Praise for Larry Hatcher The writing is exceptionally clear and easy to follow, and precise definitions are provided to avoid confusion. Examples are used to illustrate each concept, and those examples are, like everything in this book, clear and logically presented. Sample SAS output is provided for every analysis, with each part labeled and thoroughly explained so the reader understands the results. Sheri Bauman, Ph.D. Assistant Professor Department of Educational Psychology University of Arizona, Tucson [Larry Hatcher] once again manages to provide clear, concise, and detailed explanations of the SAS program and procedures, including appropriate examples and sample write-ups. Frank Pajares Winship Distinguished Research Professor Emory University The Student Guide and the Exercises books are excellent choices for use in quantitative courses in psychology and education. Bert W. Westbrook, Ph.D. Professor of Psychology Alumni Distinguished Undergraduate Professor North Carolina State University Step-by-Step S T U D E N T G U I D E BASIC STATISTICS Using SAS ® LARRY HATCHER, P H . D . The correct bibliographic citation for this manual is as follows: Hatcher, Larry. 2003. Step-by-Step Basic Statistics Using SAS®: Student Guide. Cary, NC: SAS Institute Inc. Step-by-Step Basic Statistics Using SAS®: Student Guide Copyright © 2003 by SAS Institute Inc., Cary, NC, USA ISBN 1-59047-148-2 All rights reserved. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR 52.227-19, Commercial Computer Software-Restricted Rights (June 1987). SAS Institute Inc., SAS Campus Drive, Cary, North Carolina 27513. 1st printing, April 2003 SAS Publishing provides a complete selection of books and electronic products to help customers use SAS software to its fullest potential. For more information about our e-books, e-learning products, CDs, and hardcopy books, visit the SAS Publishing Web site at support.sas.com/pubs or call 1-800-727-3228. SAS® and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are trademarks of their respective companies. Dedication To my friends at Saginaw Valley State University. ii Step-by-Step Basic Statistics Using SAS: Student Guide Contents Acknowledgments .............................................................................................ix Chapter 1: Using This Student Guide ..............................................................1 Introduction...........................................................................................................................3 Introduction to the SAS System............................................................................................4 Contents of This Student Guide............................................................................................6 Conclusion..........................................................................................................................11 Chapter 2: Terms and Concepts Used in This Guide..................................13 Introduction.........................................................................................................................15 Research Hypotheses and Statistical Hypotheses.............................................................16 Data, Variables, Values, and Observations........................................................................21 Classifying Variables According to Their Scales of Measurement......................................24 Classifying Variables According to the Number of Values They Display............................27 Basic Approaches to Research...........................................................................................29 Using Type-of-Variable Figures to Represent Dependent and Independent Variables.....................................................................................................32 The Three Types of SAS Files............................................................................................37 Conclusion..........................................................................................................................45 Chapter 3: Tutorial: Writing and Submitting SAS Programs.......................47 Introduction.........................................................................................................................48 Tutorial Part I: Basics of Using the SAS Windowing Environment.....................................50 Tutorial Part II: Opening and Editing an Existing SAS Program.........................................75 Tutorial Part III: Submitting a Program with an Error.........................................................94 Tutorial Part IV: Practicing What You Have Learned.......................................................102 Summary of Steps for Frequently Performed Activities....................................................105 Controlling the Size of the Output Page with the OPTIONS Statement............................109 For More Information.........................................................................................................110 Conclusion........................................................................................................................110 Chapter 4: Data Input.....................................................................................111 Introduction.......................................................................................................................113 Example 4.1: Creating a Simple SAS Data Set...............................................................117 Example 4.2: A More Complex Data Set.........................................................................122 Using PROC MEANS and PROC FREQ to Identify Obvious Problems with the Data Set...........................................................................................................131 Using PROC PRINT to Create a Printout of Raw Data.....................................................139 The Complete SAS Program.............................................................................................142 Conclusion........................................................................................................................144 Chapter 5: Creating Frequency Tables........................................................145 Introduction.......................................................................................................................146 Example 5.1: A Political Donation Study..........................................................................147 Using PROC FREQ to Create a Frequency Table............................................................152 iv Contents Examples of Questions That Can Be Answered by Interpreting a Frequency Table........................................................................................................ 155 Conclusion........................................................................................................................157 Chapter 6: Creating Graphs..........................................................................159 Introduction.......................................................................................................................160 Reprise of Example 5.1: the Political Donation Study.......................................................161 Using PROC CHART to Create a Frequency Bar Chart...................................................162 Using PROC CHART to Plot Means for Subgroups..........................................................174 Conclusion........................................................................................................................177 Chapter 7: Measures of Central Tendency and Variability ........................179 Introduction.......................................................................................................................181 Reprise of Example 5.1: The Political Donation Study......................................................181 Measures of Central Tendency: The Mode, Median, and Mean......................................183 Interpreting a Stem-and-Leaf Plot Created by PROC UNIVARIATE................................187 Using PROC UNIVARIATE to Determine the Shape of Distributions...............................190 Simple Measures of Variability: The Range, the Interquartile Range, and the Semi-Interquartile Range.................................................................................200 More Complex Measures of Central Tendency: The Variance and Standard Deviation........................................................................................................204 Variance and Standard Deviation: Three Formulas.........................................................207 Using PROC MEANS to Compute the Variance and Standard Deviation........................210 Conclusion........................................................................................................................214 Chapter 8: Creating and Modifying Variables and Data Sets ....................215 Introduction.......................................................................................................................217 Example 8.1: An Achievement Motivation Study.............................................................218 Using PROC PRINT to Create a Printout of Raw Data.....................................................222 Where to Place Data Manipulation and Data Subsetting Statements...............................225 Basic Data Manipulation...................................................................................................228 Recoding a Reversed Item and Creating a New Variable for the Achievement Motivation Study......................................................................................235 Using IF-THEN Control Statements..................................................................................239 Data Subsetting.................................................................................................................248 Combining a Large Number of Data Manipulation and Data Subsetting Statements in a Single Program.........................................................256 Conclusion........................................................................................................................260 Chapter 9: z Scores........................................................................................261 Introduction.......................................................................................................................262 Example 9.1: Comparing Mid-Term Test Scores for Two Courses.................................266 Converting a Single Raw-Score Variable into a z-Score Variable....................................268 Converting Two Raw-Score Variables into z-Score Variables..........................................278 Standardizing Variables with PROC STANDARD.............................................................285 Conclusion........................................................................................................................286 Contents v Chapter 10: Bivariate Correlation.................................................................287 Introduction.......................................................................................................................290 Situations Appropriate for the Pearson Correlation Coefficient.........................................290 Interpreting the Sign and Size of a Correlation Coefficient...............................................293 Interpreting the Statistical Significance of a Correlation Coefficient .................................297 Problems with Using Correlations to Investigate Causal Relationships............................ 299 Example 10.1: Correlating Weight Loss with a Variety of Predictor Variables................. 303 Using PROC PLOT to Create a Scattergram.................................................................... 307 Using PROC CORR to Compute the Pearson Correlation between Two Variables................................................................................................. 313 Using PROC CORR to Compute All Possible Correlations for a Group of Variables................................................................................................ 320 Summarizing Results Involving a Nonsignificant Correlation............................................ 324 Using the VAR and WITH Statements to Suppress the Printing of Some Correlations ........................................................................................................ 329 Computing the Spearman Rank-Order Correlation Coefficient for Ordinal-Level Variables................................................................................................. 332 Some Options Available with PROC CORR ..................................................................... 333 Problems with Seeking Significant Results....................................................................... 335 Conclusion ........................................................................................................................ 338 Chapter 11: Bivariate Regression.................................................................339 Introduction ....................................................................................................................... 341 Choosing between the Terms Predictor Variable, Criterion Variable, Independent Variable, and Dependent Variable ............................................................... 341 Situations Appropriate for Bivariate Linear Regression .................................................... 344 Example 11.1: Predicting Weight Loss from a Variety of Predictor Variables.................. 346 Using PROC REG: Example with a Significant Positive Regression Coefficient ..................................................................................................350 Using PROC REG: Example with a Significant Negative Regression Coefficient ........... 371 Using PROC REG: Example with a Nonsignificant Regression Coefficient..................... 379 Conclusion ........................................................................................................................ 383 Chapter 12: Single-Sample t Test.................................................................385 Introduction ....................................................................................................................... 387 Situations Appropriate for the Single-Sample t Test ......................................................... 387 Results Produced in a Single-Sample t Test..................................................................... 388 Example 12.1: Assessing Spatial Recall in a Reading Comprehension Task (Significant Results) ............................................................................................. 393 One-Tailed Tests versus Two-Tailed Tests ...................................................................... 406 Example 12.2: An Illustration of Nonsignificant Results................................................... 407 Conclusion ........................................................................................................................ 412 Chapter 13: Independent-Samples t Test ....................................................413 Introduction ....................................................................................................................... 415 Situations Appropriate for the Independent-Samples t Test ............................................. 417 Results Produced in an Independent-Samples t Test....................................................... 420