Essential Statistics for the Social and Behavioral Sciences : A Conceptual Approach

by Walsh, Anthony; Ollenburger, Jane C.

• ISBN13: 9780130193391
• ISBN10: 0130193399
• Edition: 1st
• Format: Paperback
• Copyright: 2000-10-02
• Publisher: Pearson

Summary

This book helps readers become intelligent consumers of the social/behavioral science literature and familiarizes them with the fundamental tools of research. It features a conceptual, intuitive approach that is less math-oriented (e.g., not cluttered with all sorts of sub-and superscripts, and not concerned with mathematical derivatives of the various statistics), and that clearly shows the continuity and interrelatedness of the techniques discussed. After the necessary concepts have been explained and the calculations have been performed for each statistic, the text walks readers through a line-by-line explanation of a computer printout (based on actual data) containing that statistic. "Practice Applications" provide research examples with step-by-step solutions to all statistical procedures.Describing Data. Central Tendency and Dispersion. Probability and the Normal Curve. The Sampling Distribution and Estimation Procedures. Hypothesis Testing: Interval/Ratio Data. Analysis of Variance. Hypothesis Testing with Categorical Data: Chi-Square. Measures of Association with Nominal and Ordinal Data. Elaboration and Causal Analysis. Bivariate Correlation and Regression. Multivariate Correlation and Regression.For anyone in the social/behavioral sciences who needs an accessible introduction to statistics.

Table of Contents

Preface	xi
Introduction to Statistical Analysis	1	(16)
Why Study Statistics?	1	(1)
Thinking Statistically	1	(2)
Descriptive and Inferential Statistics	3	(5)
Descriptive Statistics	3	(1)
Inferential Statistics	3	(2)
Statistics and Error	5	(1)
Parametric and Nonparametric Statistics	5	(1)
Operationalization	5	(1)
Reliability and Validity	6	(2)
Measurement	8	(3)
Dependent and Independent Variables	8	(1)
Nominal Level	9	(1)
Ordinal Level	9	(1)
Interval Level	10	(1)
Ratio Level	10	(1)
The Role of Statistics in Science	11	(1)
Summary	12	(1)
Practice Application: Variables and Levels of Measurement	13	(1)
Problems	14	(3)
Presenting and Summarizing Data	17	(16)
Types of Frequency Distributions	17	(4)
Interpreting Cumulative Frequencies	18	(1)
Frequency Distribution of Grouped Data	19	(1)
Limits, Sizes, and Midpoints of Class Intervals	19	(1)
Advantages and Disadvantages of Grouping Data	20	(1)
Bar Graphs and Pie Charts	21	(4)
Histograms and Frequency Polygons	23	(2)
Numerical Summation of Data: Percentages, Proportions, and Ratios	25	(1)
Summary	26	(1)
Practice Application: Displaying and Summarizing Data	26	(4)
Problems	30	(3)
Central Tendency and Dispersion	33	(22)
Measures of Central Tendency	33	(7)
Mode	33	(1)
Median	34	(1)
Computing the Median with Grouped Data	34	(1)
The Mean	35	(1)
Computing the Mean from Grouped Data	36	(1)
A Research Example	37	(1)
Choosing a Measure of Central Tendency	38	(2)
Measures of Dispersion	40	(8)
Range	40	(2)
Standard Deviation	42	(2)
Computational Formula for s	44	(1)
Variability and Variance	45	(1)
Computing the Standard Deviation from Grouped Data	46	(1)
Coefficient of Variation	46	(1)
Index of Qualitative Variation	47	(1)
Summary	48	(1)
Practice Application: Central Tendency and Dispersion	49	(1)
Reference	49	(1)
Problems	50	(5)
Probability and the Normal Curve	55	(22)
Probability	55	(6)
The Multiplication Rule	55	(1)
The Addition Rule	56	(2)
Theoretical Probability Distributions	58	(3)
The Normal Curve	61	(10)
Different Kinds of Curves	63	(1)
The Standard Normal Curve	64	(1)
The z Scores	65	(3)
Finding Area of the Curve Below the Mean	68	(3)
Summary	71	(1)
Practice Application: The Normal Curve and z Scores	71	(1)
References	72	(1)
Problems	73	(4)
The Sampling Distribution and Estimation Procedures	77	(20)
Sampling	77	(2)
Simple Random Sampling	78	(1)
Stratified Random Sampling	79	(1)
The Sampling Distribution	79	(4)
The Central Limit Theorem	83	(6)
Standard Error of the Sampling Distribution	84	(1)
Point and Interval Estimates	84	(1)
Confidence Intervals and Alpha Levels	85	(1)
Calculating Confidence Intervals	86	(2)
Sampling and Confidence Intervals	88	(1)
Interval Estimates for Proportions	88	(1)
Estimating Sample Size	89	(1)
Estimating Sample Size for Proportions	90	(1)
Summary	90	(1)
Practice Application: The Sampling Distribution and Estimation	91	(2)
Problems	93	(4)
Hypothesis Testing: Interval/Ratio Data	97	(26)
The Logic of Hypothesis Testing	97	(2)
The Evidence and Statistical Significance	99	(1)
Errors in Hypothesis Testing	100	(1)
One Sample z Test	101	(3)
Decision Rule	102	(2)
The t Test	104	(6)
Degrees of Freedom	104	(1)
The t Distribution	105	(1)
Directional Hypotheses: One-and Two-Tailed Tests	105	(1)
Computing t	106	(2)
t Test for Correlated (Dependent) Means	108	(2)
Effects of Sample Variance on H0 Decision	110	(3)
Large Sample t Test: A Computer Example	110	(1)
Interpreting the Printout	110	(3)
Calculating t with Unequal Variances	113	(1)
Testing Hypotheses for Single-Sample Proportions	113	(1)
Statistical Versus Substantive Significance, and Strength of Association	114	(1)
Summary	115	(1)
Practice Application: t Test	116	(2)
Problems	118	(5)
Analysis of Variance	123	(24)
Assumptions of Analysis of Variance	123	(1)
The Basic Logic of ANOVA	123	(3)
The Idea of Variance Revisited	124	(1)
The Advantage of ANOVA over Multiple Tests	125	(1)
The F Distribution	126	(2)
An Example of ANOVA	126	(2)
Determining Statistical Significance: Mean Square and the F Ratio	128	(2)
ETA Squared	130	(1)
Multiple Comparisons: The Scheffe Test	130	(1)
Two-Way Analysis of Variance	131	(3)
Determining Statistical Significance	134	(6)
Significance Levels	134	(2)
Understanding Interaction	136	(2)
A Research Example of a Significant Interaction Effect	138	(2)
Summary	140	(1)
Practice Application	141	(1)
Problems	142	(5)
Hypothesis Testing with Categorical Data: Chi-Square Test	147	(20)
Table Construction	147	(5)
Putting Percentages in Tables	149	(1)
Assumptions for the Use of Chi-Square	149	(3)
The Chi-Square Distribution	152	(2)
Yates' Correction for Continuity	153	(1)
Chi-Square Distribution and Goodness of Fit	153	(1)
Chi-Square-Based Measures of Association	154	(2)
Sample Size and Chi-Square	155	(1)
Contingency Coefficient	156	(3)
Cramer's V	157	(1)
A Computer Example of Chi-Square	157	(2)
Kruskal-Wallis One-Way Analysis of Variance	159	(1)
Summary	160	(1)
Practice Application: Chi-Square	160	(2)
Reference	162	(1)
Problems	163	(4)
Nonparametric Measures of Association	167	(24)
The Idea of Association	167	(2)
Does an Association Exist?	167	(1)
What Is the Strength of the Association?	168	(1)
What Is the Direction of the Association?	168	(1)
Proportional Reduction in Error	169	(3)
The Concept of Paired Cases	172	(1)
A Computer Example	173	(1)
Gamma	174	(3)
Lambda	177	(1)
Somer's d	178	(1)
Tau-B	179	(1)
The Odd's Ratio and Yule's Q	180	(2)
Spearman's Rank Order Correlation	182	(1)
Which Test of Association Should We Use?	183	(1)
Summary	184	(1)
Practice Application: Nonparametric Measures of Association	184	(3)
References	187	(1)
Problems	188	(3)
Elaboration of Tabular Data	191	(22)
Causal Analysis	191	(1)
Criteria for Causality	191	(3)
Association	191	(1)
Temporal Order	192	(1)
Spuriousness	192	(1)
Necessary Cause	193	(1)
Sufficient Cause	193	(1)
Necessary and Sufficient Cause	193	(1)
A Statistical Demonstration of Cause-and-Effect Relationships	194	(1)
Multivariate Contingency Analysis	195	(5)
Introducing a Third Variable	196	(2)
Explanation and Interpretation	198	(2)
Illustrating Elaboration Outcomes	200	(7)
Controlling for One Variable	200	(2)
Further Elaboration: Two Control Variables	202	(1)
Partial Gamma	202	(2)
When Not to Compute Partial Gamma	204	(2)
Problems with Tabular Elaboration	206	(1)
Summary	207	(1)
Practice Application: Bivariate Elaboration	207	(2)
Reference	209	(1)
Problems	210	(3)
Bivariate Correlation and Regression	213	(24)
Preliminary Investigation: The Scattergram	215	(2)
The Slope	217	(1)
The Intercept	218	(1)
The Pearson Correlation Coefficient	219	(5)
Covariance and Correlation	220	(4)
Partitioning r Squared and Sum of Squares	224	(1)
Standard Error of the Estimate	224	(2)
Standard Error of r	225	(1)
Significance Testing for Pearson's r	226	(1)
The Interrelationship of b, r, and β	226	(1)
Summarizing Properties of r, b, and β	227	(1)
Summarizing Prediction Formulas	227	(1)
A Computer Example of Bivariate Correlation and Regression	228	(2)
Practice Application: Bivariate Correlation and Regression	230	(1)
Practice Application: Bivariate Correlation and Regression	231	(1)
Reference	232	(1)
Problems	233	(4)
Multivariate Correlation and Regression	237	(24)
Partial Correlation	237	(6)
Computing Partial Correlations	238	(1)
Computer Example and Interpretation	239	(2)
Second-Order Partials: Controlling for Two Independent Variables	241	(1)
The Multiple Correlation Coefficient	241	(2)
Multiple Regression	243	(3)
The Unstandardized Partial Slope	243	(2)
The Standardized Slope (β)	245	(1)
A Computer Example of Multiple Regression and Interpretation	246	(3)
Summary Statistics: Multiple R, R2, sy.x, and ANOVA	246	(2)
The Predictor Variables: b, β, and t	248	(1)
A Visual Representation of Multiple Regression	249	(1)
Dummy Variable Regression	249	(2)
Regression and Interaction	251	(2)
Summary	253	(1)
Practice Application: Partial Correlation	253	(2)
Problems	255	(6)
Introduction to Logistic Regression	261	(12)
An Example of Logit Regression	261	(4)
Interpretation: Probabilities and Odds	262	(3)
Assessing the Model Fit	265	(1)
Multiple Logistic Regression	265	(3)
Summary	268	(1)
Practice Application: Logistic Regression	268	(2)
Problem	270	(3)
Appendix A Statistical Tables	273	(10)
Appendix B Answers to Odd Numbered Problems	283	(12)
Chapter 1	283	(1)
Chapter 2	283	(3)
Chapter 3	286	(1)
Chapter 4	286	(1)
Chapter 5	287	(2)
Chapter 6	289	(1)
Chapter 7	289	(1)
Chapter 8	290	(1)
Chapter 9	291	(1)
Chapter 10	291	(1)
Chapter 11	291	(1)
Chapter 12	292	(1)
Chapter 13	293	(2)
Glossary	295	(8)
Index	303

Excerpts

PREFACEThis text is the result of a combined total of 30 years of teaching statistics and research methods to both graduate and undergraduate students. Teaching statistics to students in the social and behavioral sciences at any level is a challenge. Each of us has tried numerous approaches over the years using a variety of statistics texts from relatively simple "cookbooks" to the more rigorous and complex texts. Students learn fairly easily from the former, but uniformly come away with no conceptual understanding of statistics. Rigorous texts are more meaningful to the better prepared students, but leave many students perplexed and frustrated. We have tried to strike a balance here between ease of learning the material and the student's obtaining a satisfactory grasp of the role of statistics in the human sciences. We propose to do this in a number of ways, beginning with providing straightforward and consistent formulas, step-by-step instructions, and thorough interpretations. COMPUTING NUMBERSOne of the important things we have learned from our teaching is that many students come to our classes with a minimal background in mathematics. Some are math phobic and dread the idea of a class requiring them to fiddle with numbers. The only assumption we make about the mathematical backgrounds of students is that they have an elementary grasp of algebra. The calculation of each statistic is introduced with a very simple example, and students are given step-by-step instructions to reach its solution. We also provide sufficient problems at the end of each chapter so students can readily improve their calculational competence. Solutions are given for odd-numbered problems in order to provide immediate feedback and improve calculating abilities. WHAT DOES IT MEAN?It doesn't mean much to arrive at the correct solution (a computer can do that) if we do not know what the solution means or what to do with it. To facilitate understanding, we include a line-by-line discussion of computer printouts for the majority of statistics. These printouts are based on actual data, and thus convey the feel of real-world research problems. We interpret the findings in the printouts in the simplest language possible while still endeavoring to include the necessary formal terminology of statistics. The combination of simple prose and formal terminology will help you become statistically literate, which is necessary to become proficient in reading and understanding the professional literature. Because so many excellent statistical packages are available for use, we do not rely on any one package.The practice applications at the end of each chapter facilitate understanding. These applications pose a social science problem and use each of the statistical techniques taught in the chapter to provide answers. If you follow the applications from start to finish, you will greatly improve both your computational and interpretation skills. These exercises further develop an appreciation for the relevance of statistics in the social science. THE SCOPE OF THE TEXTStatistics texts usually conform to one of two types. The first emphasizes statistical techniques that are rarely used nowadays and introduce many techniques that are beyond the understanding of undergraduates. Few of these texts give adequate treatment to multivariate techniques, such as multiple ordinary least squares regression or the increasingly popular logistic regression. Students come away from such texts with an impression that social scientists are only interested in univariate and bivariate analysis, when in. fact this is rarely the case. A basic understanding of multivariate techniques is an absolute must.The second type of text is encyclopedic in its coverage, and includes statistics that most practicing researchers rarely, if ever, employ. While we have attempted to include only the most relevant techniques, we do incl