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| Preface | |
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| Introduction | |
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| Uses of Statistics | |
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| Methodological Terms | |
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| Data | |
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| Information | |
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| Variables and Constants | |
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| Conceptualization | |
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| Operationalization | |
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| Reliability | |
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| Validity | |
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| Research Hypotheses | |
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| Measurement Levels | |
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| Nominal | |
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| Ordinal | |
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| Interval | |
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| Ratio | |
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| Measurement Levels and Data Analysis | |
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| Additional Measurement Classifications | |
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| Discrete and Continuous Variables | |
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| Dichotomous, Binary, and Dummy Variables | |
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| Categories of Statistical Analyses | |
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| Number of Variables in an Analysis | |
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| Primary Purpose of the Analysis | |
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| Analysis of Qualitative Data | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Frequency Distributions and Graphs | |
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| Frequency Distributions | |
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| Absolute Frequency Distributions | |
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| Cumulative Frequency Distributions | |
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| Percentage Frequency Distributions | |
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| Cumulative Percentage Frequency Distributions | |
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| Grouped Frequency Distributions | |
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| Using Frequency Distributions to Analyze Data | |
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| Misrepresentation of Data | |
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| Graphs | |
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| Bar Graphs and Line Diagrams | |
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| Pie Charts | |
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| Histograms | |
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| Frequency Polygons | |
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| Stem-and-Leaf Plots | |
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| A Common Mistake in Displaying Data | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Measures of Central Tendency and Variability | |
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| Measures of Central Tendency | |
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| The Mode | |
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| The Median | |
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| The Mean | |
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| Which Measure of Central Tendency to Use? | |
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| Measures of Variability | |
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| The Range | |
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| The Interquartile Range | |
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| The Mean Deviation | |
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| Variance | |
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| Standard Deviation | |
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| Reporting Measures of Variability | |
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| Other Uses for Central Tendency and Variability | |
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| Concluding Thoughts | |
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| Study Questions | |
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| The Normal Distribution | |
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| Skewness | |
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| Kurtosis | |
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| Normal Distributions | |
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| Converting Raw Scores to Z Scores and Percentiles | |
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| Practical Uses of z Scores | |
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| Deriving Raw Scores from Percentiles | |
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| Concluding Thoughts | |
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| Study Questions | |
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| The Basics of Hypothesis Testing | |
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| Alternative Explanations | |
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| Rival Hypotheses | |
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| Research Design Flaws | |
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| Sampling Error | |
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| Probability and Inference | |
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| Refuting Sampling Error | |
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| Replication | |
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| Statistical Analyses | |
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| More About Research Hypotheses | |
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| The One-Tailed Research Hypothesis | |
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| The Two-Tailed Research Hypothesis | |
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| The "No Relationship" Research Hypothesis | |
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| Testing the Null Hypothesis | |
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| Statistical Significance | |
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| p Values | |
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| Rejection Levels ("Alpha") | |
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| Errors in Drawing Conclusions About Relationships | |
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| Avoiding Type I Errors | |
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| Statistically Significant Relationships and Meaningful Findings | |
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| Assessing Strength of Relationships (Effect Size) | |
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| Is the Relationship Surprising? | |
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| Complex Interpretations of Statistically Significant Relationships | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Sampling Distributions and the Null Hypothesis Testing | |
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| Sample Size and Sampling Error | |
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| Sampling Distributions and Inference | |
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| Comparing an Experimental Sample with Its Population | |
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| Comparing a Non-Experimental Sample with Its Population | |
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| Sampling Distribution of Means | |
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| Samples Drawn from Normal Distributions | |
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| Samples Drawn from Skewed Distributions | |
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| Estimating Parameters | |
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| Constructing a 95 Percent Confidence Interval | |
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| Constructing a 99 Percent Confidence Interval | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Selecting a Statistical Test | |
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| The Importance of Selecting the Correct Test | |
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| Where Can We Go Wrong? | |
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| Factors to Consider | |
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| Sampling Method(s) Used | |
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| Distribution of the Variables within the Population | |
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| Level of Measurement of the Variables | |
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| Desirable Amount of Statistical Power | |
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| Robustness of Tests Being Considered | |
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| Parametric and Nonparametric Tests | |
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| Multivariate Tests | |
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| Deciding Which Test to Use | |
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| More About Getting Help | |
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| The Process of Hypothesis Testing | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Correlation | |
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| Uses of Correlation | |
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| Scattergrams | |
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| Perfect Correlations | |
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| Nonperfect Correlations | |
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| Interpreting Linear Correlations | |
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| Understanding Correlation Coefficients | |
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| Very Strong Correlations | |
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| Correlation Is Not Causation | |
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| Using Correlation For Inference | |
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| Pearson's r | |
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| Computation and Presentation | |
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| Nonparametric Alternatives | |
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| Spearman's Rho and Kendall's Tau | |
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| Correlation with three or More Variables | |
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| Partial r | |
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| Multiple R | |
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| Variations of Multiple R | |
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| Other Multivariate Tests that Use Correlation | |
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| Factor Analysis | |
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| Cluster Analysis | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Regression Analyses | |
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| What is Prediction? | |
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| What is Simple Linear Regression? | |
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| Formulating a Research Question | |
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| Limitations of Simple Linear Regression | |
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| Computation of the Regression Equation | |
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| More About the Regression Line | |
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| The Least-Squares Criterion | |
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| Interchanging X and Y Variables | |
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| Interpreting Results | |
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| Presentation of Y' | |
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| The Standard Error | |
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| Using Regression in Social Work Practice | |
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| Regression with Three or More Variables | |
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| Other Types of Regression Analyses | |
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| Discriminant Analysis | |
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| Logistic Regression | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Cross Tabulation | |
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| The Chi-Square Test of Association | |
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| Observed Frequencies | |
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| Expected Frequencies | |
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| Degrees of Freedom | |
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| Using Chi-Square | |
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| Presentation of Findings | |
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| Interpreting the Results of a Chi-Square Analysis | |
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| Meaningfulness and Sample Size | |
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| Restrictions on the Use of Chi-Square | |
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| An Alternative: Fisher's Exact Test | |
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| Using Chi-Square in Social Work Practice | |
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| Cross Tabulation with Three or More Variables | |
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| Problems with Sizes of Expected Frequencies | |
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| Effects of Introducing Additional Variables | |
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| Special Applications of the Chi-Square Formula | |
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| McNemar's Test | |
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| The Median Test | |
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| Concluding Thoughts | |
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| Study Questions | |
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| t Tests and Analysis of Variance | |
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| The Use of t Tests | |
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| Misuse of t | |
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| The One-Sample t Test | |
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| Determining If a Sample Is Representative | |
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| Hypothesis Testing | |
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| Presentation of Findings | |
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| A Nonparametric Alternative: Chi-Square Goodness of Fit | |
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| The Dependent t Test | |
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| Use with Two Connected (or Matched) Samples Measured Once | |
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| Use with One Sample Measured Twice | |
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| A Nonparametric Alternative: Wilcoxon Sign | |
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| The Independent t Test | |
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| Nonparametric Alternatives: U and K-S | |
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| A Multivariate Alternative: T[superscript 2] | |
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| Simple Analysis of Variance (Simple Anova) | |
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| Additional Data Analyses | |
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| A Nonparametric Alternative: Kruskal-Wallis | |
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| Multivariate Analysis of Variance | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Other Contributions of Statistics to Evidence-Based Practice | |
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| Meta-Analysis | |
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| Answers Sought in Program Evaluations | |
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| Needs Assessments and Formative Evaluations | |
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| Outcome Evaluations | |
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| Hypothesis Testing in Outcome Evaluations | |
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| Statistical Analyses of Outcome Evaluation Data | |
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| Answers Sought in Single-System Research | |
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| Hypothesis Testing in Single-System Research | |
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| Statistical Analyses of Single-System Data | |
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| Using Familiar Statistical Tests | |
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| Two Other Popular Tests | |
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| Concluding Thoughts | |
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| Study Questions | |
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| Beginning to Select a Statistical Test | |
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| Glossary | |
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| Index | |