Statistics for Social Workers, 8th Edition

Preface

1 Introduction
USE OF STATISTICS
METHODOLOGICAL TERMS   

Data    
Information   
Variables and Constants   
Conceptualization  
Operationalization  
Reliability   
Validity 

  
RESEARCH HYPOTHESES

Three Forms of Research Hypotheses
Causal and Non-causal Research Hypotheses   
Independent and Dependent Variables

MEASUREMENT LEVELS   

Nominal   
Ordinal   
Interval    
Ratio   

MEASUREMENT LEVELS AND DATA ANALYSIS   
ADDITIONAL MEASUREMENT CLASSIFICATIONS   

Discrete and Continuous Variables   
Dichotomous, Binary, and Dummy Variables   

CATEGORIES OF STATISTICAL ANALYSES   

Number of Variables in an Analysis   
Primary Purpose of the Analysis   

CONCLUDING THOUGHTS   
STUDY QUESTIONS   

 

2 Frequency Distributions and Graphs 
FREQUENCY DISTRIBUTIONS   

Absolute Frequency Distributions   
Cumulative Frequency Distributions   
Percentage Frequency Distributions   
Cumulative Percentage Frequency Distributions   

GROUPED FREQUENCY DISTRIBUTIONS   
USING FREQUENCY DISTRIBUTIONS TO ANALYZE DATA  
MISREPRESENTATION OF DATA   
GRAPHS   

Bar Graphs and Line Diagrams   
Pie Charts   
Histograms   
Frequency Polygons   
Stem-and-Leaf Plots   

A COMMON MISTAKE IN DISPLAYING DATA   
CONCLUDING THOUGHTS   
STUDY QUESTIONS   

 

3 Measures of Central Tendency and Variability 
MEASURES OF CENTRAL TENDENCY   

The Mode   
The Median   
The Mean   
Which Measure of Central Tendency to Use?   

MEASURES OF VARIABILITY   

The Range   
The Interquartile Range   
The Mean Deviation   
Variance   
Standard Deviation   
Reporting Measures of Variability   

OTHER USES FOR CENTRAL TENDENCY AND VARIABILITY   
CONCLUDING THOUGHTS   
STUDY QUESTIONS   

 

4 Normal Distributions  
SKEWNESS   
KURTOSIS   
NORMAL DISTRIBUTIONS   
CONVERTING RAW SCORES TO Z SCORES AND PERCENTILES   

Practical Uses of z Scores   

DERIVING RAW SCORES FROM PERCENTILES   
CONCLUDING THOUGHTS   
STUDY QUESTIONS   

 

5  Hypothesis Testing: Basic Principles 
ALTERNATIVE EXPLANATIONS FOR RELATIONSHIPS WITHIN SAMPLES   

Rival Hypotheses   
Research Design Flaws   
Sampling Error   

PROBABILITY AND INFERENCE   
REFUTING SAMPLING ERROR   

Replication   
Statistical Analyses   

STATISTICAL SIGNIFICANCE

p values
Rejection Levels (Alpha)

ERRORS IN DRAWING CONCLUSIONS ABOUT RELATIONSHIPS   

Avoiding Type I Errors   
Avoiding Type II Errors

STATISTICALLY SIGNIFICANT RELATIONSHIPS AND MEANINGFUL FINDINGS   

More about Effect Size
Is the Relationship Valuable?   
Complex Interpretations of Statistically Significant Relationships   

THE PROCESS OF HYPOTHESIS TESTING
CONCLUDING THOUGHTS   
STUDY QUESTIONS   

 

6 Sampling Distributions, Rejection Regions, and Statistical Test Selection 

SAMPLE SIZE AND SAMPLING ERROR   
SAMPLING DISTRIBUTIONS AND INFERENCE   

Comparing an Experimental Sample with Its Population   
Comparing a Non-Experimental Sample with Its Population   

SAMPLING DISTRIBUTION OF MEANS   

Samples Drawn from Normal Distributions   
Samples Drawn from Skewed Distributions   

ESTIMATING PARAMETERS   

Constructing a 95 Percent Confidence Interval   
Constructing a 99 Percent Confidence Interval   

SELECTING A STATISTICAL TEST

The Importance of Selecting the Correct Test
Factors to Consider in Selecting the Correct Test

PARAMETRIC AND NONPARAMETRIC TESTS
MULTIVARIATE TESTS  
DECIDING WHICH TEST TO USE 

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CONCLUDING THOUGHTS   
STUDY QUESTIONS    
 

7   t Tests and Analysis of Variance 
THE USE OF t TESTS   

Misuse of t  

THE ONE-SAMPLE t TEST   

Determining If a Sample Is Representative   
Seeking Support for a Research Hypothesis
Presentation of Findings   
A Nonparametric Alternative: Chi-Square Goodness of Fit   

THE DEPENDENT t TEST   

Use with Two Connected (or Matched) Samples Measured Once   
Use with One Sample Measured Twice   
A Nonparametric Alternative: Wilcoxon Sign   

THE INDEPENDENT t TEST   

Nonparametric Alternatives: U and K-S   
A Multivariate Alternative: T2   

SIMPLE ANALYSIS OF VARIANCE (SIMPLE ANOVA)   

Additional Data Analyses   
A Nonparametric Alternative: Kruskal-Wallis   

MULTIVARIATE ANALYSIS OF VARIANCE   
CONCLUDING THOUGHTS   
STUDY QUESTIONS    
 

8 The Chi-square Test of Association Between Variables 
WHEN CHI-SQUARE IS APPROPRIATE
CROSS-TABULATION TABLES

Degrees of Freedom   
Using Chi-Square   
Presentation of Findings   
Interpreting the Results of a Chi-Square Analysis   
Meaningfulness and Sample Size   
Restrictions on the Use of Chi-Square   
An Alternative: Fisher’s Exact Test   
Using Chi-Square in Social Work Practice  

 
CROSS TABULATION WITH THREE OR MORE VARIABLES   

Problems with Sizes of Expected Frequencies   
Effects of Introducing Additional Variables   

SPECIAL APPLICATIONS OF THE CHI-SQUARE FORMULA   

McNemar’s Test   
The Median Test   

CONCLUDING THOUGHTS   
STUDY QUESTIONS   

 

9   Correlation Analyses 
USES OF CORRELATION   
SCATTERGRAMS   
PERFECT CORRELATIONS   
NONPERFECT CORRELATIONS   
INTERPRETING LINEAR CORRELATIONS   

Understanding Correlation Coefficients   
Very Strong Correlations   
Remember,Correlation Is Not Causation!   
Using Correlation For Inference   

PEARSON’S r   

Computation and Presentation   

NONPARAMETRIC ALTERNATIVES   

Spearman’s Rho and Kendall’s Tau   

CORRELATION WITH THREE OR MORE VARIABLES   

Partial r   
Multiple R   
Variations of Multiple R   

OTHER MULTIVARIATE TESTS THAT USE CORRELATION   

Factor Analysis   
Cluster Analysis   

CONCLUDING THOUGHTS   
STUDY QUESTIONS   

 

10  Regression Analyses 
PREDICTION AND EVIDENCE BASED PRACTICE
PREDICTION AND STATISTICAL ANALYSIS   
WHAT IS SIMPLE LINEAR REGRESSION?   

Research Questions in Simple Linear Regression   
Limitations of Simple Linear Regression   

COMPUTATION OF THE REGRESSION EQUATION   
MORE ABOUT THE REGRESSION LINE   

The Least-Squares Criterion   
Interchanging X and Y Variables   

INTERPRETING RESULTS   

Presentation of Y ?   
The Standard Error   
Using Regression in Social Work Practice   

REGRESSION WITH THREE OR MORE VARIABLES   

Options for Entering Variables

OTHER TYPES OF REGRESSION ANALYSES   

Discriminant Analysis   
Logistic Regression   

CONCLUDING THOUGHTS   
STUDY QUESTIONS   
 

11Other Ways that Statistical Analyses Contribute to Evidence-Based Practice 
META-ANALYSIS   
ANSWERS SOUGHT IN PROGRAM EVALUATIONS   
NEEDS ASSESSMENTS AND FORMATIVE EVALUATIONS   
OUTCOME EVALUATIONS   

Hypothesis Testing in Outcome Evaluations   
Statistical Analyses of Outcome Evaluation Data   

ANSWERS SOUGHT IN SINGLE-SYSTEM RESEARCH   

Hypothesis Testing in Single-System Research   
Statistical Analyses of Single-System Data   
Using Familiar Statistical Tests   
Two Other Popular Tests   

CONCLUDING THOUGHTS   
STUDY QUESTIONS   
Appendix A    Beginning to Select a Statistical Test   
Glossary   
Index