Statistics and Data Interpretation for Social Work
Published on 16. December 2011
Book
Paperback/Softback
512 pages
978-0-8261-0720-6 (ISBN)
Description
Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice.
The first section introduces basic concepts and terms to provide a solid foundation in statistics. It also addresses tools used by researchers to describe and summarize data ranging from single variables to assessing the relationship between variables and cause and effect among variables. The second section focuses on inferential statistics, describing how researchers draw conclusions about whole populations based on data from samples. This section also covers confidence intervals and a variety of significance tests for examining relationships between different types of variables. Additionally, tools for multivariate analyses and data interpretation are presented.
Key Features:
Addresses the role of statistics in evidence-based practice and program evaluation Features examples of qualitative and quantitative analysis Each chapter contains exercise problems and questions to enhance student learning Includes electronic data sets taken from actual social work arenas Offers a full ancillary digital packet including a student guide to SPSS with accompanying Data Set, an Instructor's Manual, PowerPoint slides, and a Test Bank
The first section introduces basic concepts and terms to provide a solid foundation in statistics. It also addresses tools used by researchers to describe and summarize data ranging from single variables to assessing the relationship between variables and cause and effect among variables. The second section focuses on inferential statistics, describing how researchers draw conclusions about whole populations based on data from samples. This section also covers confidence intervals and a variety of significance tests for examining relationships between different types of variables. Additionally, tools for multivariate analyses and data interpretation are presented.
Key Features:
Addresses the role of statistics in evidence-based practice and program evaluation Features examples of qualitative and quantitative analysis Each chapter contains exercise problems and questions to enhance student learning Includes electronic data sets taken from actual social work arenas Offers a full ancillary digital packet including a student guide to SPSS with accompanying Data Set, an Instructor's Manual, PowerPoint slides, and a Test Bank
More details
Language
English
Place of publication
New York
United States
Target group
College/higher education
Professional and scholarly
Illustrations
50 illustrations; 50 Illustrations
Dimensions
Height: 254 mm
Width: 178 mm
ISBN-13
978-0-8261-0720-6 (9780826107206)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Jim A. Rosenthal, PhD, is a professor at the University of Oklahoma School of Social Work and Coordinator of the Graduate Program.
Content
STATISTICS AND DATA INTERPRETATION FOR SOCIAL WORK
TABLE OF CONTENTS
PART ONE: INTRODUCTION AND DESCRIPTIVE STATISTICS
CHAPTER 1
INTRODUCTION AND OVERVIEW
1. 1 CHAPTER OVERVIEW
1.2 STATISTICS AND SOCIAL WORK
1.3 SCIENCE AND RESEARCH
1.4 VARIABLES AND MEASUREMENT
1.5 SAMPLES AND POPULATIONS
1.6 DESCRIPTIVE AND INFERENTIAL STATISTICS
1.7 UNIVARIATE, BIVARIATE, AND MULTIVARIATE STATISTICS
1.8 RANDOM ASSIGNMENT
1.9 LEVELS OF MEASUREMENT
1.9.1 Basics
1.9.2 Fine Points
1.10 CHAPTER SUMMARY
1.11 PROBLEMS AND QUESTIONS
CHAPTER 2
DATA PRESENTATION
2.1 CHAPTER OVERVIEW
2.2 FREQUENCY DISTRIBUTIONS AND TABLES
2.3 FIGURES
2.4 CHAPTER SUMMARY
2.5 PROBLEMS AND QUESTIONS
CHAPTER 3
CENTRAL TENDENCY
3.1 CHAPTER OVERVIEW
3.2 KEY CONCEPTS IN UNIVARIATE DESCRIPTIVE STATISTICS
3.3 THREE KEY MEASURES OF CENTRAL TENDENCY
3.4 THE MODE
3.5 THE MEDIAN
3.6 THE MEAN
3.7 CHOOSING BETWEEN MEASURES
3.8 CHAPTER SUMMARY
3.9 PROBLEMS AND QUESTIONS
CHAPTER 4
MEASURES OF VARIABILITY
4.1 CHAPTER OVERVIEW
4.2 THE CONCEPT OF VARIABILITY
4.3 ASSESSING THE VARIABILITY OF CATEGORICAL VARIABLES
4.4 THE RANGE
4.5 THE INTERQUARTILERANGE
4.6 THE MEAN DEVIATION
4.7 THE STANDARD DEVIATION
4.8 THE VARIANCE
4.9 CHAPTER SUMMARY
4.10 PROBLEMS AND QUESTIONS
CHAPTER 5
SHAPE OF DISTRIBUTION
5.1 CHAPTER OVERVIEW
5.2 THE NORMAL DISTRIBUTION
5.3 SKEWED DISTRIBUTIONS
5.3.1 Characteristics
5.3.2 Skewness and Measures of Central Tendency
5.4 KURTOSIS
5.5 UNIFORM AND BIMODAL DISTRIBUTIONS
5.6 PERCENTAGES AND THE NORMAL DISTRIBUTION
5.7 INTRODUCTION TO Z SCORES
5.7.1 z Score Calculation
5.7.2 Basics of z Scores
5.7.3 Uses of z Scores
5.8 z SCORES AND THE NORMAL DISTRIBUTION
5.8.1 Problems about Percentages of Cases
5.8.2 Reminders and Cautions
5.9 CHAPTER SUMMARY
5.10 PROBLEMS AND QUESTIONS
CHAPTER 6
THE CONCEPT OF RELATIONSHIP AND RELATIONSHIP BETWEEN CATEGORICAL VARIABLES
6.1 CHAPTER OVERVIEW
6.2 DEFINITION OF RELATIONSHIP
6.3 COMMENTS ON RELATIONSHIP
6.4 CONTINGENCY TABLES AND CATEGORICAL VARIABLES
6.4.1 Reading a Contingency (Crosstabs) Table
6.4.2 Assessing Relationship Using a Contingency Table
6.5 SIZE OF ASSOCIATION
6.6 DIFFERENCE IN PERCENTAGES (D%)
6.7 QUALITATIVE DESCRIPTORS OF SIZE OF ASSOCIATION
6.8 RISK RATIO (RR)
6.9 DIFFERENCE IN PERCENTAGES OR RISK RATIO?
6.10 CHAPTER SUMMARY
6.11 PROBLEMS AND QUESTIONS
CHAPTER 7
THE ODDS RATIO AND OTHER MEASURES FOR CATEGORICAL VARIABLES
7.1 Chapter Overview
7.2 ODDS RATIO (OR):
7.2.1 Basics and Formula
7.2.2 Interpretation
7.2.3 Advantages
7.3 RELATIONSHIP IN CONTINGENCY TABLES LARGER THAN 2 ? 2
7.4 DIRECTIONAL RELATIONSHIP
7.5 MEASURE OF DIRECTIONAL ASSOCIATION BETWEEN CATEGORICAL VARIABLES.
7.6 CHAPTER SUMMARY
7.7 PROBLEMS AND QUESTIONS
CHAPTER 8
CORRELATION AND REGRESSION
8.1 CHAPTER OVERVIEW
8.2 POSITIVE AND NEGATIVE CORRELATION
8.3 SCATTERPLOTS
8.4 FORMULA FOR THE CORRELATION COEFFICIENT, r
8.5 UNDERSTANDING r
8.6 INTERPRETATIONS USING r AND z SCORES
8.6.1 Predictions with z Scores
8.6.2 Predicted Change in Standard Deviation Units
8.7 CURVILINEAR RELATIONSHIP
8.8 A CAUTION IN INTERPRETING r
8.9 REGRESSION
8.9.1 Regression Equation and Regression Line
8.9.2 Contrast between r and B
8.10 CORRELATION FOR NOMINAL AND ORDINAL-LEVEL VARIABLES
8.11 CHAPTER SUMMARY
8.12 PROBLEMS AND QUESTIONS
CHAPTER 9
STANDARDIZED MEAN DIFFERENCE
9.1 CHAPTER OVERVIEW
9.2 INTRODUCTION TO THE SMD
9.3 GRAPHICAL INTERPRETATION OF THE SMD
9.4 A CAUTION REGARDING THE SMD
9.5 MORE MEASURES OF DIFFERENCES BETWEEN TWO MEANS
9.6 DIFFERENCES BETWEEN THREE OR MORE MEANS
9.7 CHAPTER SUMMARY
9.8 PROBLEMS AND QUESTIONS
CHAPTER 10
RESEARCH DESIGN AND CAUSALITY
10.1 CHAPTER OVERVIEW
10.2 INTRODUCTION TO CAUSALITY
10.3 WHAT DOES "CAUSE" MEAN IN SOCIAL SCIENCE?
10.4 CONFOUNDING VARIABLES
10.5 EXPERIMENTAL AND SURVEY DESIGNS
10.5.1 Experiments vs. Surveys
10.5.2 Random Assignment to Groups
10.6 RANDOM ASSIGNMENT AND CAUSALITY
10.7 CHAPTER SUMMARY
10.8 PROBLEMS AND QUESTIONS
CHAPTER 11
CONTROLLING FOR CONFOUNDING VARIABLES
11.1 CHAPTER OVERVIEW
11.2 CONTROLLING FOR A VARIABLE
11.2.1 Basic Concepts
11.2.2 Different Patterns Following Control
11.2.3 Initial Relationship Persists
11.2.4 Initial Relationship Weakens
11.2.5 Initial Relationship Disappears
11.3 CAUSAL MODELS AND ADDITIONAL CONSIDERATIONS
11.4 CONTROL FOR MULTIPLE VARIABLES AND CAUSALITY
11.5 INTERACTION EFFECTS
11.6 CHAPTER SUMMARY
11.7 PROBLEMS AND QUESTIONS
PART 2: INFERENTIAL STATISTICS AND DATA INTERPRETATION
CHAPTER 12
AN INTRODUCTION TO INFERENTIAL STATISTICS
12.1 CHAPTER OVERVIEW
12.2 DESCRIPTIVE VERSUS INFERENTIAL STATISTICS
12.3 CHARACTERISTICS OF RANDOM SAMPLES
12.4 THE ADVANTAGE OF RANDOM SAMPLES
12.5 STATISTICS AND PARAMETERS
12.6 CHARACTERISTICS OF ESTIMATORS
12.7 SAMPLING ERROR AND SAMPLING DISTRIBUTIONS
12.7.1 Concepts
12.7.2 Sampling Distribution of the Mean.
12.8 SAMPLE SIZE AND THE SAMPLING DISTRIBUTION OF
12.9 CHAPTER SUMMARY
12.10 PROBLEMS AND QUESTIONS
CHAPTER 13
CONFIDENCE INTERVALS FOR MEANS AND PROPORTIONS
13.1 CHAPTER OVERVIEW
13.2. WHAT IS A CONFIDENCE INTERVAL?
13.3 CONFIDENCE INTERVALS FOR MEANS
13.3.1 Theory
13.3.2 Formulas and Computation
13.4 CONFIDENCE INTERVALS FOR PROPORTIONS AND PERCENTAGES
13.4.1 Theory
13.4.2 Formulae and Application
13.5 FIVE MORE THINGS TO KNOW
13.5 CHAPTER SUMMARY
13.6 PROBLEMS AND QUESTIONS
CHAPTER 14
THE LOGIC OF STATISTICAL SIGNIFICANCE TESTS
14.1 CHAPTER OVERVIEW
14.2 INTRODUCTION TO SIGNIFICANCE TESTING
14.3 PROBABILITY
14.3.1 Definition and Formula
14.3.2 Probability and the Normal Distribution
14.4 NULL AND RESEARCH HYPOTHESES
14.5 A COMMON PATTERN FOR HYPOTHESIS PAIRS
14.6 DIRECTIONAL AND NONDIRECTIONAL HYPOTHESIS PAIRS
14.6.1 Definitions and Examples
14.6.2 Guidelines for Usage
14.7 SAMPLING ERROR AND THE NULL HYPOTHESIS
14.8 STATISTICAL SIGNIFICANCE LEVELS
14.9 EXAMPLES OF STATISTICAL SIGNIFICANCE TESTING
14.9.1 An Example in Which We Reject the Null
14.9.2 An Example in Which We Fail to Reject (Accept) the Null
14.9.3 More interpretations of p
14.9.4 What Does it Mean to Reject the Null?
14.9.5 What Does It Mean to Fail to Reject (Accept) the Null?
14.10 NULL AND ALTERNATIVE HYPOTHESES AND SCIENTIFIC INQUIRY
14.11 WHAT IS A STATISTICALLY SIGNIFICANT RESULT?
14.12 CHAPTER SUMMARY
14.13 PROBLEMS AND QUESTIONS
CHAPTER 15
THE LARGE SAMPLE TEST OF THE MEAN AND NEW CONCEPTS
15.1 CHAPTER OVERVIEW
15.2 A MODEL FOR HYPOTHESIS TESTING
15.3 ASSUMPTIONS OF STATISTICAL SIGNIFICANCE TESTS
15.3.1 Definition and Assumptions of the Large Sample Test of
15.3.2 Assumptions Common to All Tests
15. 4 THE FIRST TWO STEPS OF THE HYPOTHESIS TESTING MODEL
15.5 STATISTICAL TESTS AND SAMPLING DISTRIBUTIONS
15.6 DIFFERENCES: DIRECTIONAL VS. NONDIRECTIONAL HYPOTHESIS PAIRS
15.6.1 Overview
15.6.2 Nondirectional Hypothesis Pair:
15.6.3 Directional Hypothesis Pair:
15.7 CARRYING OUT THE SIGNIFICANCE TEST USING THE SAMPLING DISTRIBUTION
15.8 FINISHING THE EXAMPLE USING THE FORMULA
15.8.1 Step 3: Carry Out the Test
15.8.2 Decision Rules
15.8.3 Step 4: Make a Decision
15.9 EFFECT OF CHOICE OF SIGNIFICANCE LEVEL ON DECISION MAKING
15.10 TYPE I AND TYPE II ERRORS
15.11 TWO-TAILED VS. ONE-TAILED TESTS
15.11.1 Carrying out our Example
15.11.2 Determining the Exact Value of the Study Sample Result (p)
15.12 MORE DECISION RULES FOR THE ONE-TAILED, LARGE SAMPLE TEST OF
15.13 REJECTING THE NULL AND "REAL" THINGS
15.15 CHAPTER SUMMARY
15.16 PROBLEMS AND QUESTIONS
CHAPTER 16
STATISTICAL POWER AND SELECTED TOPICS
16.1 CHAPTER OVERVIEW
16.2 DEFINITION OF POWER
16.3 SAMPLE SIZE AND POWER
16.4 EXAMPLES OF HOW SAMPLE SIZE AFFECTS POWER
16.4.1 The Parenting Skills Example
16.4.2 More Examples of Sample Size and Power
16.5 FACTORS OTHER THAN SAMPLE SIZE THAT INFLUENCE POWER
16.5.1 Overview
16.5.2 Size of Relationship or Difference in the Population
16.5.3 Reduced Variability of Independent or Dependent Variable
16.5.4 Control for Third Variables
16.5.5 Significance Level
16.5.6 Directional Hypotheses and One-tailed Tests
16.5.7 Statistical Significance Test
16.6 HOW MUCH POWER IS ENOUGH?
16.7 HOW LARGE SHOULD SAMPLE SIZE BE?
16.8 NONRANDOM SAMPLES AND SIGNIFICANCE TESTS
16.9 REPORTING STATISTICAL SIGNIFICANCE
16.10 WHAT STATISTICAL SIGNIFICANCE IS (AND IS NOT)
16.11 CHAPTER SUMMARY
16.12 PROBLEMS AND QUESTIONS
CHAPTER 17
THE t DISTRIBUTION AND ONE-SAMPLE PROCEDURES FOR MEANS
17.1 CHAPTER OVERVIEW
17.2 SMALL SAMPLE SIZE AND DISTRIBUTIONS
17.3 DEGREES OF FREEDOM
17.4 THE FAMILY OF t DISTRIBUTIONS
17.5 CONFIDENCE INTERVALS FOR MEANS FOR SMALL SAMPLES (AND LARGE)
17.6 INTRODUCTION TO THE ONE-SAMPLE t TEST
17.6.1 Assumptions, Hypothesis Pairs, and Formula
17.6.2 Decision Rules
17.7 CARRYING OUT THE ONE-SAMPLE t TEST
17.8 CHAPTER SUMMARY
17.9 PROBLEMS AND QUESTIONS
CHAPTER 18
INDEPENDENT SAMPLES t TEST AND DEPENDENT SAMPLES t TEST
18.1 CHAPTER OVERVIEW
18.2 INTRODUCTION TO THE INDEPENDENT SAMPLES t TEST
18.2.1 Purpose and Sampling Distribution
18.2.2 Hypothesis Pairs
18.2.3 Assumptions and Formulas
18.3 CARRYING OUT THE INDEPENDENT SAMPLES t TEST USING THE SPSS SOFTWARE PACKAGE
18.4 THE INDEPENDENCE ASSUMPTION
18.5 THE DEPENDENT SAMPLES t TEST
18.5.1 Dependent Samples and Statistical Power
18.5.2 Requirements
18.5.3 Example Demonstrating Increase in Power from Positive Correlation
18.6 CHAPTER SUMMARY
18.7 PROBLEMS AND QUESTIONS
CHAPTER 19
SINGLE SAMPLE TESTS OF PROPORTIONS
19.1 CHAPTER OVERVIEW
19.2 ONE-SAMPLE TEST OF A PROPORTION
19.2.1 Introduction
19.2.2 Theory and Basics
19.2.3 Carrying Out the Behavior Problems Example
19.3 THE BINOMIAL TEST
19.3.1 Background
19.3.2 Carrying Out the Test.
19.4 THE ONE VARIABLE CHI-SQUARE TEST
19.4.1 Background
19.4.2 The Chi-Square Distribution
19.3.3 Observed and Expected Frequencies
19.4.4 Particulars for the Test
19.4.4 Completing Our Example
19.5 CHAPTER SUMMARY
19.6 PROBLEMS AND QUESTIONS
CHAPTER 20
THE CHI-SQUARE TEST OF INDEPENDENCE
20.1 Chapter Overview
20.2 INTRODUCTION TO THE CHI-SQUARE TEST OF INDEPENDENCE
20.3 SELECTED CHARACTERISTICS OF ?2 TEST
20.3.1 Hypothesis Pair
20.3.2 Distribution and Degrees of Freedom
20.3.3 Observed and Expected Proportions
20.3.4 Formula, Observed and Expected Frequencies, Decision Rule, and Requirements
20.4 CARRYING OUT THE ?2 TEST
20.4.1 Hypothesis Testing Model and Calculations
20.4.2 Comments on the Example
20.5 COMMENTS ON THE ?2 TEST
20.6 THE ?2 TEST IS NOT A MEASURE OF SIZE OF ASSOCIATION
20.7 CHAPTER SUMMARY
20.8 PROBLEMS AND QUESTIONS
CHAPTER 21
ANALYSIS OF VARIANCE
21.1 CHAPTER OVERVIEW
21.2 INTRODUCTION TO ANOVA
21.3 THE LOGIC OF ANOVA
21.3.1 Hypothesis and Overview
21.3.2 Two Estimates of the Population Variance
21.3.3 The F Distribution
21.4 PARTICULARS OF ANOVA
21.4.1 Assumptions and Level of Measurement
21.4.2 Hypothesis Pair
21.4.3 Critical Values and Decision Rules
21.5 CALCULATION EXAMPLE USING SPSS
21.6 MULTIPLE COMPARISON PROCEDURES
21.7 FISHING EXPEDITIONS
21.7.1 The Dangers of Fishing
21.7.2 The Dangers of Not Fishing
21.8 CHAPTER SUMMARY
21.9 PROBLEMS AND QUESTIONS
CHAPTER 22
MORE SIGNIFICANCE TESTS AND REASONING WITH TEST RESULTS
22.1 CHAPTER OVERVIEW
22.2 STATISTICAL SIGNIFICANCE TEST OF PEARSON'S r
22.2.1 Basic Logic
22.2.2 Assumptions and Levels of Measurement
22.2.3 Hypothesis Pair
22.2.4 Decision Rules and Degrees of Freedom
22.2.5 Carrying Out the Hypothesis Testing Model
22.3 A CORRELATION MATRIX
22.4 COMMENTS ON HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
22.4.1 Hypothesis Testing
22.4.2 Confidence Intervals
22.5 PARAMETRIC AND NONPARAMETRIC TESTS
22.6 SELECTED PARAMETRIC TESTS
22.6.1 Significance Test of Spearman's r
22.6.2 Tests of Association Between Two Ordinal-Level Categorical Variables
22.6.3 Tests for Independent Samples
22.6.4 Tests for Dependent Samples
22.7 Parametric or Nonparametric Test?
22.8 DATA TRANSFORMATION
22.9 SINGLE-CASE DESIGNS
22.9.1 Basic Applications:
22.9.3 Serial Dependency:
22.10 QUALITATIVE METHODS AND STATISTICS
22.11 REASONING WITH DATA: A BRIEF REVIEW
22.12 CHAPTER SUMMARY
22.13 PROBLEMS AND QUESTIONS
CHAPTER 23
AN OVERVIEW OF SELECTED MULTIVARIATE PROCEDURES
23.1 CHAPTER OVERVIEW
23.2 MULTIPLE REGRESSION ANALYSIS
23.2.1 Equation and Introduction
23.2.2 Assumptions of Multiple Regression
23.3 ADVANTAGES OF MULTIVARIATE ANALYSES.
23.4 LOGISTIC REGRESSION
23.5 FACTORIAL ANALYSIS OF VARIANCE
23.6 MULTIVARIATE PROCEDURES RELATED TO ANOVA
23.7 A GLIMPSE AT SELECTED PROCEDURES
23.8 CHAPTER SUMMARY
23.9 PROBLEMS AND QUESTIONS
CHAPTER 24
GENERALIZABILITY, IMPORTANCE, AND A DATA INTERPRETATION MODEL
24.1 CHAPTER OVERVIEW
24.2 Generalizability
24.2.1 Inferential Statistics and Generalizability
24.2.2 Generalization using Nonstatistical Tools
24.3 IMPORTANCE
24.4 THE BALANCED MODEL FOR DATA INTERPRETATION
24.5 CHAPTER SUMMARY
24.6 PROBLEMS AND QUESTIONS
APPENDIX A
TABLES
A.1 PERCENTAGE OF CASES IN SELECTED AREAS OF THE NORMAL DISTRIBUTION
A.2 CRITICAL VALUES FOR THE T DISTRIBUTION AND VALUES FOR
CONFIDENCE INTERVALS
A.3 CRITICAL VALUES (FREQUENCIES) FOR THE BINOMIAL DISTRIBUTION: ONE-TAILED TEST , ALPHA = .05
A.4 CRITICAL VALUES FOR THE CHI-SQUARE DISTRIBUTION
A.5 CRITICAL VALUES FOR THE F DISTRIBUTION
A.6 CRITICAL VALUES FOR PEARSON'S r
APPENDIX B
REVIEW OF BASIC MATH
APPENDIX C
APPROPRIATE MEASURES FOR DIFFERENT SITUATIONS
APPENDIX D
SYMBOLS IN THE TEXT
APPENDIX E
FORMULAS IN THE TEXT
APPENDIX F
ANSWERS TO END OF CHAPTER PROBLEMS AND QUESTIONS
TABLE OF CONTENTS
PART ONE: INTRODUCTION AND DESCRIPTIVE STATISTICS
CHAPTER 1
INTRODUCTION AND OVERVIEW
1. 1 CHAPTER OVERVIEW
1.2 STATISTICS AND SOCIAL WORK
1.3 SCIENCE AND RESEARCH
1.4 VARIABLES AND MEASUREMENT
1.5 SAMPLES AND POPULATIONS
1.6 DESCRIPTIVE AND INFERENTIAL STATISTICS
1.7 UNIVARIATE, BIVARIATE, AND MULTIVARIATE STATISTICS
1.8 RANDOM ASSIGNMENT
1.9 LEVELS OF MEASUREMENT
1.9.1 Basics
1.9.2 Fine Points
1.10 CHAPTER SUMMARY
1.11 PROBLEMS AND QUESTIONS
CHAPTER 2
DATA PRESENTATION
2.1 CHAPTER OVERVIEW
2.2 FREQUENCY DISTRIBUTIONS AND TABLES
2.3 FIGURES
2.4 CHAPTER SUMMARY
2.5 PROBLEMS AND QUESTIONS
CHAPTER 3
CENTRAL TENDENCY
3.1 CHAPTER OVERVIEW
3.2 KEY CONCEPTS IN UNIVARIATE DESCRIPTIVE STATISTICS
3.3 THREE KEY MEASURES OF CENTRAL TENDENCY
3.4 THE MODE
3.5 THE MEDIAN
3.6 THE MEAN
3.7 CHOOSING BETWEEN MEASURES
3.8 CHAPTER SUMMARY
3.9 PROBLEMS AND QUESTIONS
CHAPTER 4
MEASURES OF VARIABILITY
4.1 CHAPTER OVERVIEW
4.2 THE CONCEPT OF VARIABILITY
4.3 ASSESSING THE VARIABILITY OF CATEGORICAL VARIABLES
4.4 THE RANGE
4.5 THE INTERQUARTILERANGE
4.6 THE MEAN DEVIATION
4.7 THE STANDARD DEVIATION
4.8 THE VARIANCE
4.9 CHAPTER SUMMARY
4.10 PROBLEMS AND QUESTIONS
CHAPTER 5
SHAPE OF DISTRIBUTION
5.1 CHAPTER OVERVIEW
5.2 THE NORMAL DISTRIBUTION
5.3 SKEWED DISTRIBUTIONS
5.3.1 Characteristics
5.3.2 Skewness and Measures of Central Tendency
5.4 KURTOSIS
5.5 UNIFORM AND BIMODAL DISTRIBUTIONS
5.6 PERCENTAGES AND THE NORMAL DISTRIBUTION
5.7 INTRODUCTION TO Z SCORES
5.7.1 z Score Calculation
5.7.2 Basics of z Scores
5.7.3 Uses of z Scores
5.8 z SCORES AND THE NORMAL DISTRIBUTION
5.8.1 Problems about Percentages of Cases
5.8.2 Reminders and Cautions
5.9 CHAPTER SUMMARY
5.10 PROBLEMS AND QUESTIONS
CHAPTER 6
THE CONCEPT OF RELATIONSHIP AND RELATIONSHIP BETWEEN CATEGORICAL VARIABLES
6.1 CHAPTER OVERVIEW
6.2 DEFINITION OF RELATIONSHIP
6.3 COMMENTS ON RELATIONSHIP
6.4 CONTINGENCY TABLES AND CATEGORICAL VARIABLES
6.4.1 Reading a Contingency (Crosstabs) Table
6.4.2 Assessing Relationship Using a Contingency Table
6.5 SIZE OF ASSOCIATION
6.6 DIFFERENCE IN PERCENTAGES (D%)
6.7 QUALITATIVE DESCRIPTORS OF SIZE OF ASSOCIATION
6.8 RISK RATIO (RR)
6.9 DIFFERENCE IN PERCENTAGES OR RISK RATIO?
6.10 CHAPTER SUMMARY
6.11 PROBLEMS AND QUESTIONS
CHAPTER 7
THE ODDS RATIO AND OTHER MEASURES FOR CATEGORICAL VARIABLES
7.1 Chapter Overview
7.2 ODDS RATIO (OR):
7.2.1 Basics and Formula
7.2.2 Interpretation
7.2.3 Advantages
7.3 RELATIONSHIP IN CONTINGENCY TABLES LARGER THAN 2 ? 2
7.4 DIRECTIONAL RELATIONSHIP
7.5 MEASURE OF DIRECTIONAL ASSOCIATION BETWEEN CATEGORICAL VARIABLES.
7.6 CHAPTER SUMMARY
7.7 PROBLEMS AND QUESTIONS
CHAPTER 8
CORRELATION AND REGRESSION
8.1 CHAPTER OVERVIEW
8.2 POSITIVE AND NEGATIVE CORRELATION
8.3 SCATTERPLOTS
8.4 FORMULA FOR THE CORRELATION COEFFICIENT, r
8.5 UNDERSTANDING r
8.6 INTERPRETATIONS USING r AND z SCORES
8.6.1 Predictions with z Scores
8.6.2 Predicted Change in Standard Deviation Units
8.7 CURVILINEAR RELATIONSHIP
8.8 A CAUTION IN INTERPRETING r
8.9 REGRESSION
8.9.1 Regression Equation and Regression Line
8.9.2 Contrast between r and B
8.10 CORRELATION FOR NOMINAL AND ORDINAL-LEVEL VARIABLES
8.11 CHAPTER SUMMARY
8.12 PROBLEMS AND QUESTIONS
CHAPTER 9
STANDARDIZED MEAN DIFFERENCE
9.1 CHAPTER OVERVIEW
9.2 INTRODUCTION TO THE SMD
9.3 GRAPHICAL INTERPRETATION OF THE SMD
9.4 A CAUTION REGARDING THE SMD
9.5 MORE MEASURES OF DIFFERENCES BETWEEN TWO MEANS
9.6 DIFFERENCES BETWEEN THREE OR MORE MEANS
9.7 CHAPTER SUMMARY
9.8 PROBLEMS AND QUESTIONS
CHAPTER 10
RESEARCH DESIGN AND CAUSALITY
10.1 CHAPTER OVERVIEW
10.2 INTRODUCTION TO CAUSALITY
10.3 WHAT DOES "CAUSE" MEAN IN SOCIAL SCIENCE?
10.4 CONFOUNDING VARIABLES
10.5 EXPERIMENTAL AND SURVEY DESIGNS
10.5.1 Experiments vs. Surveys
10.5.2 Random Assignment to Groups
10.6 RANDOM ASSIGNMENT AND CAUSALITY
10.7 CHAPTER SUMMARY
10.8 PROBLEMS AND QUESTIONS
CHAPTER 11
CONTROLLING FOR CONFOUNDING VARIABLES
11.1 CHAPTER OVERVIEW
11.2 CONTROLLING FOR A VARIABLE
11.2.1 Basic Concepts
11.2.2 Different Patterns Following Control
11.2.3 Initial Relationship Persists
11.2.4 Initial Relationship Weakens
11.2.5 Initial Relationship Disappears
11.3 CAUSAL MODELS AND ADDITIONAL CONSIDERATIONS
11.4 CONTROL FOR MULTIPLE VARIABLES AND CAUSALITY
11.5 INTERACTION EFFECTS
11.6 CHAPTER SUMMARY
11.7 PROBLEMS AND QUESTIONS
PART 2: INFERENTIAL STATISTICS AND DATA INTERPRETATION
CHAPTER 12
AN INTRODUCTION TO INFERENTIAL STATISTICS
12.1 CHAPTER OVERVIEW
12.2 DESCRIPTIVE VERSUS INFERENTIAL STATISTICS
12.3 CHARACTERISTICS OF RANDOM SAMPLES
12.4 THE ADVANTAGE OF RANDOM SAMPLES
12.5 STATISTICS AND PARAMETERS
12.6 CHARACTERISTICS OF ESTIMATORS
12.7 SAMPLING ERROR AND SAMPLING DISTRIBUTIONS
12.7.1 Concepts
12.7.2 Sampling Distribution of the Mean.
12.8 SAMPLE SIZE AND THE SAMPLING DISTRIBUTION OF
12.9 CHAPTER SUMMARY
12.10 PROBLEMS AND QUESTIONS
CHAPTER 13
CONFIDENCE INTERVALS FOR MEANS AND PROPORTIONS
13.1 CHAPTER OVERVIEW
13.2. WHAT IS A CONFIDENCE INTERVAL?
13.3 CONFIDENCE INTERVALS FOR MEANS
13.3.1 Theory
13.3.2 Formulas and Computation
13.4 CONFIDENCE INTERVALS FOR PROPORTIONS AND PERCENTAGES
13.4.1 Theory
13.4.2 Formulae and Application
13.5 FIVE MORE THINGS TO KNOW
13.5 CHAPTER SUMMARY
13.6 PROBLEMS AND QUESTIONS
CHAPTER 14
THE LOGIC OF STATISTICAL SIGNIFICANCE TESTS
14.1 CHAPTER OVERVIEW
14.2 INTRODUCTION TO SIGNIFICANCE TESTING
14.3 PROBABILITY
14.3.1 Definition and Formula
14.3.2 Probability and the Normal Distribution
14.4 NULL AND RESEARCH HYPOTHESES
14.5 A COMMON PATTERN FOR HYPOTHESIS PAIRS
14.6 DIRECTIONAL AND NONDIRECTIONAL HYPOTHESIS PAIRS
14.6.1 Definitions and Examples
14.6.2 Guidelines for Usage
14.7 SAMPLING ERROR AND THE NULL HYPOTHESIS
14.8 STATISTICAL SIGNIFICANCE LEVELS
14.9 EXAMPLES OF STATISTICAL SIGNIFICANCE TESTING
14.9.1 An Example in Which We Reject the Null
14.9.2 An Example in Which We Fail to Reject (Accept) the Null
14.9.3 More interpretations of p
14.9.4 What Does it Mean to Reject the Null?
14.9.5 What Does It Mean to Fail to Reject (Accept) the Null?
14.10 NULL AND ALTERNATIVE HYPOTHESES AND SCIENTIFIC INQUIRY
14.11 WHAT IS A STATISTICALLY SIGNIFICANT RESULT?
14.12 CHAPTER SUMMARY
14.13 PROBLEMS AND QUESTIONS
CHAPTER 15
THE LARGE SAMPLE TEST OF THE MEAN AND NEW CONCEPTS
15.1 CHAPTER OVERVIEW
15.2 A MODEL FOR HYPOTHESIS TESTING
15.3 ASSUMPTIONS OF STATISTICAL SIGNIFICANCE TESTS
15.3.1 Definition and Assumptions of the Large Sample Test of
15.3.2 Assumptions Common to All Tests
15. 4 THE FIRST TWO STEPS OF THE HYPOTHESIS TESTING MODEL
15.5 STATISTICAL TESTS AND SAMPLING DISTRIBUTIONS
15.6 DIFFERENCES: DIRECTIONAL VS. NONDIRECTIONAL HYPOTHESIS PAIRS
15.6.1 Overview
15.6.2 Nondirectional Hypothesis Pair:
15.6.3 Directional Hypothesis Pair:
15.7 CARRYING OUT THE SIGNIFICANCE TEST USING THE SAMPLING DISTRIBUTION
15.8 FINISHING THE EXAMPLE USING THE FORMULA
15.8.1 Step 3: Carry Out the Test
15.8.2 Decision Rules
15.8.3 Step 4: Make a Decision
15.9 EFFECT OF CHOICE OF SIGNIFICANCE LEVEL ON DECISION MAKING
15.10 TYPE I AND TYPE II ERRORS
15.11 TWO-TAILED VS. ONE-TAILED TESTS
15.11.1 Carrying out our Example
15.11.2 Determining the Exact Value of the Study Sample Result (p)
15.12 MORE DECISION RULES FOR THE ONE-TAILED, LARGE SAMPLE TEST OF
15.13 REJECTING THE NULL AND "REAL" THINGS
15.15 CHAPTER SUMMARY
15.16 PROBLEMS AND QUESTIONS
CHAPTER 16
STATISTICAL POWER AND SELECTED TOPICS
16.1 CHAPTER OVERVIEW
16.2 DEFINITION OF POWER
16.3 SAMPLE SIZE AND POWER
16.4 EXAMPLES OF HOW SAMPLE SIZE AFFECTS POWER
16.4.1 The Parenting Skills Example
16.4.2 More Examples of Sample Size and Power
16.5 FACTORS OTHER THAN SAMPLE SIZE THAT INFLUENCE POWER
16.5.1 Overview
16.5.2 Size of Relationship or Difference in the Population
16.5.3 Reduced Variability of Independent or Dependent Variable
16.5.4 Control for Third Variables
16.5.5 Significance Level
16.5.6 Directional Hypotheses and One-tailed Tests
16.5.7 Statistical Significance Test
16.6 HOW MUCH POWER IS ENOUGH?
16.7 HOW LARGE SHOULD SAMPLE SIZE BE?
16.8 NONRANDOM SAMPLES AND SIGNIFICANCE TESTS
16.9 REPORTING STATISTICAL SIGNIFICANCE
16.10 WHAT STATISTICAL SIGNIFICANCE IS (AND IS NOT)
16.11 CHAPTER SUMMARY
16.12 PROBLEMS AND QUESTIONS
CHAPTER 17
THE t DISTRIBUTION AND ONE-SAMPLE PROCEDURES FOR MEANS
17.1 CHAPTER OVERVIEW
17.2 SMALL SAMPLE SIZE AND DISTRIBUTIONS
17.3 DEGREES OF FREEDOM
17.4 THE FAMILY OF t DISTRIBUTIONS
17.5 CONFIDENCE INTERVALS FOR MEANS FOR SMALL SAMPLES (AND LARGE)
17.6 INTRODUCTION TO THE ONE-SAMPLE t TEST
17.6.1 Assumptions, Hypothesis Pairs, and Formula
17.6.2 Decision Rules
17.7 CARRYING OUT THE ONE-SAMPLE t TEST
17.8 CHAPTER SUMMARY
17.9 PROBLEMS AND QUESTIONS
CHAPTER 18
INDEPENDENT SAMPLES t TEST AND DEPENDENT SAMPLES t TEST
18.1 CHAPTER OVERVIEW
18.2 INTRODUCTION TO THE INDEPENDENT SAMPLES t TEST
18.2.1 Purpose and Sampling Distribution
18.2.2 Hypothesis Pairs
18.2.3 Assumptions and Formulas
18.3 CARRYING OUT THE INDEPENDENT SAMPLES t TEST USING THE SPSS SOFTWARE PACKAGE
18.4 THE INDEPENDENCE ASSUMPTION
18.5 THE DEPENDENT SAMPLES t TEST
18.5.1 Dependent Samples and Statistical Power
18.5.2 Requirements
18.5.3 Example Demonstrating Increase in Power from Positive Correlation
18.6 CHAPTER SUMMARY
18.7 PROBLEMS AND QUESTIONS
CHAPTER 19
SINGLE SAMPLE TESTS OF PROPORTIONS
19.1 CHAPTER OVERVIEW
19.2 ONE-SAMPLE TEST OF A PROPORTION
19.2.1 Introduction
19.2.2 Theory and Basics
19.2.3 Carrying Out the Behavior Problems Example
19.3 THE BINOMIAL TEST
19.3.1 Background
19.3.2 Carrying Out the Test.
19.4 THE ONE VARIABLE CHI-SQUARE TEST
19.4.1 Background
19.4.2 The Chi-Square Distribution
19.3.3 Observed and Expected Frequencies
19.4.4 Particulars for the Test
19.4.4 Completing Our Example
19.5 CHAPTER SUMMARY
19.6 PROBLEMS AND QUESTIONS
CHAPTER 20
THE CHI-SQUARE TEST OF INDEPENDENCE
20.1 Chapter Overview
20.2 INTRODUCTION TO THE CHI-SQUARE TEST OF INDEPENDENCE
20.3 SELECTED CHARACTERISTICS OF ?2 TEST
20.3.1 Hypothesis Pair
20.3.2 Distribution and Degrees of Freedom
20.3.3 Observed and Expected Proportions
20.3.4 Formula, Observed and Expected Frequencies, Decision Rule, and Requirements
20.4 CARRYING OUT THE ?2 TEST
20.4.1 Hypothesis Testing Model and Calculations
20.4.2 Comments on the Example
20.5 COMMENTS ON THE ?2 TEST
20.6 THE ?2 TEST IS NOT A MEASURE OF SIZE OF ASSOCIATION
20.7 CHAPTER SUMMARY
20.8 PROBLEMS AND QUESTIONS
CHAPTER 21
ANALYSIS OF VARIANCE
21.1 CHAPTER OVERVIEW
21.2 INTRODUCTION TO ANOVA
21.3 THE LOGIC OF ANOVA
21.3.1 Hypothesis and Overview
21.3.2 Two Estimates of the Population Variance
21.3.3 The F Distribution
21.4 PARTICULARS OF ANOVA
21.4.1 Assumptions and Level of Measurement
21.4.2 Hypothesis Pair
21.4.3 Critical Values and Decision Rules
21.5 CALCULATION EXAMPLE USING SPSS
21.6 MULTIPLE COMPARISON PROCEDURES
21.7 FISHING EXPEDITIONS
21.7.1 The Dangers of Fishing
21.7.2 The Dangers of Not Fishing
21.8 CHAPTER SUMMARY
21.9 PROBLEMS AND QUESTIONS
CHAPTER 22
MORE SIGNIFICANCE TESTS AND REASONING WITH TEST RESULTS
22.1 CHAPTER OVERVIEW
22.2 STATISTICAL SIGNIFICANCE TEST OF PEARSON'S r
22.2.1 Basic Logic
22.2.2 Assumptions and Levels of Measurement
22.2.3 Hypothesis Pair
22.2.4 Decision Rules and Degrees of Freedom
22.2.5 Carrying Out the Hypothesis Testing Model
22.3 A CORRELATION MATRIX
22.4 COMMENTS ON HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
22.4.1 Hypothesis Testing
22.4.2 Confidence Intervals
22.5 PARAMETRIC AND NONPARAMETRIC TESTS
22.6 SELECTED PARAMETRIC TESTS
22.6.1 Significance Test of Spearman's r
22.6.2 Tests of Association Between Two Ordinal-Level Categorical Variables
22.6.3 Tests for Independent Samples
22.6.4 Tests for Dependent Samples
22.7 Parametric or Nonparametric Test?
22.8 DATA TRANSFORMATION
22.9 SINGLE-CASE DESIGNS
22.9.1 Basic Applications:
22.9.3 Serial Dependency:
22.10 QUALITATIVE METHODS AND STATISTICS
22.11 REASONING WITH DATA: A BRIEF REVIEW
22.12 CHAPTER SUMMARY
22.13 PROBLEMS AND QUESTIONS
CHAPTER 23
AN OVERVIEW OF SELECTED MULTIVARIATE PROCEDURES
23.1 CHAPTER OVERVIEW
23.2 MULTIPLE REGRESSION ANALYSIS
23.2.1 Equation and Introduction
23.2.2 Assumptions of Multiple Regression
23.3 ADVANTAGES OF MULTIVARIATE ANALYSES.
23.4 LOGISTIC REGRESSION
23.5 FACTORIAL ANALYSIS OF VARIANCE
23.6 MULTIVARIATE PROCEDURES RELATED TO ANOVA
23.7 A GLIMPSE AT SELECTED PROCEDURES
23.8 CHAPTER SUMMARY
23.9 PROBLEMS AND QUESTIONS
CHAPTER 24
GENERALIZABILITY, IMPORTANCE, AND A DATA INTERPRETATION MODEL
24.1 CHAPTER OVERVIEW
24.2 Generalizability
24.2.1 Inferential Statistics and Generalizability
24.2.2 Generalization using Nonstatistical Tools
24.3 IMPORTANCE
24.4 THE BALANCED MODEL FOR DATA INTERPRETATION
24.5 CHAPTER SUMMARY
24.6 PROBLEMS AND QUESTIONS
APPENDIX A
TABLES
A.1 PERCENTAGE OF CASES IN SELECTED AREAS OF THE NORMAL DISTRIBUTION
A.2 CRITICAL VALUES FOR THE T DISTRIBUTION AND VALUES FOR
CONFIDENCE INTERVALS
A.3 CRITICAL VALUES (FREQUENCIES) FOR THE BINOMIAL DISTRIBUTION: ONE-TAILED TEST , ALPHA = .05
A.4 CRITICAL VALUES FOR THE CHI-SQUARE DISTRIBUTION
A.5 CRITICAL VALUES FOR THE F DISTRIBUTION
A.6 CRITICAL VALUES FOR PEARSON'S r
APPENDIX B
REVIEW OF BASIC MATH
APPENDIX C
APPROPRIATE MEASURES FOR DIFFERENT SITUATIONS
APPENDIX D
SYMBOLS IN THE TEXT
APPENDIX E
FORMULAS IN THE TEXT
APPENDIX F
ANSWERS TO END OF CHAPTER PROBLEMS AND QUESTIONS