Statistical Analysis for the Social Sciences: An Interactive Approach

by Abrami, Philip C.; Cholmsky, Paul; Gordon, Robert

• ISBN13: 9780205294930
• ISBN10: 0205294936
• Edition: CD
• Format: Hardcover w/CD
• Copyright: 2001-01-01
• Publisher: Allyn & Bacon

Summary

Integrated book and CD-ROM package emphasizes the logic of statistical procedures, fundamental concepts, and application of quantitative techniques to statistical problems.Every book is packaged with a free CD-ROM featuring Activities and Problem Generators that reinforce the key concepts that are most difficult for students. Users actively participate in experiments by directly manipulating data points and varying numerical values, and by observing real-time changes to graphs and equations. Sets of questions structure exploration. Problem Generators provide a wide variety of problems with worked solutions, helping students develop confidence in statistical analysis. Annotated icons link text content with practice opportunities on the CD. This CD-ROM is not a computational tool such as SPSS, but provides a learning environment for exploration and application of key concepts.For anyone who needs experience in statistical analysis for the social sciences.

Table of Contents

Preface	xiii
Introduction	1	(12)
Overview	1	(6)
Statistics	2	(2)
Variables and Variability	4	(3)
Preparing Data for Analysis	7	(4)
Putting It All Together	11	(1)
Key Terms	11	(1)
References	11	(1)
Problems	11	(2)
Research Methodology: A Primer	13	(38)
Overview	13	(1)
The Importance of Good Research Design	14	(4)
Statistical Analysis and the Big Picture	15	(1)
Research Ethics	16	(2)
Basics of Research Design	18	(6)
Experimental and Correlational Investigations	18	(2)
Two Basic Questions	20	(3)
Notational System	23	(1)
Types of Designs	23	(1)
Pre-Experimental Designs	24	(8)
One-Shot Case Study	24	(1)
The One-Group Pretest-Posttest Design	25	(2)
Static Group Comparison Design	27	(1)
Experimental versus Statistical Control	28	(1)
More on Internal Validity	29	(1)
Possible or Probable?	29	(3)
True Experimental Designs	32	(3)
Pretest-Posttest Control Group Design	32	(2)
Posttest-Only Control Group Design	34	(1)
External Validity	34	(1)
Quasi-Experimental Designs	35	(3)
Time Series Design	36	(1)
Nonequivalent Control Group Design	37	(1)
Measurement Issues	38	(4)
Scales of Measurement	38	(4)
Reliability and Validity	42	(5)
Tests and Self-Report Measures	42	(1)
Desirable Characteristics of Standardized Tests	43	(1)
Test Reliability	43	(2)
Test Validity	45	(1)
Other Characteristics of Standardized Tests	46	(1)
Putting It All Together	47	(2)
Key Terms	49	(1)
References	49	(1)
Problems	49	(2)
Organizing and Displaying Data	51	(34)
Overview	51	(1)
Why Organize and Display Data?	52	(1)
Ways of Organizing Data	53	(1)
Data Screening	53	(1)
Organizing the Data	53	(8)
Ranking	54	(1)
Percentages and Percentiles	55	(3)
Uses of Percentiles and Percentile Ranks	58	(3)
Grouping the Data	61	(7)
Selecting a Class Interval	61	(3)
Estimating Percentiles and Percentile Ranks from Grouped Frequency Distributions	64	(3)
Grouping: Advantages and Disadvantages	67	(1)
Crosstabulation	68	(1)
Displaying the Data	69	(10)
What Exactly Are Visual Displays?	70	(4)
Plots and Charts	74	(5)
Putting It All Together	79	(3)
Key Terms	82	(1)
References	83	(1)
Problems	83	(2)
Descriptive Statistics	85	(35)
Overview	85	(1)
Why Summarize the Data?	86	(1)
Summation Notation	87	(1)
Measures of Central Tendency	87	(14)
The Basics	88	(4)
Selecting a Measure of Central Tendency	92	(2)
Other Measures of Central Tendency	94	(1)
Shapes of Distributions	95	(6)
Measures of Dispersion	101	(10)
The Basics	101	(10)
Moments About the Mean	111	(3)
Measures of Bivariate Relationship	114	(1)
Putting It All Together	114	(4)
Measures of Central Tendency	115	(1)
Shapes of Distributions	115	(1)
Measures of Dispersion	115	(1)
Moments About the Mean	116	(1)
Measures of Bivariate Relationship	116	(2)
Key Terms	118	(1)
References	118	(1)
Problems	118	(2)
Building Blocks of Inferential Statistics: Probability, Chance, Variability, and Distributions	120	(35)
Overview	120	(1)
Probability: The Foundation of Inferential Statistics	121	(4)
Probability	121	(1)
Interpreting the Findings	122	(1)
Approaches to Probability	123	(2)
The Role of Probability Theory in Inferential Statistics	125	(5)
Samples and Populations	125	(1)
Variability	126	(4)
The Shape of Chance Variability: More Pieces of the Puzzle	130	(5)
The Binomial Distribution	130	(5)
Properties of the Normal Distribution	135	(14)
Binomial Distribution: The Normal Approximation	135	(2)
Normal Distribution: Some Other Important Properties	137	(5)
Areas Under the Normal Distribution	142	(2)
The Standard Normal Distribution and z-Scores	144	(3)
Other Issues in Understanding and Using the Normal Distribution	147	(2)
T-Scores	149	(1)
Putting It All Together	150	(2)
The Binomial Distribution	150	(1)
Properties of the Normal Distribution	151	(1)
T-Scores	152	(1)
Key Terms	152	(1)
References	153	(1)
Problems	153	(2)
Sampling Distributions	155	(32)
Overview	155	(1)
Basic Concepts in Statistical Inference	156	(5)
Key Terms in Statistical Inference	157	(4)
Using Sample Statistics to Estimate Population Parameters	161	(4)
Desirable Properties of Estimators	161	(1)
Good Estimators	162	(1)
Formulas for Samples, Populations, and Population Estimators	163	(2)
Sampling Distributions	165	(8)
Interval Estimation of the Mean	169	(4)
Hypothesis Testing	173	(8)
Hypothesis Testing Using the z-Test	177	(3)
Interval Estimation of the Mean Difference	180	(1)
Putting It All Together	181	(3)
Formulas for Samples, Populations, Population Estimators, Sampling Distributions, and Sampling Distribution Estimators	182	(1)
Using the Sampling Distribution for Hypothesis Testing	183	(1)
Key Terms	184	(1)
References	185	(1)
Problems	185	(2)
Statistical Issues in Hypothesis Testing	187	(35)
Overview	187	(1)
Steps in Hypothesis Testing	188	(11)
State the Null and Alternative Hypotheses	188	(4)
Select Alpha: The Probability Value for Significance Testing	192	(2)
Select the Appropriate Test Statistic	194	(1)
Compute the Calculated Value of the Test Statistic	195	(1)
Find the Critical Value of the Test Statistic	195	(1)
Compare the Calculated and Critical Values	195	(1)
An Important Caveat on the Six Steps in Hypothesis Testing	196	(1)
Devil's Advocate Example	196	(3)
z-Test Interval Estimation	199	(1)
One-Sided Confidence Intervals	199	(1)
Statistical Power	200	(6)
The Alternative Distribution	200	(2)
Steps in Estimating Power	202	(4)
Interpretation and Guidelines for Acceptable Statistical Power	206	(6)
Estimating the Power of Your Research	207	(1)
Ways to Increase Statistical Power	207	(4)
Other Considerations	211	(1)
Effect Size and Practical Importance	212	(2)
The Effect Size	212	(1)
Effect Size Calculation for the Devil's Advocate Scenario	213	(1)
Effect Sizes and Power	213	(1)
Is John Correct?	213	(1)
Guidelines for using Statistics	214	(5)
Putting It All Together	219	(1)
Key Terms	220	(1)
References	220	(1)
Problems	221	(1)
Testing the Difference Between Two Independent Groups: The t-Test	222	(31)
Overview	222	(1)
What's Wrong with the z-Test?	223	(3)
Review and Application of the z-Test	223	(2)
The Contribution of William Gosset	225	(1)
The Separate Variance Model t-Test	226	(10)
Effect of Sample Size on the Critical Value	226	(1)
Degrees of Freedom	227	(3)
Finding the Correct Critical Value	230	(2)
Exact Probabilities	232	(1)
Confidence Intervals	233	(1)
Effect Sizes Calculations and Power	234	(2)
The Drill Press Example	236	(1)
The Pooled Variance Model t-Test	236	(7)
Pooled Standard Error	236	(4)
Pooled Variance Model t-Test	240	(1)
Confidence Intervals Based on the Pooled Variance Approach	240	(1)
Effect Size Calculations Based on the Pooled Variance Approach	240	(1)
Comparison of Two Approaches	241	(2)
Underlying Assumptions	243	(2)
The Variability Within Each Group Should Be Normally Distributed	243	(1)
Each Data Point, or Score, Should Be Independent of Every Other Data Point	243	(1)
The Variances of the Two Groups Should Be Equal or Homogeneous	244	(1)
Choosing Between the Separate and Pooled Variance Models	245	(1)
Guidelines for Choosing Between the Two Models	246	(1)
Putting It All Together	246	(5)
Key Terms	251	(1)
References	251	(1)
Problems	251	(2)
Testing the Difference Between Two or More Independent Groups: The Oneway between-Groups Analysis of Variance	253	(37)
Overview	253	(1)
Omnibus Tests of Significance	254	(2)
Multilevel Independent Variables	254	(2)
Specific or General Hypotheses?	256	(8)
Partitioning Variability	259	(5)
The Simple Mathematics of Variance Partitioning	264	(2)
Total Variability	265	(1)
Between-Groups Variability	266	(4)
Within-Groups Variability	267	(3)
The F-Test	270	(6)
From Sums of Squares to Variances	270	(1)
Mean Squares	271	(1)
F as a Ratio of Variances	272	(4)
Reporting ANOVA Results	276	(1)
Underlying Assumptions	276	(2)
Assumptions	277	(1)
Effects of Assumption Violations	277	(1)
Effect Size Calculations and Power	278	(5)
Effect Size Calculations for Two Groups	278	(1)
Using R2 and f to Estimate the General Effect Size	279	(2)
Another Method for Estimating General Effect Sizes: ω2	281	(1)
Power	282	(1)
Putting It All Together	283	(3)
Key Terms	286	(1)
References	286	(1)
Problems	286	(2)
Appendix 9.1: A Proof That t2 = F	288	(2)
Testing the Difference Between Two or More Independent Groups: Multiple Comparisons	290	(24)
Overview	290	(1)
Multiple Comparisons Basics	291	(2)
What Is a Comparison?	291	(1)
When Multiple Comparisons Should Be Avoided	291	(1)
Why Use Multiple Comparisons?	291	(1)
Planned Comparisons (Also Known as A Priori Comparisons)	292	(1)
Post Hoc Comparisons (Also Known as A Posteriori Comparisons)	292	(1)
Planned Comparisons	293	(7)
Specific Hypotheses	293	(1)
Rules for Evaluating Planned Comparisons	294	(1)
Symbol System	294	(1)
Valid Planned Comparisons	295	(1)
Independence of Planned Comparisons	295	(2)
Statistically Evaluating Planned Comparisons	297	(3)
Dealing with Variance Heterogeneity	300	(1)
Post Hoc Comparisons	300	(8)
Conceptual Unit for Error Rate	301	(2)
Tukey's HSD	303	(1)
Scheffe's S Method	304	(4)
Putting It All Together	308	(3)
Planned Comparisons	309	(1)
Post Hoc Comparisons	310	(1)
Key Terms	311	(1)
References	311	(1)
Problems	311	(3)
Analyzing More Than a Single Independent Variable: Factorial Between-Groups Analysis of Variance	314	(48)
Overview	314	(2)
Factorial Designs	316	(10)
The Simplest Case: A 2 x 2 Factorial	317	(7)
A Bit More on Main Effects and Interactions	324	(2)
Factorial Analysis of Variance	326	(12)
Subdividing Between-Groups Variability	327	(1)
Omnibus Hypotheses	327	(1)
The General Linear Model	328	(2)
Partitioning Variability in Twoway ANOVA	330	(2)
From SS to MS to F	332	(1)
Twoway Factorial ANOVA: Computational Example	333	(1)
Other Issues in Factorial ANOVA	333	(5)
Multiple Comparison and Simple Effect Tests	338	(16)
Overview	339	(1)
Planned Orthogonal Comparisons Procedures for Factorial ANOVA	339	(3)
Post Hoc Comparisons for Factorial ANOVA	342	(4)
Tests of Simple Effects	346	(6)
Probing Significant Simple Effects	352	(2)
Putting It All Together	354	(5)
Partitioning Variability in Twoway ANOVA	354	(5)
Key Terms	359	(1)
References	359	(1)
Problems	359	(3)
Within-Groups Designs: Analyzing Repeated Measures	362	(45)
Overview	362	(2)
Basics of Within-Groups Designs	364	(4)
Designs with a Single Treatment	364	(1)
Designs with More Than a Single Treatment	365	(1)
Other Uses of Within-Groups Analyses	366	(1)
The Advantages of Within-Groups Designs	366	(1)
The Disadvantages of Within-Groups Designs	366	(1)
Counterbalancing	367	(1)
Correlated or Dependent Samples t-Test	368	(8)
Review of the Independent Samples t-Test	369	(1)
Correlated Samples t-Test: Raw Score Method	369	(3)
Correlated Samples t-Test: Individual Difference Score Method	372	(2)
Effect Size and Power	374	(2)
Oneway Within-Groups ANOVA	376	(13)
Underlying Logic	376	(1)
Analyzing the Data with and Without the Dependencies	377	(2)
Computational Procedures for the Oneway Within-Groups ANOVA	379	(2)
Assumptions and Assumption Violations	381	(2)
Multiple Comparisons	383	(4)
Effect Size and Power	387	(2)
Mixed Designs	389	(6)
Underlying Logic	389	(1)
Computational Procedures for the Twoway Mixed Design ANOVA	390	(5)
Putting It All Together	395	(8)
Correlated Samples t-Test	396	(2)
Oneway Within-Groups ANOVA	398	(3)
Mixed Designs	401	(2)
Key Terms	403	(1)
References	403	(1)
Problems	404	(3)
Determining the Relationship Between Two Variables: Correlation	407	(35)
Overview	407	(1)
Correlation Basics	408	(4)
Similarities with Other Research Situations	409	(1)
Differences from Other Research Situations	409	(1)
Correlation and Causation	410	(2)
Oneway ANOVA versus Correlation: What Is the Difference?	412	(1)
Correlation: Scatterplots	412	(4)
Creating a Scatterplot	413	(1)
Interpreting a Scatterplot	413	(3)
The Pearson Product Moment Correlation	416	(6)
Describing Linear Relationships	416	(1)
Range of Values	417	(1)
The Contribution of Karl Pearson	418	(1)
Computing the Pearson Product Moment Correlation	418	(1)
The z-Score Method	419	(2)
The Covariation Method	421	(1)
Inferential Uses	422	(4)
Hypothesis Testing	423	(1)
Calculated and Critical Values	424	(1)
Parental Performance Example	425	(1)
Underlying Assumptions	426	(1)
Confidence Intervals	426	(2)
Skewed Distribution of r	426	(1)
Fisher's Transformation	427	(1)
Estimating Confidence Intervals	427	(1)
The Value of Confidence Intervals	428	(1)
Strength of Association	428	(1)
Coefficient of Determination	429	(1)
Parental Performance Example	429	(1)
Derivatives of the Pearson Product Moment Correlation	429	(1)
Some Cautions and Limitations	430	(7)
Restriction of Range	430	(2)
Attenuation Due to Measurement Error	432	(2)
Departures from Linearity	434	(1)
Outliers	435	(1)
Dealing with Missing Values	436	(1)
Putting It All Together	437	(2)
Computational Procedures	437	(1)
Cautions and Limitations	438	(1)
Key Terms	439	(1)
References	439	(1)
Problems	439	(3)
Determining the Relationship Between Two Variables: Simple Linear Regression	442	(34)
Overview	442	(1)
Some Simple Regression Basics	443	(5)
What Is the Difference Between Correlation and Regression?	443	(1)
Lines and Plots	444	(1)
Perfect Prediction	445	(1)
Slope	446	(1)
Intercept	447	(1)
Imperfect Prediction	448	(8)
The Best-Fit Straight Line	450	(5)
Relationship Between the Correlation Coefficient (r) and the Regression Coefficient (b')	455	(1)
The z-Score Method for Determining the Regression Equation	456	(1)
Statistical Tests for Simple Regression	456	(8)
Partitioning Variability	456	(2)
From Sums of Squares to the F-Test	458	(4)
Testing Significance Using the t-Test	462	(2)
Other Issues in Simple Linear Regression	464	(6)
Confidence Intervals	464	(1)
Strength of Association	464	(2)
Power	466	(1)
Underlying Assumptions	466	(2)
Using Standardized Residuals to Check the Data	468	(2)
Putting It All Together	470	(3)
Key Terms	473	(1)
References	473	(1)
Problems	473	(3)
Dealing with More Than a Single Predictor Variable: Multiple Linear Regression	476	(32)
Overview	476	(2)
The Logic of Multiple Linear Regression	478	(4)
The Multiple Regression Equation	479	(1)
Uncorrelated versus Correlated Predictors	480	(2)
The Multiple Regression Equation and Tests of Significance	482	(10)
Components of the Multiple Regression Equation	483	(2)
Tests of Significance	485	(7)
The Incremental Approach to Multiple Linear Regression	492	(5)
Hierarchical Regression	492	(4)
Stepwise Regression	496	(1)
Special Issues in Multiple Linear Regression	497	(3)
Outliers	497	(1)
III-Conditioned Data	497	(2)
Adjusted R2	499	(1)
Putting It All Together	500	(5)
The Multiple Regression Equation	500	(1)
Tests of Significance: Simultaneous Approach	501	(1)
Incremental Approach to Multiple Regression	502	(1)
Special Issues in Multiple Linear Regression	503	(2)
Key Terms	505	(1)
References	505	(1)
Problems	505	(3)
Nonparametric Statistical Tests	508	(31)
Overview	508	(2)
Why Nonparametric Statistical Tests?	510	(2)
Assumptions and Assumption Violations	510	(1)
Scales of Measurement	510	(1)
Advantages and Disadvantages	511	(1)
Chi-Square and the Analysis of Nominal Data	512	(11)
Requirements for Using Chi-Square	512	(1)
Frequencies and Categories	513	(1)
About Chi-Square	513	(3)
Goodness of Fit	516	(1)
Test of Independence	516	(3)
Dealing with Small Sample Sizes	519	(2)
Multiple Comparisons	521	(1)
Measures of Association or Effect Size	522	(1)
The Analysis of Ordinal Data	523	(8)
Mann-Whitney U-Test	523	(2)
Kruskal-Wallis Oneway ANOVA H-Test	525	(2)
Correlated Samples	527	(4)
Putting It All Together	531	(4)
Chi-Square and the Analysis of Nominal Data	531	(2)
The Analysis of Ordinal Data	533	(2)
Key Terms	535	(1)
References	535	(1)
Problems	536	(3)
Appendix A: Areas Under the Standard Normal Curve Corresponding to Given Values of z	539	(6)
Appendix B: Table of Random Numbers	545	(2)
Appendix C: Critical Values of the t-Distribution	547	(2)
Appendix D: Critical Values of the F Distribution	549	(4)
Appendix E: Power Tables for the Analysis of Variance	553	(4)
Appendix F: Percentage Points of the Studentized Range Statistic	557	(2)
Appendix G: Values of the Correlation Coefficient Required for Different Levels of Significance When H0: p = 0	559	(2)
Appendix H: Values of Fisher's ZF for Values of r	561	(1)
Appendix I: Upper Percentage Points of the Chi-Square Distribution	562	(1)
Appendix J: Critical Values of Mann-Whitney's U	563	(2)
Appendix K: Critical Values of Wilcoxon's T	565	(1)
Answers	566	(21)
Index	587