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Why Do You Need this New Edition?, i
Copyright, iv
Preface, xi
1. Introduction, 1
Uses of Statistics, 3
Methodological Terms, 3
Data, 3
Information, 4
Variables and Constants, 4
Conceptualization, 6
Operationalization, 6
Reliability, 7
Validity, 7
Research Hypotheses, 8
Three Forms of Research Hypotheses, 8
Causal and Noncausal Research Hypotheses, 10
Independent and Dependent Variables, 10
Measurement Levels, 12
Nominal, 13
Ordinal, 14
Interval, 15
Ratio, 16
Measurement Levels and Data Analysis, 16
Additional Measurement Classifications, 17
Discrete and Continuous Variables, 17
Dichotomous, Binary, and Dummy Variables, 18
Categories of Statistical Analyses, 18
Number of Variables in an Analysis, 18
Primary Purpose of the Analysis, 19
Concluding Thoughts, 20
Study Questions, 21
2. Frequency Distributions and Graphs, 23
Frequency Distributions, 24
Absolute Frequency Distributions, 25
Cumulative Frequency Distributions, 26
Percentage Frequency Distributions, 27
Cumulative Percentage Frequency Distributions, 27
Grouped Frequency Distributions, 28
Using Frequency Distributions to Analyze Data, 30
Misrepresentation of Data, 31
Graphs, 33
Bar Graphs and Line Diagrams, 33
Pie Charts, 35
Histograms, 35
Frequency Polygons, 36
Stem-and-Leaf Plots, 37
A Common Mistake in Displaying Data, 38
Concluding Thoughts, 39
Study Questions, 40
3. Measures of Central Tendency and Variability, 42
Measures of Central Tendency, 42
Mode, 43
Median, 45
Mean, 46
Which Measure of Central Tendency to Use?, 48
Measures of Variability, 51
Range, 52
Interquartile Range, 53
Mean Deviation, 53
Variance, 54
Standard Deviation, 55
Reporting Measures of Variability, 58
Other Uses for Central Tendency and Variability, 59
Concluding Thoughts, 60
Study Questions, 60
4. Normal Distributions, 62
Skewness, 63
Kurtosis, 64
The Normal Curve, 66
Converting Raw Scores to z Scores and Percentiles, 71
Practical Uses of z Scores, 75
Deriving Raw Scores From Percentiles, 79
Concluding Thoughts, 80
Study Questions, 81
5. Hypothesis Testing: Basic Principles, 82
Alternative Explanations for Relationships Within Samples, 83
Rival Hypotheses, 83
Research Design Flaws, 83
Sampling Error, 86
Probability and Inference, 86
Refuting Sampling Error, 88
Replication, 88
Statistical Analyses, 89
Statistical Significance, 90
p values, 90
Rejection Levels (Alpha), 91
Testing the Null Hypothesis, 92
Errors in Drawing Conclusions About Relationships, 94
Avoiding Type I Errors, 95
Avoiding Type II Errors, 96
Statistically Significant Relationships and Meaningful Findings, 99
More about Effect Size, 100
Is the Relationship Valuable?, 102
Complex Interpretations of Statistically Significant Relationships, 103
The Process of Hypothesis Testing, 103
Concluding Thoughts, 105
Study Questions, 106
6. Sampling Distributions, Rejection Regions, and Statistical Test Selection, 108
Sample Size and Sampling Error, 109
Sampling Distributions and Inference, 110
Comparing an Experimental Sample with Its Population, 111
Comparing a Nonexperimental Sample with Its Population, 112
Sampling Distribution of Means, 113
Samples Drawn from Normal Distributions, 115
Samples Drawn from Skewed Distributions, 120
Estimating Parameters, 121
Constructing a 95 Percent Confidence Interval, 122
Constructing a 99 Percent Confidence Interval, 123
Selecting a Statistical Test, 124
The Importance of Selecting the Correct Test, 124
Factors to Consider in Selecting the Correct Test, 125
Parametric and Nonparametric Tests, 129
Deciding Which Test to Use, 131
More about Getting Help, 133
Concluding Thoughts, 133
Study Questions, 134
7. t Tests and Analysis of Variance, 135
The Use of t Tests, 136
Misuse of t Tests, 136
The One-Sample t Test, 137
Determining If a Sample Is Representative, 139
Seeking Support for a Research Hypothesis, 140
Presentation of Findings, 141
A Nonparametric Alternative: Chi-Square Goodness of Fit, 142
The Dependent t Test, 145
Use with Two Connected (or Matched) Samples Measured Once, 145
Use with One Sample Measured Twice, 146
A Nonparametric Alternative: Wilcoxon Sign Test, 147
The Independent t Test, 149
Nonparametric Alternatives: U and K-S, 157
A Multivariate Alternative: T², 161
Simple Analysis of Variance (Simple Anova), 161
Additional Data Analyses, 163
A Nonparametric Alternative: Kruskal-Wallis, 164
Multivariate Analysis of Variance, 165
Concluding Thoughts, 166
Study Questions, 166
8. The Chi-Square Test of Association between Variables, 168
When Chi-Square is Appropriate, 168
Cross-Tabulation Tables, 170
Degrees of Freedom, 174
Using Chi-Square, 176
Presentation of Findings, 178
Interpreting the Results of a Chi-Square Analysis, 178
Meaningfulness and Sample Size, 180
Restrictions on the Use of Chi-Square, 182
An Alternative: Fisher’s Exact Test, 183
Using Chi-Square in Social Work Practice, 184
Cross-Tabulation with Three or More Variables, 187
Problems with Sizes of Expected Frequencies, 188
Effects of Introducing Additional Variables, 189
Special Applications of the Chi-Square Formula, 190
McNemar’s Test, 190
The Median Test, 192
Concluding Thoughts, 195
Study Questions, 195
9. Correlation Analyses, 196
Uses of Correlation, 197
Scattergrams, 198
Perfect Correlations, 200
Nonperfect Correlations, 202
Interpreting Linear Correlations, 203
Understanding Correlation Coefficients, 204
Very Strong Correlations, 205
Remember, Correlation Is Not Causation!, 206
Using Correlation for Inference, 208
Pearson’s r, 208
Computation and Presentation, 210
Nonparametric Alternatives, 215
Spearman’s Rho and Kendall’s Tau, 215
Correlation with Three or More Variables, 216
Partial r, 216
Multiple R, 217
Variations of Multiple R, 219
Other Multivariate Analyses That Use Correlation, 220
Factor Analysis, 221
Cluster Analysis, 223
Concluding Thoughts, 223
Study Questions, 224
10. Regression Analyses, 226
Prediction and Evidence-Based Practice, 226
Prediction and Statistical Analysis, 227
What is Simple Linear Regression?, 230
Research Questions in Simple Linear Regression Analyses, 231
Limitations of Simple Linear Regression, 232
Computation of the Regression Equation, 232
More About the Regression Line, 234
The Least-Squares Criterion, 236
Interchanging X and Y Variables, 239
Interpreting Results, 239
Presentation of Y′, 240
The Standard Error, 240
Using Regression in Social Work Practice, 240
Regression with Three or More Variables, 243
Options for Entering Variables, 246
Other Types of Regression Analyses, 248
Discriminant Analysis, 248
Logistic Regression, 250
Concluding Thoughts, 252
Study Questions, 252
11. Other Ways That Statistical Analyses Contribute to Evidence-Based Practice, 254
Meta-Analysis, 255
Answers Sought In Program Evaluations, 258
Needs Assessments and Formative Evaluations, 259
Outcome Evaluations, 260
Hypothesis Testing in Outcome Evaluations, 261
Statistical Analyses of Outcome Evaluation Data, 263
Answers Sought in Single-System Research, 265
Hypothesis Testing in Single-System Research, 266
Statistical Analyses of Single-System Data, 267
Using Familiar Statistical Tests, 269
Two Other Popular Tests, 269
Concluding Thoughts, 274
Study Questions, 274
Appendix A. Beginning to Select a Statistical Test, 276
Glossary, 278
Index, 293

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