The Essentials of Statistics A Tool for Social Research

by Healey, Joseph F.

• ISBN13: 9780495009757
• ISBN10: 049500975X
• Edition: 1st
• Format: Paperback
• Copyright: 2006-08-01
• Publisher: Wadsworth Publishing

Summary

Prologue: Basic Review of Mathematics. 1. Introduction. PART I. Descriptive Statistics. 2. Basic Descriptive Statistics: Percentages, Ratios and Rates, Tables, Charts, and Graphs. 3. Measures of Central Tendency. 4. Measures of Dispersion. 5. The Normal Curve. PART II. Inferential Statistics. 6. Inferential Statistics, the Sampling Distribution and Estimation. 7. Hypothesis Testing I: The One Sample Case. 8. Hypothesis Testing II: The Two Sample Case. 9. Hypothesis Testing III: The Analysis of Variance. 10. Hypothesis Testing IV: Chi Square. PART III. Measures of Association. 11. Bivariate Association For Variables Measured at the Nominal Level. 12. Bivariate Association For Variables Measured at the Ordinal Level. 13. Association Between Variables Measured at the Interval-Ratio Level. PART IV. Multivariate Techniques. 14. Partial Correlation and Multiple Regression and Correlation. Appendix A. Area under the Normal Curve. Appendix B. Distribution of t. Appendix C. Distribution of Chi Square. Appendix D. Distribution of F. Appendix E. Using Statistics: Ideas for Research Projects. Appendix F. An Introduction to Computerized Statistics Programs (SPSS for Windows). Appendix G. Code Book for the General Social Survey, 2004. Answers to Odd-Numbered Computational Problems. Glossary. Index.

Table of Contents

Preface	xv
Prologue / Basic Mathematics Review	1	(7)
Introduction	8	(19)
Why Study Statistics?	8	(1)
The Role of Statistics in Scientific Inquiry	9	(3)
The Goals of This Text	12	(1)
Descriptive and Inferential Statistics	13	(3)
Statistics in Everyday Life: Introduction	15	(1)
Level of Measurement	16	(11)
Step by Step: Determining the Level of Measurement of a Variable	19	(2)
Summary	21	(1)
Glossary	22	(1)
Problems	22	(3)
Introduction to SPSS and the General Social Survey	25	(2)
PART I DESCRIPTIVE STATISTICS	27	(96)
Basic Descriptive Statistics: Percentages, Ratios and Rates, Tables, Charts, and Graphs	28	(37)
Percentages and Proportions	28	(3)
Application 2.1	30	(1)
Step by Step: Computing Percentages and Proportions	31	(1)
Ratios, Rates, and Percentage Change	31	(5)
Application 2.2	33	(1)
Application 2.3	33	(1)
Application 2.4	34	(1)
Statistics in Everyday Life: Road Rage	35	(1)
Step by Step: Computing Ratios, Rates, and Percent Change	36	(1)
Frequency Distributions: Introduction	36	(1)
Frequency Distributions for Variables Measured at the Nominal and Ordinal Levels	37	(2)
Frequency Distributions for Variables Measured at the Interval-Ratio Level	39	(7)
Step by Step: Computing Midpoints	42	(3)
Step by Step: Constructing Frequency Distributions for Interval-Ratio Variables	45	(1)
Constructing Frequency Distributions for Interval-Ratio-Level Variables: A Review	46	(1)
Application 2.5	47	(1)
Charts and Graphs	47	(18)
Statistics in Everyday Life: Increasing Congestion and Lost Time on the Road	52	(1)
Summary	53	(1)
Summary of Formulas	53	(1)
Glossary	53	(1)
Multimedia Resources	54	(1)
Problems	54	(5)
Using SPSS for Windows to Produce Frequency Distributions and Graphs	59	(6)
Measures of Central Tendency	65	(20)
Introduction	65	(1)
The Mode	65	(2)
The Median	67	(2)
Step by Step: Computing the Median	69	(1)
The Mean	69	(1)
Application 3.1	70	(1)
Some Characteristics of the Mean	70	(4)
Step by Step: Computing the Mean	71	(3)
Statistics in Everyday Life: Housing Costs, Football Salaries, and Skew	74	(1)
Choosing a Measure of Central Tendency	74	(11)
Summary	76	(1)
Summary of Formulas	77	(1)
Glossary	77	(1)
Multimedia Resources	77	(1)
Problems	77	(5)
Using SPSS for Windows for Measures of Central Tendency	82	(3)
Measures of Dispersion	85	(18)
Introduction	85	(1)
The Range (R) and Interquartile Range (Q)	86	(1)
Computing the Range and Interquartile Range	87	(1)
The Standard Deviation and Variance	88	(5)
Step by Step: Computing the Standard Deviation	91	(1)
Application 4.1	91	(1)
Application 4.2	92	(1)
Computing the Standard Deviation: An Additional Example	93	(1)
Statistics in Everyday Life: Where's the Nicest Place to Live?	94	(1)
Interpreting the Standard Deviation	94	(9)
Summary	95	(1)
Summary of Formulas	96	(1)
Glossary	96	(1)
Multimedia Resources	96	(1)
Problems	96	(3)
Using SPSS for Windows for Measures of Dispersion	99	(4)
The Normal Curve	103	(20)
Introduction	103	(3)
Statistics in Everyday Life: How Normal Is the Normal Curve?	106	(1)
Computing Z Scores	106	(1)
Step by Step: Computing Z Scores	107	(1)
The Normal Curve Table	107	(2)
Finding Total Area Above and Below a Score	109	(2)
Finding Areas Between Two Scores	111	(3)
Step by Step: Finding Areas Above and Below Positive and Negative Z Scores	111	(1)
Application 5.1	112	(1)
Step by Step: Finding Areas Between Z Scores	113	(1)
Application 5.2	114	(1)
Using the Normal Curve to Estimate Probabilities	114	(9)
Step by Step: Finding Probabilities	117	(1)
Application 5.3	117	(1)
Statistics in Everyday Life: Applying the Laws of Probability	118	(1)
Summary	119	(1)
Summary of Formulas	119	(1)
Glossary	119	(1)
Multimedia Resources	119	(1)
Problems	120	(3)
PART II INFERENTIAL STATISTICS	123	(128)
Introduction to Inferential Statistics, the Sampling Distribution, and Estimation	124	(28)
Introduction	124	(1)
Probability Sampling	125	(1)
The Sampling Distribution	126	(4)
The Sampling Distribution: An Additional Example	130	(2)
Symbols and Terminology	132	(1)
Introduction to Estimation	133	(1)
Bias and Efficiency	133	(3)
Estimation Procedures: Introduction	136	(2)
Interval Estimation Procedures for Sample Means (Large Samples)	138	(2)
Step by Step: Constructing Confidence Intervals for Sample Means	140	(1)
Interval Estimation Procedures for Sample Proportions (Large Samples)	140	(3)
Application 6.1	141	(1)
Step by Step: Constructing Confidence Intervals for Sample Proportions	142	(1)
Application 6.2	143	(1)
A Summary of the Computation of Confidence Intervals	143	(1)
Statistics in Everyday Life: Election Projections, Polls, and Surveys	144	(1)
Controlling the Width of Interval Estimates	144	(8)
Summary	148	(1)
Summary of Formulas	148	(1)
Glossary	148	(1)
Multimedia Resources	149	(1)
Problems	149	(3)
Hypothesis Testing I: The One-Sample Case	152	(30)
Introduction	152	(1)
An Overview of Hypothesis Testing	153	(5)
The Five-Step Model for Hypothesis Testing	158	(3)
Step by Step: Testing the Significance of the Difference Between a Sample Mean and a Population Mean (Large Samples): Computing Z(obtained) and Interpreting Results	161	(1)
One-Tailed and Two-Tailed Tests of Hypothesis	161	(6)
Application 7.1	162	(5)
Selecting an Alpha Level	167	(1)
The Student's t Distribution	168	(5)
Step by Step: Testing the Significance of the Difference Between a Sample Mean and a Population Mean (Small Samples): Computing t(obtained) and Interpreting Results	172	(1)
Tests of Hypotheses for Single-Sample Proportions (Large Samples)	173	(9)
Step by Step: Testing the Significance of the Difference Between a Sample Proportion and a Population Proportion (Large Samples): Computing Z(obtained) and Interpreting Results	175	(1)
Application 7.2	175	(1)
Summary	176	(1)
Summary of Formulas	177	(1)
Glossary	177	(1)
Multimedia Resources	178	(1)
Problems	178	(4)
Hypothesis Testing II: The Two-Sample Case	182	(25)
Introduction	182	(1)
Hypothesis Testing with Sample Means (Large Samples)	182	(8)
Step by Step: Testing the Difference in Sample Means for Significance (Large Samples): Computing Z(obtained) and Interpreting Results	186	(1)
Application 8.1	187	(1)
Statistics in Everyday Life: Culture Wars	187	(3)
Hypothesis Testing with Sample Means (Small Samples)	190	(2)
Step by Step: Testing the Difference in Sample Means for Significance (Small Samples): Computing t(obtained) and Interpreting Results	192	(1)
Hypothesis Testing with Sample Proportions (Large Samples)	192	(2)
The Limitations of Hypothesis Testing: Significance Versus Importance	194	(13)
Step by Step: Testing the Difference in Sample Proportions for Significance (Large Samples): Computing Z(obtained) and Interpreting Results	195	(1)
Application 8.2	196	(1)
Summary	197	(1)
Summary of Formulas	198	(1)
Glossary	198	(1)
Multimedia Resources	199	(1)
Problems	199	(4)
Using SPSS for Windows to Test The Significance of the Difference Between Two Means	203	(4)
Hypothesis Testing III: The Analysis of Variance	207	(21)
Introduction	207	(1)
The Logic of the Analysis of Variance	208	(1)
The Computation of ANOVA	209	(2)
A Computational Shortcut	211	(1)
Step by Step: Computing ANOVA	211	(1)
A Computational Example	212	(1)
A Test of Significance for ANOVA	212	(3)
Application 9.1	214	(1)
An Additional Example for Computing and Testing the Analysis of Variance	215	(3)
Statistics in Everyday Life: Who Gets Rich?	217	(1)
The Limitations of the Test	218	(10)
Summary	219	(1)
Summary of Formulas	220	(1)
Glossary	220	(1)
Multimedia Resources	221	(1)
Problems	221	(3)
Using SPSS for Windows to Conduct Analysis of Variance	224	(4)
Hypothesis Testing IV: Chi Square	228	(23)
Introduction	228	(1)
Bivariate Tables	229	(1)
The Logic of Chi Square	230	(1)
The Computation of Chi Square	231	(2)
Step by Step: Computing Chi Square	233	(1)
The Chi Square Test for Independence	233	(3)
Step by Step: Computing Column Percents	236	(1)
The Chi Square Test: An Additional Example	236	(4)
Application 10.1	237	(3)
The Limitations of the Chi Square Test	240	(11)
Summary	241	(1)
Summary of Formulas	241	(1)
Glossary	242	(1)
Multimedia Resources	242	(1)
Problems	242	(4)
Using SPSS for Windows to Conduct the Chi Square Test	246	(5)
PART III BIVARIATE MEASURES OF ASSOCIATION	251	(78)
Introduction to Bivariate Association and Measures of Association for Variables Measured at the Nominal Level	252	(27)
Statistical Significance and Theoretical Importance	252	(1)
Association Between Variables and Bivariate Tables	253	(2)
Three Characteristics of Bivariate Associations	255	(4)
Introduction to Measures of Association	259	(1)
Application 11.1	260	(1)
Measures of Association for Variables Measured at the Nominal Level: Chi Square-Based Measures	260	(4)
Step by Step: Calculating and Interpreting Phi and Cramer's V	263	(1)
Application 11.2	264	(1)
Lambda: A Proportional Reduction in Error Measure of Association for Nominal-Level Variables	264	(15)
Step by Step: Calculating and Interpreting Lambda	268	(1)
Statistics in Everyday Life: The Truth About Astrology	269	(1)
Summary	270	(1)
Summary of Formulas	270	(1)
Glossary	270	(1)
Multimedia Resources	271	(1)
Problems	271	(3)
Using SPSS for Windows to Test Bivariate Association for Significance and Association	274	(5)
Association Between Variables Measured at the Ordinal Level	279	(23)
Introduction	279	(1)
Proportional Reduction in Error (PRE)	279	(1)
Gamma	280	(4)
Determining the Direction of Relationships	284	(4)
Step by Step: Computing and Interpreting Gamma	287	(1)
Application 12.1	288	(1)
Spearman's Rho (rs)	288	(14)
Step by Step: Computing and Interpreting Spearman's Rho	291	(1)
Application 12.2	292	(1)
Summary	292	(1)
Summary of Formulas	293	(1)
Glossary	293	(1)
Multimedia Resources	293	(1)
Problems	293	(5)
Using SPSS for Windows to Produce Ordinal-Level Measures of Association	298	(4)
Association Between Variables Measured at the Interval-Ratio Level	302	(27)
Introduction	302	(1)
Scattergrams	302	(4)
Regression and Prediction	306	(2)
The Computation of a and b	308	(3)
Step by Step: Computing the Slope (b)	310	(1)
Step by Step: Computing the Y Intercept (a)	311	(1)
The Correlation Coefficient (Pearson's r)	311	(2)
Step by Step: Computing Pearson's r	312	(1)
Interpreting the Correlation Coefficient: r2	313	(4)
Application 13.1	316	(1)
The Correlation Matrix	317	(12)
Statistics in Everyday Life: Correlation, Causation, and Cancer	319	(1)
Summary	320	(1)
Summary of Formulas	321	(1)
Glossary	321	(1)
Multimedia Resources	322	(1)
Problems	322	(3)
Using SPSS for Windows to Produce Pearson's r	325	(4)
PART IV MULTIVARIATE TECHNIQUES	329	(26)
Partial Correlation and Multiple Regression and Correlation	330	(25)
Introduction	330	(1)
Partial Correlation	330	(5)
Step by Step: Computing and Interpreting Partial Correlations	334	(1)
Multiple Regression: Predicting the Dependent Variable	335	(3)
Step by Step: Computing the Regression Coefficients (b and a)	338	(1)
Multiple Regression: Assessing the Effects of the Independent Variables	338	(3)
Step by Step: Computing Beta-Weight (b*)	340	(1)
Multiple Correlation	341	(1)
Step by Step: Computing R2	342	(1)
The Limitations of Multiple Regression and Correlation	342	(13)
Application 14.1	343	(2)
Statistics in Everyday Life: Beta-Weights and Baseball	345	(1)
Summary	346	(1)
Summary of Formulas	346	(1)
Glossary	347	(1)
Multimedia Resources	347	(1)
Problems	348	(3)
Using SPSS for Windows for Regression Analysis	351	(4)
Appendix A Area Under the Normal Curve	355	(4)
Appendix B Distribution of t	359	(1)
Appendix C Distribution of Chi Square	360	(1)
Appendix D Distribution of F	361	(2)
Appendix E Using Statistics: Ideas for Research Projects	363	(5)
Appendix F An Introduction to SPSS for Windows	368	(9)
Appendix G Codebook for the General Social Survey, 2004	377	(8)
Appendix H Glossary of Symbols	385	(2)
Answers to Odd-Numbered Computational Problems	387	(8)
Glossary	395	(5)
Index	400