Preface 

xiii  

Introduction to Statistical Analysis 


1  (19) 

Uses of Statistical Analysis 


2  (1) 

General Methodological Terms 


3  (6) 


3  (1) 


3  (1) 


3  (2) 


5  (1) 


5  (2) 


7  (1) 


7  (1) 


8  (1) 


9  (5) 


10  (1) 


11  (2) 


13  (1) 


13  (1) 

Other Measurement Classifications 


14  (1) 

Discrete Variables and Continuous Variables 


14  (1) 

Dichotomous, Binary, and Dummy Variables 


14  (1) 

Levels of Measurement and Analysis of Data 


15  (1) 

Categories of Statistical Analyses 


16  (1) 

Number of Variables Analyzed 


16  (1) 

Descriptive and Inferential 


16  (1) 


17  (1) 


17  (3) 

Frequency Distributions and Graphs 


20  (19) 


20  (4) 

Absolute Frequency Distributions 


22  (1) 

Cumulative Frequency Distributions 


22  (1) 

Percentage Frequency Distributions 


23  (1) 

Cumulative Percentage Distributions 


24  (1) 

Grouped Frequency Distributions 


24  (2) 

Using Frequency Distributions to Analyze Data 


26  (2) 

Misrepresentation of Data 


28  (1) 

Example: An Administrator's Efforts to Hire More Women 


28  (1) 

Graphical Presentation of Data 


29  (6) 


30  (1) 


30  (2) 


32  (1) 


32  (2) 


34  (1) 


34  (1) 

A Common Mistake in Displaying Data 


35  (1) 


36  (1) 


37  (2) 

Central Tendency and Variability 


39  (19) 


39  (9) 


40  (2) 


42  (1) 


43  (2) 

Which Measure of Central Tendency to Use? 


45  (3) 


48  (8) 


48  (1) 


49  (1) 


50  (1) 


51  (1) 


51  (4) 

Reporting Measures of Variability 


55  (1) 


56  (1) 


56  (2) 


58  (18) 


58  (2) 


60  (4) 

Converting Raw Scores to z Scores and Percentiles 


64  (8) 

Practical Uses of z Scores 


69  (1) 


70  (2) 

Deriving Raw Scores from Percentiles 


72  (2) 


74  (1) 


74  (2) 

Introduction to Hypothesis Testing 


76  (22) 


76  (3) 


77  (1) 


77  (2) 


79  (1) 


79  (3) 


82  (1) 


82  (1) 


83  (1) 


83  (2) 

The OneTailed Research Hypothesis 


84  (1) 

The TwoTailed Research Hypothesis 


84  (1) 

The Null Research Hypothesis 


85  (1) 

Testing the Null Hypothesis 


85  (3) 


88  (2) 


88  (1) 


88  (2) 

Errors in Drawing Conclusions About Relationships 


90  (2) 


91  (1) 

Statistically Significant Relationships and Meaningful Findings 


92  (3) 

Assessing Strength (Effect Size) 


92  (2) 

Is the Relationship Surprising? 


94  (1) 

Complex Interpretations of Statistically Significant Relationships 


95  (1) 


95  (1) 


96  (2) 

Sampling Distributions and Hypothesis Testing 


98  (18) 

Sample Size and Sampling Error 


98  (2) 

Sampling Distributions and Inference 


100  (2) 

Comparing an Experimental Sample with Its Population 


100  (1) 

Comparing a Nonexperimental Sample with Its Population 


101  (1) 

Sampling Distribution of Means 


102  (9) 

Samples Drawn from Normal Distributions 


105  (5) 

Samples Drawn from Skewed Distributions 


110  (1) 

Estimating Parameters from Statistics 


111  (3) 

Constructing a 95 Percent Confidence Interval 


112  (1) 

Constructing a 99 Percent Confidence Interval 


112  (2) 


114  (1) 


114  (1) 


115  (1) 

Selecting a Statistical Test 


116  (18) 

The Importance of Selecting the Correct Statistical Test 


116  (2) 

Factors to Consider When Selecting a Statistical Test 


118  (7) 


118  (1) 

Distribution of the Variables within the Population 


119  (1) 

Level of Measurement of the Independent and Dependent Variables 


120  (1) 

Amount of Statistical Power That is Desirable 


121  (3) 

Robustness of Tests Being Considered 


124  (1) 

Parametric and Nonparametric Tests 


125  (1) 

Multivariate Statistical Tests 


126  (1) 

General Guidelines for Test Selection 


127  (2) 

Getting Help With Data Analyses 


129  (1) 


130  (2) 


132  (2) 


134  (30) 


135  (3) 


135  (3) 


138  (2) 


140  (2) 

Interpreting Linear Correlations 


142  (4) 

The Range of Correlation Coefficients 


143  (1) 

Interpreting Very Strong Correlations 


143  (1) 

The Coefficient of Determination 


144  (1) 

Correlation is Not Causation 


145  (1) 

Computation and Presentation of Pearson's r 


146  (2) 

Using Pearsons's r for Inference 


148  (6) 

Example: Verbal Participation among Female Group Members 


149  (3) 

Example: Worker Experience and Error Rates 


152  (2) 

Nonparametric Alternatives 


154  (1) 

Spearman's rho and Kendall's tau 


154  (1) 

Example: Caregiver Attitudes and Longevity of Hospice Patients 


154  (1) 

Using Correlation with Three or More Variables 


155  (4) 


155  (1) 


156  (3) 

Other Multivariate Tests That Use Correlation 


159  (3) 


159  (2) 


161  (1) 


162  (1) 


162  (2) 


164  (23) 


164  (3) 

What is Simple Linear Regression? 


167  (2) 

Formulating a Research Question 


168  (1) 

Limitations of Simple Linear Regression 


168  (1) 

Computation of the Regression Equation 


169  (3) 

More About the Regression Line 


172  (4) 

The LeastSquares Criterion 


172  (2) 

The Regression Coefficient (b) 


174  (1) 


174  (1) 


175  (1) 

Interchanging X and Y Variables 


176  (1) 


176  (1) 


177  (1) 


177  (1) 

Using Regression Analyses in Social Work Practice 


177  (3) 

Example: Socializing with Family Members and Life Satisfaction 


177  (2) 

Example: Worker's Case Load Size and Number of Sick Days Taken 


179  (1) 

Regression with Three or More Variables 


180  (2) 

Other Types of Regression Analyses 


182  (2) 


182  (1) 


183  (1) 


184  (1) 


185  (2) 


187  (28) 

The ChiSquare Test of Association 


187  (15) 


189  (2) 


191  (2) 


193  (3) 

Computation of ChiSquare 


196  (1) 

Presentation of ChiSquare 


197  (1) 

Interpreting the Results of a ChiSquare Analysis 


197  (1) 

Meaningfulness and Sample Size 


198  (2) 

Related Indicators of the Strength of a Relationship 


200  (1) 

Restrictions on the Use of ChiSquare 


201  (1) 

An Alternative to ChiSquare: Fisher's Exact Test 


202  (1) 

Using ChiSquare in Social Work Practice 


202  (4) 

Example: Discharge Planning and Readmission 


202  (3) 

Example: Legislators' Voting Patterns and Tax Issues 


205  (1) 

ChiSquare with Three or More Variables 


206  (3) 

Problems with Sizes of Expected Frequencies 


207  (1) 

Effects of Introducing Additional Variables 


208  (1) 

Special Applications of the ChiSquare Formula 


209  (4) 


209  (2) 


211  (2) 


213  (1) 


214  (1) 

t Tests and Analysis of Variance 


215  (28) 


216  (2) 


218  (6) 

Comparing a Sample's Mean to a Population's Mean 


218  (2) 


220  (1) 


221  (1) 

A Nonparametric Alternative: The ChiSquare GoodnessofFit Test 


221  (3) 


224  (3) 

Use with Two Connected (or Matched) Samples Measured Once 


224  (1) 

Use with One Sample Measured Twice 


224  (1) 

A Nonparametric Alternative: The Wilcoxon Sign Test 


225  (2) 


227  (11) 

Example: Study Guide for the State Merit Exam 


228  (1) 

Example: Treatment of Marital Problems 


229  (3) 


232  (3) 

Nonparametric Alternatives: U and KS 


235  (3) 

Simple Analysis of Variance (OneWay Anova) 


238  (2) 


239  (1) 

A Nonparametric Alternative: The KruskalWallis Test 


240  (1) 

Multiple Analysis of Variance 


240  (1) 


241  (1) 


241  (2) 
References and Further Reading 

243  (2) 
Glossary 

245  (17) 
Index 

262  