Preface 

xiii  


1  (21) 


2  (1) 


3  (7) 


3  (1) 


3  (1) 


4  (1) 


5  (1) 


6  (1) 


7  (1) 


7  (1) 


8  (2) 


10  (4) 


11  (1) 


12  (1) 


13  (1) 


14  (1) 

Measurement Levels and Data Analysis 


14  (2) 

Additional Measurement Classifications 


16  (1) 

Discrete and Continuous Variables 


16  (1) 

Dichotomous, Binary, and Dummy Variables 


16  (1) 

Categories of Statistical Analyses 


17  (1) 

Number of Variables in an Analysis 


17  (1) 

Primary Purpose of the Analysis 


17  (1) 

Analysis of Qualitative Data 


18  (1) 


19  (1) 


20  (2) 

Frequency Distributions and Graphs 


22  (18) 


23  (4) 

Absolute Frequency Distributions 


24  (1) 

Cumulative Frequency Distributions 


25  (1) 

Percentage Frequency Distributions 


25  (1) 

Cumulative Percentage Frequency Distributions 


26  (1) 

Grouped Frequency Distributions 


27  (1) 

Using Frequency Distributions to Analyze Data 


28  (2) 

Misrepresentation of Data 


30  (1) 


31  (6) 

Bar Graphs and Line Diagrams 


32  (1) 


32  (2) 


34  (1) 


35  (1) 


36  (1) 

A Common Mistake in Displaying Data 


37  (1) 


38  (1) 


38  (2) 

Measures of Central Tendency and Variability 


40  (20) 

Measures of Central Tendency 


40  (8) 


41  (1) 


41  (2) 


43  (3) 

Which Measure of Central Tendency to Use? 


46  (2) 


48  (9) 


49  (1) 


50  (1) 


51  (1) 


52  (1) 


52  (4) 

Reporting Measures of Variability 


56  (52) 

Other Uses for Central Tendency and Variability 


57  (1) 


58  (1) 


58  (2) 


60  (19) 


60  (2) 


62  (1) 


63  (5) 

Converting Raw Scores to Z Scores and Percentiles 


68  (7) 

Practical Uses of z Scores 


72  (3) 

Deriving Raw Scores from Percentiles 


75  (2) 


77  (1) 


77  (2) 

The Basics of Hypothesis Testing 


79  (23) 


80  (4) 


80  (1) 


81  (2) 


83  (1) 

Probability and Inference 


84  (1) 


85  (2) 


85  (1) 


86  (1) 

More About Research Hypotheses 


87  (2) 

The OneTailed Research Hypothesis 


88  (1) 

The TwoTailed Research Hypothesis 


88  (1) 

The ``No Relationship'' Research Hypothesis 


88  (1) 

Testing the Null Hypothesis 


89  (2) 


91  (3) 


92  (1) 

Rejection Levels (``Alpha'') 


93  (1) 

Errors in Drawing Conclusions About Relationships 


94  (2) 


95  (1) 

Statistically Significant Relationships and Meaningful Findings 


96  (3) 

Assessing Strength of Relationships (Effect Size) 


97  (1) 

Is the Relationship Surprising? 


98  (1) 

Complex Interpretations of Statistically Significant Relationships 


99  (1) 


99  (1) 


100  (2) 

Sampling Distributions and the Null Hypothesis Testing 


102  (17) 

Sample Size and Sampling Error 


103  (1) 

Sampling Distributions and Inference 


104  (3) 

Comparing an Experimental Sample with Its Population 


105  (1) 

Comparing a NonExperimental Sample with Its Population 


106  (1) 

Sampling Distribution of Means 


107  (8) 

Samples Drawn from Normal Distributions 


109  (5) 

Samples Drawn from Skewed Distributions 


114  (1) 


115  (3) 

Constructing a 95 Percent Confidence Interval 


116  (1) 

Constructing a 99 Percent Confidence Interval 


116  (2) 


118  (1) 


118  (1) 

Selecting a Statistical Test 


119  (18) 

The Importance of Selecting the Correct Test 


119  (2) 


120  (1) 


121  (7) 


122  (1) 

Distribution of the Variables within the Population 


123  (1) 

Level of Measurement of the Variables 


123  (1) 

Desirable Amount of Statistical Power 


124  (4) 

Robustness of Tests Being Considered 


128  (1) 

Parametric and Nonparametric Tests 


128  (2) 


130  (1) 

Deciding Which Test to Use 


131  (1) 


132  (1) 

The Process of Hypothesis Testing 


133  (2) 


135  (1) 


135  (2) 


137  (28) 


137  (1) 


138  (3) 


141  (2) 


143  (1) 

Interpreting Linear Correlations 


143  (7) 

Understanding Correlation Coefficients 


144  (1) 


145  (2) 

Correlation is Not Causation 


147  (1) 

Using Correlation for Inference 


148  (2) 


150  (5) 

Computation and Presentation 


150  (5) 

Nonparametric Alternatives 


155  (2) 

Spearman's Rho and Kendall's Tau 


155  (2) 

Correlation with Three or More Variables 


157  (3) 


157  (1) 


158  (1) 


159  (1) 

Other Multivariate Tests That Use Correlation 


160  (3) 


161  (1) 


162  (1) 


163  (1) 


164  (1) 


165  (25) 


165  (3) 

What is Simple Linear Regression? 


168  (2) 

Formulating a Research Question 


169  (1) 

Limitations of Simple Linear Regression 


170  (1) 

Computation of the Regression Equation 


170  (2) 

More About the Regression Line 


172  (6) 

The Leastsquares Criterion 


174  (3) 

Interchanging X and Y Variables 


177  (1) 


178  (3) 


178  (1) 


178  (1) 

Using Regression in Social Work Practice 


179  (2) 

Regression with Three or More Variables 


181  (4) 

Other Types of Regression Analyses 


185  (3) 


185  (1) 


186  (2) 


188  (1) 


189  (1) 


190  (27) 

The ChiSquare Test of Association 


190  (18) 


192  (2) 


194  (2) 


196  (1) 


196  (3) 


199  (1) 

Interpreting the Results of a ChiSquare Analysis 


200  (1) 

Meaningfulness and Sample Size 


201  (3) 

Restrictions on the Use of ChiSquare 


204  (1) 

An Alternative: Fisher's Exact Test 


204  (1) 

Using ChiSquare in Social Work Practice 


205  (3) 

Cross Tabulation with Three or More Variables 


208  (3) 

Problems with Sizes of Expected Frequencies 


210  (1) 

Effects of Introducing Additional Variables 


210  (1) 

Special Applications of the ChiSquare Formula 


211  (4) 


211  (2) 


213  (2) 


215  (1) 


216  (1) 

t Tests and Analysis of Variance 


217  (32) 


218  (1) 


218  (1) 


219  (7) 

Determining If a Sample is Representative 


221  (1) 


222  (1) 


223  (1) 

A Nonparametric Alternative: ChiSquare Goodness of Fit 


223  (3) 


226  (4) 

Use with Two Connected (or Matched) Samples Measured Once 


226  (1) 

Use with One Sample Measured Twice 


227  (1) 

A Nonparametric Alternative: Wilcoxon Sign 


228  (2) 


230  (13) 

Nonparametric Alternatives: U and Ks 


239  (3) 

A Multivariate Alternative: T2 


242  (1) 

Simple Analysis of Variance (Simple Anova) 


243  (3) 


245  (1) 

A Nonparametric Alternative: KruskalWallis 


246  (1) 

Multivariate Analysis of Variance 


246  (1) 


247  (1) 


247  (2) 

Other Contributions of Statistics to EvidenceBased Practice 


249  (19) 


250  (3) 

Answers Sought in Program Evaluations 


253  (1) 

Needs Assessments and Formative Evaluations 


253  (1) 


254  (5) 

Hypothesis Testing in Outcome Evaluations 


254  (3) 

Statistical Analyses of Outcome Evaluation Data 


257  (2) 

Answers Sought in SingleSystem Research 


259  (7) 

Hypothesis Testing in SingleSystem Research 


259  (1) 

Statistical Analyses of SingleSystem Data 


260  (1) 

Using Familiar Statistical Tests 


261  (1) 


262  (4) 


266  (1) 


267  (1) 
Appendix A Beginning to Select a Statistical Test 

268  (2) 
Glossary 

270  (19) 
Index 

289  