Statistics for Social Workers

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

• ISBN13: 9780205375981
• ISBN10: 0205375987
• Edition: 6th
• Format: Paperback
• Copyright: 2004-01-01
• Publisher: Allyn & Bacon

Summary

This best-selling social work statistics book requires no prior knowledge of statistics, emphasizing a conceptual understanding of the topic and its usefulness to social work practice and research. Rather than focusing on mathematical computation, Statistics for Social Workers instead focuses on providing an understanding of the logical underpinnings of statistical analysis and how to apply the results of analysis in a social work practice environment. the authors have used this approach to teaching statistics for over 25 years, and it remains the most widely used book of its kind.

Table of Contents

Preface	xiii
1 Introduction to Statistical Analysis	1	(19)
USES OF STATISTICAL ANALYSIS	2	(1)
GENERAL METHODOLOGICAL TERMS	3	(7)
Data	3	(1)
Information	3	(1)
Variables and Constants	3	(2)
Conceptualization	5	(1)
Operationalization	6	(1)
Reliability	7	(1)
Validity	7	(1)
Research Hypotheses	8	(2)
LEVELS OF MEASUREMENT	10	(4)
Nominal	10	(1)
Ordinal	11	(2)
Interval	13	(1)
Ratio	13	(1)
LEVELS OF MEASUREMENT AND ANALYSIS OF DATA	14	(1)
OTHER MEASUREMENT CLASSIFICATIONS	15	(1)
Discrete Variables and Continuous Variables	15	(1)
Dichotomous, Binary, and Dummy Variables	15	(1)
CATEGORIES OF STATISTICAL ANALYSES	16	(1)
Number of Variables Analyzed	16	(1)
Purpose of the Analysis	16	(1)
CONCLUDING THOUGHTS	17	(1)
STUDY QUESTIONS	17	(3)
2 Frequency Distributions and Graphs	20	(19)
FREQUENCY DISTRIBUTIONS	21	(3)
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	(7)
Bar Graphs	30	(2)
Pie Charts	32	(1)
Histograms	32	(1)
Frequency Polygons	33	(1)
Pareto Charts	34	(1)
Stem-and-Leaf Plots	35	(1)
A COMMON MISTAKE IN DISPLAYING DATA	36	(1)
CONCLUDING THOUGHTS	37	(1)
STUDY QUESTIONS	37	(2)
3 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	49	(1)
The Interquartile Range	50	(1)
The Mean Deviation	50	(1)
The Variance	51	(1)
The Standard Deviation	52	(3)
Reporting Measures of Variability	55	(1)
CONCLUDING THOUGHTS	56	(1)
STUDY QUESTIONS	56	(2)
4 Normal Distributions	58	(18)
SKEWED DISTRIBUTIONS	58	(2)
NORMAL DISTRIBUTIONS	60	(4)
CONVERTING RAW SCORES TO z SCORES AND PERCENTILES	64	(9)
Practical Uses of z Scores	69	(1)
Example: Student Anxiety	70	(3)
DERIVING RAW SCORES FROM PERCENTILES	73	(1)
CONCLUDING THOUGHTS	74	(1)
STUDY QUESTIONS	74	(2)
5 Introduction to Hypothesis Testing	76	(24)
ALTERNATIVE EXPLANATIONS	76	(5)
Rival Hypotheses	77	(1)
Design Flaws	77	(3)
Sampling Error	80	(1)
PROBABILITY	81	(2)
REFUTING SAMPLING ERROR	83	(2)
Replication	83	(1)
Statistical Analyses	84	(1)
RESEARCH HYPOTHESES	85	(2)
The One-Tailed Research Hypothesis	86	(1)
The Two-Tailed Research Hypothesis	86	(1)
The "No Relationship" Research Hypothesis	87	(1)
TESTING THE NULL HYPOTHESIS	87	(2)
STATISTICAL SIGNIFICANCE	89	(3)
p-Values	90	(1)
Rejection Levels	90	(2)
ERRORS IN DRAWING CONCLUSIONS ABOUT RELATIONSHIPS	92	(1)
Avoiding Type I Errors	93	(1)
STATISTICALLY SIGNIFICANT RELATIONSHIPS AND MEANINGFUL FINDINGS	93	(4)
Assessing Strength (Effect Size)	95	(1)
Is the Relationship Surprising?	96	(1)
Complex Interpretations of Statistically Significant Relationships	97	(1)
CONCLUDING THOUGHTS	97	(1)
STUDY QUESTIONS	98	(2)
6 Sampling Distributions and Hypothesis Testing	100	(18)
SAMPLE SIZE AND SAMPLING ERROR	100	(2)
SAMPLING DISTRIBUTIONS AND INFERENCE	102	(2)
Comparing an Experimental Sample with Its Population	102	(1)
Comparing a Nonexperimental Sample with Its Population	103	(1)
SAMPLING DISTRIBUTION OF MEANS	104	(9)
Samples Drawn from Normal Distributions	107	(5)
Samples Drawn from Skewed Distributions	112	(1)
ESTIMATING PARAMETERS FROM STATISTICS	113	(3)
Constructing a 95 Percent Confidence Interval	114	(1)
Constructing a 99 Percent Confidence Interval	114	(2)
OTHER DISTRIBUTIONS	116	(1)
CONCLUDING THOUGHTS	116	(1)
STUDY QUESTIONS	117	(1)
7 Selecting a Statistical Test	118	(18)
THE IMPORTANCE OF SELECTING THE CORRECT STATISTICAL TEST	118	(2)
FACTORS TO CONSIDER WHEN SELECTING A STATISTICAL TEST	120	(7)
Sampling Method(s) Used	120	(1)
Distribution of the Variables within the Population	121	(1)
Level of Measurement of the Independent and Dependent Variables	122	(1)
Amount of Statistical Power That Is Desirable	123	(3)
Robustness of Tests Being Considered	126	(1)
PARAMETRIC AND NONPARAMETRIC TESTS	127	(1)
MULTIVARIATE STATISTICAL TESTS	128	(1)
GENERAL GUIDELINES FOR TEST SELECTION	129	(2)
GETTING HELP WITH DATA ANALYSES	131	(1)
CONCLUDING THOUGHTS	132	(2)
STUDY QUESTIONS	134	(2)
8 Correlation	136	(29)
USES OF CORRELATION	136	(4)
Scattergrams	137	(3)
PERFECT CORRELATIONS	140	(2)
NONPERFECT CORRELATIONS	142	(1)
INTERPRETING LINEAR CORRELATIONS	143	(4)
Understanding Correlation Coefficients	143	(2)
Interpreting Very Strong Correlations	145	(1)
The Coefficient of Determination	146	(1)
Correlation Is Not Causation	146	(1)
USING CORRELATION FOR INFERENCE	147	(1)
COMPUTATION AND PRESENTATION OF PEARSON'S r	148	(6)
Example: Verbal Participation among Female Group Members	151	(2)
Example: Worker Experience and Error Rates	153	(1)
NONPARAMETRIC ALTERNATIVES	154	(2)
Spearman's rho and Kendall's tau	154	(1)
Example: Caregiver Attitudes and Longevity of Hospice Patients	155	(1)
USING CORRELATION WITH THREE OR MORE VARIABLES	156	(3)
Partial r	156	(1)
Multiple R	156	(2)
Variations of Multiple R	158	(1)
OTHER MULTIVARIATE TESTS THAT USE CORRELATION	159	(3)
Factor Analysis	160	(2)
Cluster Analysis	162	(1)
CONCLUDING THOUGHTS	162	(1)
STUDY QUESTIONS	163	(2)
9 Regression Analyses	165	(24)
WHAT IS PREDICTION?	165	(3)
WHAT IS SIMPLE LINEAR REGRESSION?	168	(2)
Formulating a Research Question	168	(1)
Limitations of Simple Linear Regression	169	(1)
COMPUTATION OF THE REGRESSION EQUATION	170	(3)
MORE ABOUT THE REGRESSION LINE	173	(4)
The Least-Squares Criterion	174	(1)
The Regression Coefficient (b)	174	(1)
The y-Intercept (a)	175	(1)
Predicted Y (Y')	176	(1)
Interchanging X and Y Variables	177	(1)
INTERPRETING RESULTS	177	(1)
Presentation of Y'	177	(1)
The Standard Error	178	(1)
USING REGRESSION ANALYSES IN SOCIAL WORK PRACTICE	178	(2)
Example: Socializing with Family Members and Life Satisfaction	178	(1)
Example: Worker's Caseload Size and Number of Sick Days Taken	179	(1)
REGRESSION WITH THREE OR MORE VARIABLES	180	(4)
OTHER TYPES OF REGRESSION ANALYSES	184	(3)
Discriminant Analysis	184	(1)
Logistic Regression	185	(2)
CONCLUDING THOUGHTS	187	(1)
STUDY QUESTIONS	188	(1)
10 Cross-Tabulation	189	(28)
THE CHI-SQUARE TEST OF ASSOCIATION	189	(15)
Observed Frequencies	191	(2)
Expected Frequencies	193	(2)
Degrees of Freedom	195	(3)
Computation of Chi-Square	198	(1)
Presentation of Chi-Square	199	(1)
Interpreting the Results of a Chi-Square Analysis	199	(1)
Meaningfulness and Sample Size	200	(3)
Reporting the Strength of a Relationship	203	(1)
Restrictions on the Use of Chi-Square	203	(1)
An Alternative to Chi-Square: Fisher's Exact Test	204	(1)
USING CHI-SQUARE IN SOCIAL WORK PRACTICE	204	(4)
Example: Discharge Planning and Readmission	205	(2)
Example: Legislators' Voting Patterns and Tax Issues	207	(1)
CHI-SQUARE 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 CHI-SQUARE FORMULA	211	(4)
McNemar's Test	211	(2)
Median Test	213	(2)
CONCLUDING THOUGHTS	215	(1)
STUDY QUESTIONS	216	(1)
11 t Tests and Analysis of Variance	217	(30)
THE USE OF t TESTS	218	(1)
THE ONE-SAMPLE t TEST	219	(7)
Determining If a Sample Is Representative	220	(2)
Hypothesis Testing	222	(1)
Presentation of Findings	223	(1)
A Nonparametric Alternative: The Chi-Square Goodness-of-Fit Test	223	(3)
THE DEPENDENT t TEST	226	(3)
Use with Two Connected (or Matched) Samples Measured Once	226	(1)
Use with One Sample Measured Twice	226	(1)
A Nonparametric Alternative: The Wilcoxon Sign Test	227	(2)
THE INDEPENDENT t TEST	229	(13)
Example: Treatment of Marital Problems	231	(2)
Example: Study Guide for the State Merit Exam	233	(2)
Example: Staff Turnover	235	(3)
Nonparametric Alternatives: U and K-S	238	(4)
A MULTIVARIATE ALTERNATIVE TO THE t TESTS: T2	242	(1)
SIMPLE ANALYSIS OF VARIANCE (ONE-WAY ANOVA)	242	(3)
A Nonparametric Alternative: The Kruskal-Wallis Test	244	(1)
MULTIPLE ANALYSIS OF VARIANCE	245	(1)
CONCLUDING THOUGHTS	245	(1)
STUDY QUESTIONS	246	(1)
Appendix A Using Statistics to Evaluate Practice Effectiveness	247	(13)
EVALUATING PROGRAMS	247	(5)
Needs Assessments and Formative Evaluations	248	(1)
Outcome Evaluations	248	(3)
Statistical Analyses of Program Outcome Data	251	(1)
EVALUATING INDIVIDUAL PRACTITIONER EFFECTIVENESS	252	(8)
Hypothesis Testing in Single System Research	253	(1)
Statistical Analyses of Single System Data	253	(7)
Glossary	260	(17)
Index	277