interest to those in business who use SPSS for decision‐making. References to further reading are provided where appropriate should the reader wish to follow up on these topics or expand one’s knowledge base as it pertains to theory and further applications. An early chapter reviews essential statistical and research principles usually covered in an introductory statistics course, which should be sufficient for understanding the rest of the book and interpreting analyses. Mini brief sample write‐ups are also provided for select analyses in places to give the reader a starting point to writing up his/her own results for his/her thesis, dissertation, or publication.
The book is meant to be an easy, user‐friendly introduction to a wealth of statistical methods while simultaneously demonstrat- ing their implementation in SPSS. Please contact me at daniel.edu or email@data- psyc.com with any comments or corrections. Glossary of Icons and Special Features When you see this symbol, it means a brief sample write‐up has been provided for the accompanying output. These brief write‐ups can be used as starting points to writing up your own results for your thesis/dissertation or even publication.
When you see this symbol, it means a special note, hint, or reminder has been provided or signifies extra insight into something not thoroughly discussed in the text. When you see this symbol, it means a special WARNING has been issued that if not fol- lowed may result in a serious error. Acknowledgments Thanks go out to Wiley for publishing this book, especially to Jon Gurstelle for presenting the idea to Wiley and securing the contract for the book and to Mindy Okura‐Marszycki for taking over the project after Jon left. Thank you Kathleen Pagliaro for keeping in touch about this project and the former book.
Thanks goes out to everyone (far too many to mention) who have influenced me in one way or another in my views and philosophy about statistics and science, including undergraduate and graduate students whom I have had the pleasure of teaching (and learning from) in my courses taught at the University of Montana. This book is dedicated to all military veterans of the United States of America, past, present, and future, who teach us that all problems are relative. 1 1 Review of Essential Statistical Principles Big Picture on Statistical Modeling and Inference The purpose of statistical modeling is to both describe sample data and make inferences about that sample data to the population from which the data was drawn. We compute statistics on samples (e.
sample mean) and use such statistics as estimators of population parameters (e. When we use the sample statistic to estimate a parameter in the population, we are engaged in the process of inference, which is why such statistics are referred to as inferential statistics, as opposed to descriptive statistics where we are typically simply describing something about a sample or population. All of this usually occurs in an experimental design (e. where we have a control vs.
treatment group) or nonexperimental design (where we exercise little or no control over variables). As an example of an experimental design, suppose you wanted to learn whether a pill was effective in reducing symptoms from a headache. You could sample 100 individuals with headaches, give them a pill, and compare their reduction in symptoms to 100 people suffering from a headache but not receiving the pill. If the group receiving the pill showed a decrease in symptomology compared with the nontreated group, it may indicate that your pill is effective.
However, to estimate whether the effect observed in the sample data is generalizable and inferable to the population from which the data were drawn, a statistical test could be performed to indicate whether it is plausible that such a difference between groups could have occurred simply by chance. If it were found that the difference was unlikely due to chance, then we may indeed conclude a difference in the population from which the data were drawn. The probability of data occurring under some assumption of (typically) equality is the infamous p‐value, usually set at 0. If the probability of such data is relatively low (e.05) under the null hypothesis of no difference, we reject the null and infer the statistical alter‑ native hypothesis of a difference in population means.
Much of statistical modeling follows a similar logic to that featured above – sample some data, apply a model to the data, and then estimate how good the model fits and whether there is inferential evidence to suggest an effect in the population from which the data were drawn. The actual model you will fit to your data usually depends on the type of data you are working with. For instance, if you have collected sample means and wish to test differences between means, then t‐test and ANOVA tech‑ niques are appropriate. On the other hand, if you have collected data in which you would like to see if there is a linear relationship between continuous variables, then correlation and regression are usually appropriate.
If you have collected data on numerous dependent variables and believe these variables, taken together as a set, represent some kind of composite variable, and wish to determine mean differences on this composite dependent variable, then a multivariate analysis of variance (MANOVA) technique may be useful.