Statistics in Criminal Justice

by Weisburd, David

• ISBN13: 9780534518400
• ISBN10: 0534518400
• Edition: CD
• Format: Hardcover
• Copyright: 1998-06-01
• Publisher: Wadsworth Pub Co

Summary

This text is written specifically for the criminal justice student and for student comprehension. Filled with examples and exercises pertinent for criminal justice students, the text assumes no previous exposure to statistics. It takes a research-oriented

Table of Contents

preface	xx
chapter one Introduction: Statistics as a Research Tool	2	(12)
The Purpose of Statistics Is to Clarify and Not Confuse	4	(1)
Statistics Are Used to Solve Problems	5	(1)
Basic Principles Apply across Statistical Techniques	6	(3)
The Uses of Statistics	9	(4)
Descriptive Statistics	9	(1)
Inferential Statistics	10	(2)
Taking into Account Competing Explanations: Multivariate Statistics	12	(1)
Chapter Summary	13	(1)
chapter two Measurement: The Basic Building Block of Research	14	(18)
Science and Measurement: Classification as a First Step in Research	16	(1)
Levels of Measurement	17	(4)
Nominal Scales	17	(2)
Ordinal Scales	19	(1)
Interval Scales	20	(1)
Relating Interval, Ordinal, and Nominal Scales: The Importance of Collecting Data at the Highest Level Possible	21	(1)
What Is a Good Measure?	22	(3)
Chapter Summary	25	(1)
Key Terms	26	(1)
Exercises	26	(3)
Computer Exercises	29	(3)
chapter three Describing the Typical Case: Measures of Central Tendency	32	(24)
The Mode: Central Tendency in Nominal Scales	33	(3)
The Median: Taking into Account Position	36	(4)
The Mean: Adding Value to Position	40	(7)
Comparing Results Gained Using the Mean and Median	42	(3)
Other Characteristics of the Mean	45	(2)
Using the Mean for Noninterval Scales	47	(1)
Statistics in Practice: Comparing the Median and the Mean	48	(2)
Chapter Summary	50	(1)
Key Terms	51	(1)
Symbols and Formulas	51	(1)
Exercises	52	(2)
Computer Exercises	54	(2)
chapter four How Typical Is the Typical Case? Measuring Dispersion	56	(22)
Measures of Dispersion for Nominal- and Ordinal-Level Data	57	(6)
The Proportion	58	(1)
The Percentage	58	(1)
The Variation Ratio	59	(2)
Index of Qualitative Variation	61	(2)
Measuring Dispersion in Interval Scales: The Range, Variance, and Standard Deviation	63	(7)
The Variance	65	(2)
The Standard Deviation	67	(3)
The Coefficient of Relative Variation	70	(1)
A Note on the Mean Deviation	70	(2)
Chapter Summary	72	(1)
Key Terms	73	(1)
Symbols and Formulas	74	(1)
Exercises	75	(2)
Computer Exercise	77	(1)
chapter five Representing an Array of Data: Frequency Distributions	78	(24)
What Is a Frequency Distribution?	79	(6)
Types of Distributions in Statistics	85	(3)
The Normal Frequency Distribution, or Normal Curve	88	(7)
Characteristics of the Normal Frequency Distribution	89	(2)
z-Scores	91	(4)
Chapter Summary	95	(1)
Key Terms	96	(1)
Symbols and Formulas	96	(1)
Exercises	97	(2)
Computer Exercises	99	(3)
chapter six The Logic of Statistical Inference: Making Statements about Populations on the Basis of Sample Statistics	102	(14)
The Research Hypothesis	103	(2)
Common-Sense Reasoning and the Research Hypothesis	104	(1)
The Null Hypothesis	105	(1)
The Null Hypothesis and Statistical Inference	106	(1)
Risks of Error in Hypothesis Testing	107	(2)
Risks of Error and Statistical Levels of Significance	109	(1)
Departing from Conventional Significance Criteria	110	(2)
Chapter Summary	112	(1)
Key Terms	113	(1)
Symbols and Formulas	114	(1)
Exercises	114	(2)
chapter seven Defining Risks of Error: From Probabilities to a Sampling Distribution	116	(22)
The Fair Coin Toss	118	(3)
The Multiplication Rule	118	(3)
Different Ways of Getting Similar Results	121	(3)
Solving More Complex Problems	124	(1)
The Binomial Distribution	125	(4)
Using the Binomial Distribution to Estimate Type I Error	129	(2)
Probability Distributions and Sampling Distributions	131	(1)
Chapter Summary	132	(1)
Key Terms	133	(1)
Symbols and Formulas	133	(1)
Exercises	134	(4)
chapter eight Steps in a Statistical Test: Using the Binomial Distribution to Make Decisions about Hypotheses	138	(20)
The Problem: The Impacts of Problem-oriented Policing on Disorderly Activity at Violent-Crime Hot Spots	139	(1)
Assumptions: Laying the Foundations for Statistical Inference	140	(8)
Level of Measurement	141	(1)
Shape of the Population Distribution	142	(1)
Sampling Method	142	(4)
The Hypotheses	146	(1)
Stating All of the Assumptions	147	(1)
Selecting a Sampling Distribution	148	(1)
The Significance Level and Rejection Region	149	(3)
Choosing a One-Tailed or a Two-Tailed Rejection Region	149	(3)
The Test Statistic	152	(1)
Making a Decision	152	(1)
Chapter Summary	153	(1)
Key Terms	154	(1)
Exercises	155	(2)
Computer Exercises	157	(1)
chapter nine Chi Square: A Commonly Used Test for Nominal-Level Measures	158	(26)
Testing Hypotheses Concerning the Roll of a Die	159	(6)
The Chi-Square Distribution	160	(2)
Calculating the Chi-Square Statistic	162	(1)
Linking the Chi-Square Statistic to Probabilities: The Chi-Square Table	163	(2)
Relating Two Nominal-Scale Measures in a Chi-Square Test	165	(11)
A Substantive Example: Type of Sanction and Recidivism among Convicted White-Collar Criminals	165	(2)
The Sampling Distribution	167	(1)
Significance Level and Rejection Region	168	(1)
The Test Statistic	169	(2)
The Decision	171	(1)
Extending the Chi-Square Test to Multicategory Variables: The Example of Cell Allocations in Prison	171	(2)
The Sampling Distribution	173	(1)
Significance Level and Rejection Region	174	(1)
The Test Statistic	174	(1)
Decision	175	(1)
The Use of Chi Square When Samples Are Small: A Final Note	176	(1)
Chapter Summary	176	(1)
Key Terms	177	(1)
Symbols and Formulas	178	(1)
Exercises	178	(4)
Computer Exercises	182	(2)
chapter ten An Introduction to Parametric Tests of Significance	184	(26)
Applying Normal Sampling Distributions to Nonnormal Populations	185	(6)
The Central Limit Theorem	187	(4)
Comparing a Sample to an Unknown Population: The z-Test for Proportions	191	(6)
Computing the Mean and Standard Deviation for the Sampling Distribution of a Proportion	191	(2)
Testing Hypotheses with the Normal Distribution: The Case of a New Prison Program	193	(1)
The Sampling Distribution	194	(1)
Significance Level and Rejection Region	195	(1)
The Test Statistic	196	(1)
The Decision	197	(1)
Comparing a Sample to an Unknown Population: The t-Test for Means	197	(2)
Testing Hypotheses with the t Distribution	199	(2)
The Sampling Distribution	200	(1)
The Significance Level and Rejection Region	200	(1)
The Test Statistic	200	(1)
The Decision	201	(1)
A Note about Confidence Intervals	201	(3)
Chapter Summary	204	(1)
Key Terms	205	(1)
Symbols and Formulas	205	(2)
Exercises	207	(3)
chapter eleven Parametric Tests Comparing Means and Proportions in Two Samples	210	(30)
Comparing Sample Proportions: The Case of Drug Testing and Pretrial Misconduct	211	(7)
The Sampling Distribution	214	(3)
Significance Level and Rejection Region	217	(1)
The Test Statistic	217	(1)
The Decision	218	(1)
Comparing Sample Means: The Case of Anxiety among Police Officers and Firefighters	218	(8)
The Sampling Distribution	220	(4)
Significance Level and Rejection Region	224	(1)
The Test Statistic	224	(2)
The Decision	226	(1)
The t-Test for Dependent Samples	226	(5)
The Sampling Distribution	228	(2)
Significance Level and Rejection Region	230	(1)
The Test Statistic	230	(1)
The Decision	231	(1)
A Note on Using t-Tests for Ordinal Scales	231	(1)
Chapter Summary	232	(1)
Key Terms	233	(1)
Symbols and Formulas	233	(2)
Exercises	235	(2)
Computer Exercises	237	(3)
chapter twelve Comparing Means among Multiple Samples: Analysis of Variance	240	(34)
Analysis of Variance	241	(2)
Developing Estimates of Variance between and within Groups	243	(5)
Partitioning Sums of Squares	246	(2)
Developing Estimates of Population Variances	248	(1)
A Substantive Example: Age and White-Collar Crimes	248	(7)
The Sampling Distribution	252	(1)
Significance Level and Rejection Region	253	(1)
The Test Statistic	253	(2)
The Decision	255	(1)
Defining the Strength of the Relationship Observed	255	(4)
Making Pairwise Comparisons between the Groups Studied	259	(2)
A Nonparametric Alternative: The Kruskal-Wallis Test	261	(4)
Sampling Distribution	263	(1)
Significance Level and Rejection Region	263	(1)
The Test Statistic	263	(1)
The Decision	264	(1)
Chapter Summary	265	(1)
Key Terms	266	(1)
Symbols and Formulas	267	(2)
Exercises	269	(3)
Computer Exercises	272	(2)
chapter thirteen Statistical Power: Avoiding Studies That Are Designed for Failure	274	(22)
Statistical Power	275	(2)
Statistical Significance and Statistical Power	277	(1)
Effect Size and Statistical Power	278	(4)
Sample Size and Statistical Power	282	(3)
Parametric versus Nonparametric Tests	285	(1)
Estimating Statistical Power: What Size Sample Is Needed for a Statistically Powerful Study?	285	(4)
Summing Up: Avoiding Studies Designed for Failure	289	(1)
Chapter Summary	290	(1)
Key Terms	291	(1)
Symbols and Formulas	291	(1)
Exercises	291	(4)
Computer Exercise	295	(1)
chapter fourteen Introduction to Correlation and Regression	296	(40)
Measuring Association between Two Interval-Level Variables	297	(3)
Pearson's Correlation Coefficient	300	(16)
The Calculation	304	(3)
Nonlinear Relationships and Pearson's r	307	(5)
Beware of Outliers	312	(4)
Spearman's r	316	(3)
Estimating the Influence of One Variable on Another: The Regression Coefficient	319	(2)
Calculating the Regression Coefficient	320	(1)
Statistical Significance for Correlation and Regression Coefficients	321	(7)
Testing the Statistical Significance of r or b	321	(4)
The Sampling Distribution	325	(1)
Significance Level and Rejection Region	325	(1)
The Test Statistic	326	(1)
The Decision	326	(1)
Testing the Statistical Significance of r(s)	326	(1)
The Sampling Distribution	327	(1)
Significance Level and Critical Region	327	(1)
The Test Statistic	327	(1)
The Decision	327	(1)
Chapter Summary	328	(1)
Key Terms	328	(1)
Symbols and Formulas	329	(2)
Exercises	331	(3)
Computer Exercises	334	(2)
chapter fifteen An Introduction to Bivariate and Multivariate Regression Modeling	336	(30)
Prediction in Regression: Building the Regression Line	337	(5)
The Y-Intercept	338	(1)
The Regression Line	338	(2)
Choosing the Best Line of Prediction Based on Regression Error	340	(2)
Predictions beyond the Distribution Observed in a Sample	342	(1)
Evaluating the Regression Model	342	(5)
Percent of Variance Explained	343	(2)
The F-Test for the Overall Regression	345	(2)
The Importance of Correct Model Specification	347	(6)
Errors in Prediction	347	(1)
Correctly Estimating the Effect of b	348	(5)
Correctly Specifying the Regression Model	353	(1)
Defining Relevant Independent Variables	353	(1)
The Problem of Multicolinearity	354	(2)
The Limits of Criminal Justice Theory	356	(2)
Chapter Summary	358	(1)
Key Terms	359	(1)
Symbols and Formulas	359	(2)
Exercises	361	(4)
Computer Exercises	365	(1)
appendix 1 Areas of the Standard Normal Distribution	366	(2)
appendix 2 Factorials	368	(1)
appendix 3 Critical Values of x^2 Distribution	369	(1)
appendix 4 Critical Values of Student's Distribution	370	(2)
appendix 5 Critical Values of the F Statistic	372	(3)
appendix 6 Critical Value for P (Pcrit), Tukey's HSD Test	375	(1)
appendix 7 Critical Values for Spearman's Rank-Order Correlation Coefficient	376	(1)
Glossary	377	(8)
Index	385