Statistics and Data Interpretation for Social Work

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Overview

"

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.

"

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Product Details

  • ISBN-13: 9780826107206
  • Publisher: Springer Publishing Company, Incorporated
  • Publication date: 12/16/2011
  • Edition description: New Edition
  • Pages: 512
  • Sales rank: 441,236
  • Product dimensions: 7.00 (w) x 10.00 (h) x 1.10 (d)

Meet the Author

Jim A. Rosenthal, PhD, is a professor at the University of Oklahoma School of Social Work and Coordinator of the Graduate Program. He teaches courses in research methods and statistics to both graduate and undergraduate students. His books include Statistics and Data Interpretation for the Helping Professions, 1st Edition (Brooks/Cole, 2001) and Special Needs Adoption: A Study of Intact Families (Praeger, 1992). He has also published numerous journal articles.

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Table of Contents

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 Generlizability

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

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