Statistics for Social Workers

by Weinbach, Robert W.; Grinnell, Richard M., Jr.

• ISBN13: 9780801333125
• ISBN10: 0801333121
• Edition: 5th
• Format: Paperback
• Copyright: 2000-07-01
• Publisher: Pearson College Div

Summary

This is the leading text for social work statistics courses because of its accessibility and the fact that it assumes no prior background in statistics. This text can be used in introductory-level statistics courses or as part of the research methods sequence in social work. It includes numerous social work practice examples, and discusses types of statistical analyses that are most likely to be encountered by social work practitioners and researchers. This edition has been reorganized and updated, with new content added on statistical power, effect size, and measures of association. New topics have been incorporated, including logistic regression and other methods of analysis not in prior editions. New figures and new content on sampling distributions and standard scores (z-scores) have also been added.

Table of Contents

Preface	xiii
Introduction to Statistical Analysis	1	(19)
Uses of Statistical Analysis	2	(1)
General Methodological Terms	3	(6)
Data	3	(1)
Information	3	(1)
Variables and Constants	3	(2)
Conceptualization	5	(1)
Operationalization	5	(2)
Reliability	7	(1)
Validity	7	(1)
Research Hypotheses	8	(1)
Levels of Measurement	9	(5)
Nominal	10	(1)
Ordinal	11	(2)
Interval	13	(1)
Ratio	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)
Concluding Thoughts	17	(1)
Study Questions	17	(3)
Frequency Distributions and Graphs	20	(19)
Frequency Distributions	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)
Bar Graphs	30	(1)
Pie Charts	30	(2)
Histograms	32	(1)
Frequency Polygons	32	(2)
Pareto Charts	34	(1)
Stem-and-Leaf Plots	34	(1)
A Common Mistake in Displaying Data	35	(1)
Concluding Thoughts	36	(1)
Study Questions	37	(2)
Central Tendency and Variability	39	(19)
Central Tendency	39	(9)
The Mode	40	(2)
The Median	42	(1)
The Mean	43	(2)
Which Measure of Central Tendency to Use?	45	(3)
Variability	48	(8)
The Range	48	(1)
The Interquartile Range	49	(1)
The Mean Deviation	50	(1)
The Variance	51	(1)
The Standard Deviation	51	(4)
Reporting Measures of Variability	55	(1)
Concluding Thoughts	56	(1)
Study Questions	56	(2)
Normal Distributions	58	(18)
Skewed Distributions	58	(2)
Normal Distributions	60	(4)
Converting Raw Scores to z Scores and Percentiles	64	(8)
Practical Uses of z Scores	69	(1)
Example: Student Anxiety	70	(2)
Deriving Raw Scores from Percentiles	72	(2)
Concluding Thoughts	74	(1)
Study Questions	74	(2)
Introduction to Hypothesis Testing	76	(22)
Alternative Explanations	76	(3)
Rival Hypotheses	77	(1)
Design Bias	77	(2)
Sampling Error	79	(1)
Probability	79	(3)
Refuting Sampling Error	82	(1)
Replication	82	(1)
Statistical Analyses	83	(1)
Research Hypotheses	83	(2)
The One-Tailed Research Hypothesis	84	(1)
The Two-Tailed Research Hypothesis	84	(1)
The Null Research Hypothesis	85	(1)
Testing the Null Hypothesis	85	(3)
Statistical Significance	88	(2)
p-Values	88	(1)
Rejection Levels	88	(2)
Errors in Drawing Conclusions About Relationships	90	(2)
Avoiding Type I Errors	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)
Concluding Thoughts	95	(1)
Study Questions	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)
Other Distributions	114	(1)
Concluding Thoughts	114	(1)
Study Questions	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)
Sampling Method(s) Used	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)
Concluding Thoughts	130	(2)
Study Questions	132	(2)
Correlation	134	(30)
Uses of Correlation	135	(3)
Scattergrams	135	(3)
Perfect Correlations	138	(2)
Nonperfect Correlations	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)
Partial r	155	(1)
Multiple R	156	(3)
Other Multivariate Tests That Use Correlation	159	(3)
Factor Analysis	159	(2)
Cluster Analysis	161	(1)
Concluding Thoughts	162	(1)
Study Questions	162	(2)
Regression Analyses	164	(23)
What is Prediction?	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 Least-Squares Criterion	172	(2)
The Regression Coefficient (b)	174	(1)
The y-Intercept (a)	174	(1)
Predicted Y (Y')	175	(1)
Interchanging X and Y Variables	176	(1)
Interpreting Results	176	(1)
Presentation of Y'	177	(1)
The Standard Error	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)
Discriminant Analysis	182	(1)
Logistic Regression	183	(1)
Concluding Thoughts	184	(1)
Study Questions	185	(2)
Cross-Tabulation	187	(28)
The Chi-Square Test of Association	187	(15)
Observed Frequencies	189	(2)
Expected Frequencies	191	(2)
Degrees of Freedom	193	(3)
Computation of Chi-Square	196	(1)
Presentation of Chi-Square	197	(1)
Interpreting the Results of a Chi-Square Analysis	197	(1)
Meaningfulness and Sample Size	198	(2)
Related Indicators of the Strength of a Relationship	200	(1)
Restrictions on the Use of Chi-Square	201	(1)
An Alternative to Chi-Square: Fisher's Exact Test	202	(1)
Using Chi-Square in Social Work Practice	202	(4)
Example: Discharge Planning and Readmission	202	(3)
Example: Legislators' Voting Patterns and Tax Issues	205	(1)
Chi-Square 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 Chi-Square Formula	209	(4)
McNemar's Test	209	(2)
Median Test	211	(2)
Concluding Thoughts	213	(1)
Study Questions	214	(1)
t Tests and Analysis of Variance	215	(28)
The Use of t Tests	216	(2)
The One-Sample t Test	218	(6)
Comparing a Sample's Mean to a Population's Mean	218	(2)
Hypothesis Testing	220	(1)
Presentation of Findings	221	(1)
A Nonparametric Alternative: The Chi-Square Goodness-of-Fit Test	221	(3)
The Dependent t Test	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)
The Independent t Test	227	(11)
Example: Study Guide for the State Merit Exam	228	(1)
Example: Treatment of Marital Problems	229	(3)
Example: Staff Turnover	232	(3)
Nonparametric Alternatives: U and K-S	235	(3)
Simple Analysis of Variance (One-Way Anova)	238	(2)
Computation	239	(1)
A Nonparametric Alternative: The Kruskal-Wallis Test	240	(1)
Multiple Analysis of Variance	240	(1)
Concluding Thoughts	241	(1)
Study Questions	241	(2)
References and Further Reading	243	(2)
Glossary	245	(17)
Index	262