Assessment Description Understanding the data sampling procedure and the description of the data is critical to accurately interpreting the results

Introduction to Statistical Analysis Using IBM SPSS Statistics

Student Guide

Course Code: 0G517

ERC 1.0

Introduction to Statistical Analysis Using IBM SPSS Statistics

Licensed Materials – Property of IBM © Copyright IBM Corp. 2010

0G517

Published October 2010 US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp.

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trademarks of IBM or other companies. This guide contains proprietary information which is protected by copyright. No part of this document may be photocopied, reproduced, or translated into another language without a legal license agreement from IBM Corporation. Any references in this information to non-IBM Web sites are provided for convenience only and do not in any manner serve as an endorsement of those Web sites. The materials at those Web sites are not part of the materials for this IBM product and use of those Web sites is at your own risk.

TABLE OF CONTENTS

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Table of Contents LESSON 0: COURSE INTRODUCTION ………………………………………….. 0-1

LESSON 1: INTRODUCTION TO STATISTICAL ANALYSIS …………. 1-1

LESSON 2: UNDERSTANDING DATA DISTRIBUTIONS – THEORY 2-1

LESSON 3: DATA DISTRIBUTIONS FOR CATEGORICAL VARIABLES ……………………………………………………………………………….. 3-1

0.1 INTRODUCTION ……………………………………………………………………………………………………. 0-1 0.2 COURSE OBJECTIVES ……………………………………………………………………………………………. 0-1 0.3 ABOUT SPSS ………………………………………………………………………………………………………. 0-1 0.4 SUPPORTING MATERIALS ……………………………………………………………………………………… 0-2 0.5 COURSE ASSUMPTIONS ………………………………………………………………………………………… 0-2

1.1 OBJECTIVES ………………………………………………………………………………………………………… 1-1 1.2 INTRODUCTION ……………………………………………………………………………………………………. 1-1 1.3 BASIC STEPS OF THE RESEARCH PROCESS ………………………………………………………………. 1-1 1.4 POPULATIONS AND SAMPLES ………………………………………………………………………………… 1-3 1.5 RESEARCH DESIGN ………………………………………………………………………………………………. 1-3 1.6 INDEPENDENT AND DEPENDENT VARIABLES …………………………………………………………… 1-4 1.7 NOTE ABOUT DEFAULT STARTUP FOLDER AND VARIABLE DISPLAY IN DIALOG BOXES .. 1-4 1.8 LESSON SUMMARY ………………………………………………………………………………………………. 1-5 1.9 LEARNING ACTIVITY ……………………………………………………………………………………………. 1-6

2.1 OBJECTIVES ………………………………………………………………………………………………………… 2-1 INTRODUCTION …………………………………………………………………………………………………………. 2-1 2.2 LEVELS OF MEASUREMENT AND STATISTICAL METHODS …………………………………………. 2-1 2.3 MEASURES OF CENTRAL TENDENCY AND DISPERSION …………………………………………….. 2-5 2.4 NORMAL DISTRIBUTIONS ……………………………………………………………………………………… 2-7 2.5 STANDARDIZED (Z-) SCORES ………………………………………………………………………………… 2-8 2.6 REQUESTING STANDARDIZED (Z-) SCORES……………………………………………………………. 2-10 2.7 STANDARDIZED (Z-) SCORES OUTPUT ………………………………………………………………….. 2-10 2.8 PROCEDURE: DESCRIPTIVES FOR STANDARDIZED (Z-) SCORES ……………………………….. 2-10 2.9 DEMONSTRATION: DESCRIPTIVES FOR Z-SCORES…………………………………………………… 2-11 2.10 LESSON SUMMARY …………………………………………………………………………………………… 2-12 2.11 LEARNING ACTIVITY ………………………………………………………………………………………… 2-13

3.1 OBJECTIVES ………………………………………………………………………………………………………… 3-1 3.2 INTRODUCTION ……………………………………………………………………………………………………. 3-1 3.3 USING FREQUENCIES TO SUMMARIZE NOMINAL AND ORDINAL VARIABLES ……………….. 3-2 3.4 REQUESTING FREQUENCIES ………………………………………………………………………………….. 3-3 3.5 FREQUENCIES OUTPUT …………………………………………………………………………………………. 3-3 3.6 PROCEDURE: FREQUENCIES ………………………………………………………………………………….. 3-4 3.7 DEMONSTRATION: FREQUENCIES …………………………………………………………………………… 3-6 3.8 LESSON SUMMARY …………………………………………………………………………………………….. 3-10 3.9 LEARNING ACTIVITY ………………………………………………………………………………………….. 3-10

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LESSON 4: DATA DISTRIBUTIONS FOR SCALE VARIABLES ……… 4-1

LESSON 5: MAKING INFERENCES ABOUT POPULATIONS FROM SAMPLES ……………………………………………………………………………….. 5-1

LESSON 6: RELATIONSHIPS BETWEEN CATEGORICAL VARIABLES ………………………………………………………………………………. 6-1

4.1 OBJECTIVES ………………………………………………………………………………………………………… 4-1 4.2 INTRODUCTION ……………………………………………………………………………………………………. 4-1 4.3 SUMMARIZING SCALE VARIABLES USING FREQUENCIES …………………………………………… 4-1 4.4 REQUESTING FREQUENCIES …………………………………………………………………………………… 4-2 4.5 FREQUENCIES OUTPUT …………………………………………………………………………………………. 4-2 4.6 PROCEDURE: FREQUENCIES …………………………………………………………………………………… 4-4 4.7 DEMONSTRATION: FREQUENCIES …………………………………………………………………………… 4-6 4.8 SUMMARIZING SCALE VARIABLES USING DESCRIPTIVES…………………………………………. 4-11 4.9 REQUESTING DESCRIPTIVES ………………………………………………………………………………… 4-11 4.10 DESCRIPTIVES OUTPUT ……………………………………………………………………………………… 4-11 4.11 PROCEDURE: DESCRIPTIVES ………………………………………………………………………………. 4-11 4.12 DEMONSTRATION: DESCRIPTIVES……………………………………………………………………….. 4-12 4.13 SUMMARIZING SCALE VARIABLES USING THE EXPLORE PROCEDURE ……………………… 4-13 4.14 REQUESTING EXPLORE ……………………………………………………………………………………… 4-13 4.15 PROCEDURE: EXPLORE ……………………………………………………………………………………… 4-16 4.16 DEMONSTRATION: EXPLORE ………………………………………………………………………………. 4-19 4.17 LESSON SUMMARY …………………………………………………………………………………………… 4-24 4.18 LEARNING ACTIVITY ………………………………………………………………………………………… 4-25

5.1 OBJECTIVES ………………………………………………………………………………………………………… 5-1 5.2 INTRODUCTION ……………………………………………………………………………………………………. 5-1 5.3 BASICS OF MAKING INFERENCES ABOUT POPULATIONS FROM SAMPLES …………………….. 5-1 5.4 INFLUENCE OF SAMPLE SIZE ………………………………………………………………………………….. 5-2 5.5 HYPOTHESIS TESTING …………………………………………………………………………………………. 5-10 5.6 THE NATURE OF PROBABILITY …………………………………………………………………………….. 5-11 5.7 TYPES OF STATISTICAL ERRORS …………………………………………………………………………… 5-11 5.8 STATISTICAL SIGNIFICANCE AND PRACTICAL IMPORTANCE …………………………………….. 5-12 5.9 LESSON SUMMARY …………………………………………………………………………………………….. 5-13 5.10 LEARNING ACTIVITY ………………………………………………………………………………………… 5-13

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LESSON 7: THE INDEPENDENT- SAMPLES T TEST …………………….. 7-1

LESSON 8: THE PAIRED-SAMPLES T TEST …………………………………. 8-1

6.1 OBJECTIVES ………………………………………………………………………………………………………… 6-1 6.2 INTRODUCTION ……………………………………………………………………………………………………. 6-1 6.3 CROSSTABS…………………………………………………………………………………………………………. 6-2 6.4 CROSSTABS ASSUMPTIONS……………………………………………………………………………………. 6-3 6.5 REQUESTING CROSSTABS ……………………………………………………………………………………… 6-3 6.6 CROSSTABS OUTPUT ……………………………………………………………………………………………. 6-3 6.7 PROCEDURE: CROSSTABS ……………………………………………………………………………………… 6-4 6.8 EXAMPLE: CROSSTABS …………………………………………………………………………………………. 6-5 6.9 CHI-SQUARE TEST ……………………………………………………………………………………………….. 6-7 6.10 REQUESTING THE CHI-SQUARE TEST ……………………………………………………………………. 6-8 6.11 CHI-SQUARE OUTPUT …………………………………………………………………………………………. 6-8 6.12 PROCEDURE: CHI-SQUARE TEST ………………………………………………………………………….. 6-9 6.13 EXAMPLE: CHI-SQUARE TEST ……………………………………………………………………………. 6-10 6.14 CLUSTERED BAR CHART …………………………………………………………………………………… 6-11 6.15 REQUESTING A CLUSTERED BAR CHART WITH CHART BUILDER ……………………………. 6-12 6.16 CLUSTERED BAR CHART FROM CHART BUILDER OUTPUT …………………………………….. 6-12 6.17 PROCEDURE: CLUSTERED BAR CHART WITH CHART BUILDER ………………………………. 6-13 6.18 EXAMPLE: CLUSTERED BAR CHART WITH CHART BUILDER ………………………………….. 6-15 6.19 ADDING A CONTROL VARIABLE …………………………………………………………………………. 6-16 6.20 REQUESTING A CONTROL VARIABLE ………………………………………………………………….. 6-17 6.21 CONTROL VARIABLE OUTPUT ……………………………………………………………………………. 6-17 6.22 PROCEDURE: ADDING A CONTROL VARIABLE ……………………………………………………… 6-18 6.23 EXAMPLE: ADDING A CONTROL VARIABLE …………………………………………………………. 6-19 6.24 EXTENSIONS: BEYOND CROSSTABS ……………………………………………………………………. 6-22 6.25 ASSOCIATION MEASURES ………………………………………………………………………………….. 6-23 6.26 LESSON SUMMARY …………………………………………………………………………………………… 6-23 6.27 LEARNING ACTIVITY ………………………………………………………………………………………… 6-24

7.1 OBJECTIVES ………………………………………………………………………………………………………… 7-1 7.2 INTRODUCTION ……………………………………………………………………………………………………. 7-1 7.3 THE INDEPENDENT-SAMPLES T TEST …………………………………………………………………….. 7-1 7.4 INDEPENDENT-SAMPLES T TEST ASSUMPTIONS ………………………………………………………. 7-2 7.5 REQUESTING THE INDEPENDENT-SAMPLES T TEST ………………………………………………….. 7-2 7.6 INDEPENDENT-SAMPLES T TEST OUTPUT ……………………………………………………………….. 7-3 7.7 PROCEDURE: INDEPENDENT-SAMPLES T TEST ………………………………………………………… 7-5 7.8 DEMONSTRATION: INDEPENDENT-SAMPLES T TEST …………………………………………………. 7-6 7.9 ERROR BAR CHART ……………………………………………………………………………………………. 7-10 7.10 REQUESTING AN ERROR BAR CHART WITH CHART BUILDER …………………………………. 7-11 7.11 ERROR BAR CHART OUTPUT ……………………………………………………………………………… 7-11 7.12 DEMONSTRATION: ERROR BAR CHART WITH CHART BUILDER ……………………………… 7-12 7.13 LESSON SUMMARY …………………………………………………………………………………………… 7-14 7.14 LEARNING ACTIVITY ………………………………………………………………………………………… 7-14

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LESSON 9: ONE-WAY ANOVA ……………………………………………………… 9-1

LESSON 10: BIVARIATE PLOTS AND CORRELATIONS FOR SCALE VARIABLES ……………………………………………………………………………… 10-1

8.1 OBJECTIVES ………………………………………………………………………………………………………… 8-1 8.2 INTRODUCTION ……………………………………………………………………………………………………. 8-1 8.3 THE PAIRED-SAMPLES T TEST ……………………………………………………………………………….. 8-1 8.4 ASSUMPTIONS FOR THE PAIRED-SAMPLES T TEST ……………………………………………………. 8-2 8.5 REQUESTING A PAIRED-SAMPLES T TEST ……………………………………………………………….. 8-3 8.6 PAIRED-SAMPLES T TEST OUTPUT …………………………………………………………………………. 8-3 8.7 PROCEDURE: PAIRED-SAMPLES T TEST …………………………………………………………………… 8-4 8.8 DEMONSTRATION: PAIRED-SAMPLES T TEST …………………………………………………………… 8-4 8.9 LESSON SUMMARY ………………………………………………………………………………………………. 8-6 8.10 LEARNING ACTIVITY ………………………………………………………………………………………….. 8-6

9.1 OBJECTIVES ………………………………………………………………………………………………………… 9-1 9.2 INTRODUCTION ……………………………………………………………………………………………………. 9-1 9.3 ONE-WAY ANOVA ……………………………………………………………………………………………….. 9-1 9.4 ASSUMPTIONS OF ONE-WAY ANOVA ……………………………………………………………………. 9-2 9.5 REQUESTING ONE-WAY ANOVA ………………………………………………………………………….. 9-2 9.6 ONE-WAY ANOVA OUTPUT …………………………………………………………………………………. 9-3 9.7 PROCEDURE: ONE-WAY ANOVA ………………………………………………………………………….. 9-4 9.8 DEMONSTRATION: ONE-WAY ANOVA ………………………………………………………………….. 9-6 9.9 POST HOC TESTS WITH A ONE-WAY ANOVA …………………………………………………………. 9-8 9.10 REQUESTING POST HOC TESTS WITH A ONE-WAY ANOVA ……………………………………. 9-9 9.11 POST HOC TESTS OUTPUT……………………………………………………………………………………. 9-9 9.12 PROCEDURE: POST HOC TESTS WITH A ONE-WAY ANOVA…………………………………… 9-10 9.13 DEMONSTRATION: POST HOC TESTS WITH A ONE-WAY ANOVA …………………………… 9-12 9.14 ERROR BAR CHART WITH CHART BUILDER …………………………………………………………. 9-14 9.15 REQUESTING AN ERROR BAR CHART WITH CHART BUILDER …………………………………. 9-14 9.16 ERROR BAR CHART OUTPUT ……………………………………………………………………………… 9-14 9.17 PROCEDURE: ERROR BAR CHART WITH CHART BUILDER ………………………………………. 9-15 9.18 DEMONSTRATION: ERROR BAR CHART WITH CHART BUILDER ………………………………. 9-16 9.19 LESSON SUMMARY …………………………………………………………………………………………… 9-18 9.20 LEARNING ACTIVITY ………………………………………………………………………………………… 9-18

10.1 OBJECTIVES …………………………………………………………………………………………………….. 10-1 10.2 INTRODUCTION ………………………………………………………………………………………………… 10-1 10.3 SCATTERPLOTS ………………………………………………………………………………………………… 10-1 10.4 REQUESTING A SCATTERPLOT ……………………………………………………………………………. 10-2 10.5 SCATTERPLOT OUTPUT ……………………………………………………………………………………… 10-3 10.6 PROCEDURE: SCATTERPLOT ………………………………………………………………………………. 10-3 10.7 DEMONSTRATION: SCATTERPLOT ……………………………………………………………………….. 10-4 10.8 ADDING A BEST FIT STRAIGHT LINE TO THE SCATTERPLOT …………………………………… 10-5 10.9 PEARSON CORRELATION COEFFICIENT………………………………………………………………… 10-7 10.10 REQUESTING A PEARSON CORRELATION COEFFICIENT ………………………………………… 10-8 10.11 BIVARIATE CORRELATION OUTPUT …………………………………………………………………… 10-8 10.12 PROCEDURE: PEARSON CORRELATION WITH BIVARIATE CORRELATIONS ………………. 10-9 10.13 DEMONSTRATION: PEARSON CORRELATION WITH BIVARIATE CORRELATIONS …….. 10-10 10.14 LESSON SUMMARY ……………………………………………………………………………………….. 10-11 10.15 LEARNING ACTIVITY …………………………………………………………………………………….. 10-12

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LESSON 11: REGRESSION ANALYSIS ………………………………………… 11-1

LESSON 12: NONPARAMETRIC TESTS ………………………………………. 12-1

LESSON 13: COURSE SUMMARY ……………………………………………….. 13-1

APPENDIX A: INTRODUCTION TO STATISTICAL ANALYSIS REFERENCES 1

11.1 OBJECTIVES …………………………………………………………………………………………………….. 11-1 11.2 INTRODUCTION ………………………………………………………………………………………………… 11-1 11.3 SIMPLE LINEAR REGRESSION …………………………………………………………………………….. 11-1 11.4 SIMPLE LINEAR REGRESSION ASSUMPTIONS ……………………………………………………….. 11-3 11.5 REQUESTING SIMPLE LINEAR REGRESSION …………………………………………………………. 11-4 11.6 SIMPLE LINEAR REGRESSION OUTPUT ………………………………………………………………… 11-4 11.7 PROCEDURE: SIMPLE LINEAR REGRESSION …………………………………………………………. 11-5 11.8 DEMONSTRATION: SIMPLE LINEAR REGRESSION ………………………………………………….. 11-7 11.9 MULTIPLE REGRESSION…………………………………………………………………………………… 11-11 11.10 MULTIPLE LINEAR REGRESSION ASSUMPTIONS ……………………………………………….. 11-11 11.11 REQUESTING MULTIPLE LINEAR REGRESSION………………………………………………….. 11-11 11.12 MULTIPLE LINEAR REGRESSION OUTPUT ………………………………………………………… 11-11 11.13 PROCEDURE: MULTIPLE LINEAR REGRESSION ………………………………………………….. 11-14 11.14 DEMONSTRATION: MULTIPLE LINEAR REGRESSION ………………………………………….. 11-16 11.15 LESSON SUMMARY ……………………………………………………………………………………….. 11-22 11.16 LEARNING ACTIVITY …………………………………………………………………………………….. 11-22

12.1 OBJECTIVES …………………………………………………………………………………………………….. 12-1 12.2 INTRODUCTION ………………………………………………………………………………………………… 12-1 12.3 NONPARAMETRIC ANALYSES …………………………………………………………………………….. 12-2 12.4 THE INDEPENDENT SAMPLES NONPARAMETRIC ANALYSIS …………………………………… 12-2 12.5 REQUESTING AN INDEPENDENT SAMPLES NONPARAMETRIC ANALYSIS ………………….. 12-3 12.6 INDEPENDENT SAMPLES NONPARAMETRIC TESTS OUTPUT …………………………………… 12-3 12.7 PROCEDURE: INDEPENDENT SAMPLES NONPARAMETRIC TESTS …………………………….. 12-5 12.8 DEMONSTRATION: INDEPENDENT SAMPLES NONPARAMETRIC TESTS …………………….. 12-8 12.9 THE RELATED SAMPLES NONPARAMETRIC ANALYSIS ………………………………………… 12-11 12.10 REQUESTING A RELATED SAMPLES NONPARAMETRIC ANALYSIS ……………………….. 12-12 12.11 RELATED SAMPLES NONPARAMETRIC TESTS OUTPUT ………………………………………. 12-12 12.12 PROCEDURE: RELATED SAMPLES NONPARAMETRIC TESTS ……………………………….. 12-13 12.13 DEMONSTRATION: RELATED SAMPLES NONPARAMETRIC TESTS ………………………… 12-16 12.14 LESSON SUMMARY ……………………………………………………………………………………….. 12-19 12.15 LEARNING ACTIVITY …………………………………………………………………………………….. 12-20

13.1 COURSE OBJECTIVES REVIEW ……………………………………………………………………………. 13-1 13.2 COURSE REVIEW: DISCUSSION QUESTIONS …………………………………………………………. 13-1 13.3 NEXT STEPS …………………………………………………………………………………………………….. 13-2

1.1 INTRODUCTION …………………………………………………………………………………………………… A-1 1.2 REFERENCES ………………………………………………………………………………………………………. A-1

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COURSE INTRODUCTION

0-1

Lesson 0: Course Introduction 0.1 Introduction The focus of this two-day course is an introduction to the statistical component of IBM® SPSS® Statistics. This is an application-oriented course and the approach is practical. You'll take a look at several statistical techniques and discuss situations in which you would use each technique, the assumptions made by each method, how to set up the analysis using PASW®

0.2 Course Objectives

Statistics, as well as how to interpret the results. This includes a broad range of techniques for exploring and summarizing data, as well as investigating and testing underlying relationships. You will gain an understanding of when and why to use these various techniques as well as how to apply them with confidence, and interpret their output, and graphically display the results.

After completing this course students will be able to:

• Perform basic statistical analysis using selected statistical techniques with PASW Statistics To support the achievement of this primary objective, students will also be able to:

• Explain the basic elements of quantitative research and issues that should be considered in data analysis

• Determine the level of measurement of variables and obtain appropriate summary statistics based on the level of measurement

• Run the Frequencies procedure to obtain appropriate summary statistics for categorical variables

• Request and interpret appropriate summary statistics for scale variables • Explain how to make inferences about populations from samples • Perform crosstab analysis on categorical variables • Perform a statistical test to determine whether there is a statistically significant relationship

between categorical variables • Perform a statistical test to determine whether there is a statistically significant difference

between two groups on a scale variable • Perform a statistical test to determine whether there is a statistically significant difference

between the means of two scale variables • Perform a statistical test to determine whether there is a statistically significant difference

among three or more groups on a scale dependent variable • Perform a statistical test to determine whether two scale variables are correlated (related) • Perform linear regression to determine whether one or more variables can significantly

predict or explain a dependent variable • Perform non-parametric tests on data that don’t meet the assumptions for standard statistical

tests

0.3 About SPSS SPSS® Inc., an IBM® Company is a leading global provider of predictive analytics software and solutions. The Company’s complete portfolio of products – data collection, statistics, modeling and deployment – captures people's attitudes and opinions, predicts outcomes of future customer interactions, and then acts on these insights by embedding analytics into business processes. SPSS solutions address interconnected business objectives across an entire organization by focusing on the convergence of analytics, IT architecture and business process. Commercial, government and academic customers worldwide rely on SPSS technology as a competitive advantage in attracting,

INTRODUCTION TO STATISTICAL ANALYSIS WITH IBM SPSS STATISTICS

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retaining and growing customers, while reducing fraud and mitigating risk. SPSS was acquired by IBM®

0.4 Supporting Materials

in October 2009. For more information, visit http://www.spss.com.

We use several datasets in the course because no one data file contains all the types of variables and relationships between them that are ideal for every technique we discuss. As much as possible, we try to minimize the need within one lesson to switch between datasets, but the first priority is to use appropriate data for each method. The following data files are used in this course:

• Bank.sav • Drinks.sav • Census.sav • Employee data.sav • SPSS_CUST.sav

0.5 Course Assumptions General computer literacy. Completion of the "Introduction to PASW Statistics" and/or "Data Management and Manipulation with PASW Statistics" courses or experience with PASW Statistics including familiarity with, opening, defining, and saving data files and manipulating and saving output. Basic statistical knowledge or at least one introductory level course in statistics is recommended.

Note about Default Startup Folder and Variable Display in Dialog Boxes In this course, all of the files used for the demonstrations and exercises are located in the folder c:TrainStatistics_IntroAnalysis. Note: If the course files are stored in a different location, your instructor will give you instructions specific to that location. Either variable names or longer variable labels will appear in list boxes in dialog boxes. Additionally, variables in list boxes can be ordered alphabetically or by their position in the file. In this course, we will display variable names in alphabetical order within list boxes.

1) Select Edit…Options 2) Select the General tab (if necessary) 3) Select Display names in the Variable Lists group on the General tab 4) Select Alphabetical 5) Select OK and OK in the information box to confirm the change

INTRODUCTION TO STATISTICAL ANALYSIS

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Lesson 1: Introduction to Statistical Analysis 1.1 Objectives After completing this lesson students will be able to:

• Explain the basic elements of quantitative research and issues that should be considered in data analysis

To support the ac

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