Statistical Reasoning in the Behavioral Sciences, 5th Edition

by Bruce M. King (Univ. of New Orleans); Edward W. Minium (San Jose State Univ.)

• ISBN13: 9780470134870
• ISBN10: 0470134879
• Edition: 5th
• Format: Hardcover
• Copyright: 2007-05-01
• Publisher: Wiley

Summary

Substantially revised and updated, the new Fifth Edition reflects the changes that have occurred in the field of psychological statistics over the past decade. This revision focuses on conceptual growth. It helps readers develop an understanding of statistical logic and procedures, the properties of statistical devices, the importance of the assumptions underlying statistical tools, and what happens when the strict requirements of statistical theory meet the circumstances of real-world data.

Table of Contents

Introduction	p. 1
Descriptive Statistics	p. 3
Inferential Statistics	p. 3
Our Concern: Applied Statistics	p. 4
Variables and Constants	p. 6
Scales of Measurement	p. 7
Scales of Measurement and Problems of Statistical Treatment	p. 10
Do Statistics Lie?	p. 11
Point of Controversy: Are Statistical Procedures Necessary?	p. 13
Some Tips on Studying Statistics	p. 14
Summary	p. 15
Frequency Distributions, Percentiles, and Percentile Ranks	p. 19
Organizing Qualitative Data	p. 21
Grouped Scores	p. 21
How to Construct a Grouped Frequency Distribution	p. 23
Apparent versus Real Limits	p. 24
The Relative Frequency Distribution	p. 26
The Cumulative Frequency Distribution	p. 27
Percentiles and Percentile Pranks	p. 28
Computing Percentiles from Grouped Data	p. 29
Computation of Percentile Rank	p. 32
Summary	p. 32
Graphic Representation of Frequency Distributions	p. 37
Basic Procedures	p. 38
The Histogram	p. 39
The Frequency Polygon	p. 40
Choosing between a Histogram and a Polygon	p. 41
The Bar Diagram and the Pie Chart	p. 43
The Cumulative Percentage Curve	p. 45
Factors Affecting the Shape of Graphs	p. 47
Shape of Frequency Distributions	p. 50
Summary	p. 50
Central Tendency	p. 55
The Mode	p. 56
The Median	p. 56
The Mean	p. 58
Properties of the Mode	p. 59
Properties of the Mean	p. 60
Point of Controversy: Is It Permissible to Calculate the Mean for Tests in the Behavioral Sciences?	p. 61
Properties of the Median	p. 62
Measures of Central Tendency in Symmetrical and Asymmetrical Distributions	p. 64
The Effects of Score Transformations	p. 65
Summary	p. 65
Variability and Standard [z] Scores	p. 69
The Range and Semi-Interquartile Range	p. 71
Deviation Scores	p. 72
Deviational Measures: The Variance	p. 73
Deviational Measures: The Standard Deviation	p. 74
Calculation of the Variance and Standard Deviation: Raw-Score Method	p. 75
Properties of the Range and Semi-Interquartile Range	p. 76
Point of Controversy: Calculating the Sample Variance: Should We Divide by n or (n - 1)?	p. 77
Properties of the Standard Deviation	p. 78
How Big Is a Standard Deviation?	p. 78
Score Transformations and Measures of Variability	p. 79
Standard Scores (z Scores)	p. 80
A Comparison of z Scores and Percentile Ranks	p. 83
Summary	p. 83
Standard Scores and the Normal Curve	p. 89
Historical Aspects of the Normal Curve	p. 90
The Nature of the Normal Curve	p. 92
Standard Scores and the Normal Curve	p. 94
The Standard Normal Curve: Finding Areas When the Score Is Known	p. 94
The Standard Normal Curve: Finding Scores When the Area Is Known	p. 97
The Normal Curve as a Model for Real Variables	p. 99
The Normal Curve as a Model for Sampling Distributions	p. 100
Summary	p. 100
Point of Controversy: How Normal Is the Normal Curve?	p. 101
Correlation	p. 105
Some History	p. 107
Graphing Bivariate Distributions: The Scatter Diagram	p. 107
Correlation: A Matter of Direction	p. 111
Correlation: A Matter of Degree	p. 112
Understanding the Meaning of Degree of Correlation	p. 113
Formulas for Pearson's Coefficient of Correlation	p. 115
Calculating r from Raw Scores	p. 118
Spearman's Rank-Order Correlation Coefficient	p. 120
Correlation Does Not Prove Causation	p. 121
The Effects of Score Transformations	p. 124
Cautions Concerning Correlation Coefficients	p. 124
Summary	p. 128
Prediction	p. 133
The Problem of Prediction	p. 134
The Criterion of Best Fit	p. 136
Point of Controversy: Least-Squares Regression versus the Resistant Line	p. 137
The Regression Equation: Standard-Score Form	p. 138
The Regression Equation: Raw-Score Form	p. 139
Error of Prediction: The Standard Error of Estimate	p. 141
An Alternative (and Preferred) Formula for S[subscript YX]	p. 143
Error in Estimating Y from X	p. 143
Cautions Concerning Estimation of Predictive Error	p. 145
Summary	p. 146
Interpretive Aspects of Correlation and Regression	p. 151
Factors Influencing r: Degree of Variability in Each Variable	p. 152
Interpretation of r: The Regression Equation I	p. 152
Interpretation of r: The Regression Equation II	p. 154
Interpretation of r: Proportion of Variation in Y Not Associated with Variation in X	p. 156
Interpretation of r: Proportion of Variation in Associated with Variation in X	p. 158
Interpretation of r: Proportion of Correct Placements	p. 160
Summary	p. 161
Probability	p. 165
Defining Probability	p. 166
A Mathematical Model of Probability	p. 168
Two Theorems in Probability	p. 168
An Example of a Probability Distribution: The Binomial	p. 170
Applying the Binomial	p. 172
Are Amazing Coincidences Really That Amazing?	p. 174
Summary	p. 175
Random Sampling and Sampling Distributions	p. 179
Random Sampling	p. 181
Using a Table of Random Numbers	p. 182
The Random Sampling Distribution of the Mean: An Introduction	p. 183
Characteristics of the Random Sampling Distribution of the Mean	p. 186
Using the Sampling Distribution of X to Determine the Probability for Different Ranges of Values of X	p. 189
Random Sampling Without Replacement	p. 192
Summary	p. 192
Introduction to Statistical Inference Testing Hypotheses about Single Means (z and t)	p. 195
Testing a Hypothesis about a Single Mean	p. 197
The Null and Alternative Hypotheses	p. 197
When Do We Retain and When Do We Reject the Null Hypothesis?	p. 198
Review of the Procedure for Hypothesis Testing	p. 199
Dr. Brown's Problem: Conclusion	p. 199
The Statistical Decision	p. 201
Choice of H[subscript A] One-Tailed and Two-Tailed Tests	p. 203
Review of Assumptions in Testing Hypotheses about a Single Mean	p. 205
Estimating the Standard Error of the Mean When [sigma] Is Unknown	p. 205
Point of Controversy: The Single-Subject Research Design	p. 206
The t Distribution	p. 209
Characteristics of Student's Distribution of t	p. 210
Degrees of Freedom and Student's Distribution of t	p. 212
An Example: Professor Dyett's Question	p. 213
Computing t from Raw Scores	p. 215
Levels of Significance versus p-Values	p. 218
Summary	p. 219
Interpreting the Results of Hypothesis Testing: Effect Size, Type I and Type II Errors, and Power	p. 225
A Statistically Significant Difference versus a Practically Important Difference	p. 226
Point of Controversy: The Failure to Publish "Nonsignificant" Results	p. 227
Effect Size	p. 228
Errors in Hypothesis Testing	p. 230
The Power of a Test	p. 233
Factors Affecting Power: Discrepancy between the True Population Mean and the Hypothesized Mean (Size of Effect)	p. 233
Factors Affecting Power: Sample Size	p. 234
Factors Affecting Power: Variability of the Measure	p. 235
Factors Affecting Power: Level of Significance [(alpha)]	p. 235
Factors Affecting Power: One-Tailed versus Two-Tailed Tests	p. 236
Calculating the Power of a Test	p. 237
Point of Controversy Meta-Analysis	p. 239
Estimating Power and Sample Size for Tests of Hypotheses about Means	p. 240
Problems in Selecting a Random Sample and in Drawing Conclusions	p. 242
Summary	p. 243
Testing Hypotheses about the Difference between Two Independent Groups	p. 247
The Null and Alternative Hypotheses	p. 248
The Random Sampling Distribution of the Difference between Two Sample Means	p. 249
Properties of the Sampling Distribution of the Difference between Means	p. 251
Determining a Formula for t	p. 252
Testing the Hypothesis of No Difference between Two Independent Means: The Dyslexic Children Experiment	p. 255
Use of a One-Tailed Test	p. 257
Sample Size in Inference about Two Means	p. 258
Effect Size	p. 258
Point of Controversy: Testing for Equivalence between Two Experimental Groups	p. 259
Estimating Power and Sample Size for Tests of Hypotheses about the Difference between Two Independent Means	p. 263
Assumptions Associated with Inference about the Difference between Two Independent Means	p. 265
The Random-Sampling Model versus the Random-Assignment Model	p. 266
Random Sampling and Random Assignment as Experimental Controls	p. 267
Summary	p. 268
Testing for a Difference between Two Dependent (Correlated) Groups	p. 273
Determining a Formula for t	p. 274
Degrees of Freedom for Tests of No Difference between Dependent Means	p. 275
An Alternative Approach to the Problem of Two Dependent Means	p. 276
Testing a Hypothesis about Two Dependent Means	p. 277
Effect Size	p. 280
Power	p. 281
Assumptions When Testing a Hypothesis about the Difference between Two Dependent Means	p. 282
Problems with Using the Dependent-Samples Design	p. 282
Summary	p. 283
Inference about Correlation Coefficients	p. 287
The Random Sampling Distribution of r	p. 288
Testing the Hypothesis that [rho] = 0	p. 289
Fisher's z' Transformation	p. 290
Strength of Relationship	p. 292
A Note about Assumptions	p. 292
Inference When Using Spearman's r[subscript s]	p. 292
Summary	p. 293
An Alternative to Hypothesis Testing Confidence Intervals	p. 295
Examples of Estimation	p. 297
Confidence Intervals for [Mu subscript X]	p. 297
The Relation between Confidence Intervals and Hypothesis Testing	p. 300
The Advantages of Confidence Intervals	p. 301
Random Sampling and Generalizing Results	p. 302
Evaluating a Confidence Interval	p. 303
Point of Controversy: Objectivity and Subjectivity in Inferential Statistics: Bayesian Statistics	p. 304
Confidence Intervals for [Mu subscript X] - [Mu subscript Y]	p. 306
Sample Size Required for Confidence Intervals of [Mu subscript X] and [Mu subscript X] - [Mu subscript Y]	p. 309
Confidence Intervals for [rho]	p. 311
Summary	p. 312
Chi-Square and Inference about Frequencies	p. 315
The Chi-Squre Test for Goodness of Fit	p. 316
Chi-Square (X[superscript 2]) as a Measure of the Difference between Expected and Observed Frequencies	p. 318
The Logic of the Chi-Square Test	p. 319
Interpretation of the Outcome of a Chi-Square Test	p. 320
Different Hypothesized Proportions in the Test for Goodness of Fit	p. 321
Effect Size for Goodness-of-Fit Problems	p. 322
Assumptions in the Use of the Theoretical Distribution of Chi-Square	p. 322
Chi-Square as a Test for Independence between Two Variables	p. 323
Finding Expected Frequencies in a Contingency Table	p. 325
Calculation of X[subscript 2] and Determination of Significance in a Contingency Table	p. 326
Measures of Effect Size (Strength of Association) for Tests of Independence	p. 327
Point of Controversy: Yates Correction for Continuity	p. 328
Power and the Chi-Square Test of Independence	p. 329
Summary	p. 330
Testing for Differences among Three or More Groups: One-Way Analysis of Variance (and Some Alternatives)	p. 335
The Null Hypothesis	p. 336
The Basis of One-Way Analysis of Variance: Variation within and between Groups	p. 337
Partition of the Sums of Squares	p. 338
Degrees of Freedom	p. 341
Variance Estimates and the F Ratio	p. 342
The Summary Table	p. 344
Example	p. 344
Comparison of t and F	p. 347
Raw-Score Formulas for Analysis of Variance	p. 347
Assumptions Associated with ANOVA	p. 350
Effect Size	p. 350
ANOVA and Power	p. 352
Post Hoc Comparisons	p. 352
Some Concerns about Post Hoc Comparisons	p. 354
An Alternative to the F Test: Planned Comparisons	p. 354
How to Construct Planned Comparisons	p. 355
Analysis of Variance for Repeated Measures	p. 358
Point of Controversy: Analysis of Variance versus A Priori Comparisons	p. 359
Summary	p. 365
Factorial Analysis of Variance: The Two-Factor Design for Independent Groups	p. 369
Main Effects	p. 371
Interaction	p. 373
The Importance of Interaction	p. 375
Partition of the Sums of Squares for Two-Way ANOVA	p. 376
Degrees of Freedom	p. 381
Variance Estimates and F Tests	p. 381
Studying the Outcome of Two-Factor Analysis of Variance	p. 383
Effect Size	p. 384
Planned Comparisons	p. 385
Assumptions of the Two-Factor Design and the Problem of Unequal Numbers of Scores	p. 386
Summary	p. 386
Some (Almost) Assumption-Free Tests	p. 389
The Null Hypothesis in Assumption-Freer Tests	p. 390
Randomization Tests	p. 390
Rank-Order Tests	p. 393
An Assumption-Freer Alternative to the t Test of a Difference between Two Independent Groups: The Mann-Whitney U Test	p. 394
Point of Controversy: A Comparison of the t Test and Mann-Whitney U Test with Real-World Distributions	p. 398
An Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Sign Test	p. 399
Another Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Wilcoxon Signed-Ranks Test	p. 401
An Assumption-Freer Alternative to One-Way ANOVA for Independent Groups: The Kruskal-Wallis Test	p. 403
An Assumption-Freer Alternative to ANOVA for Repeated Measures: Friedman's Rank Test for Correlated Samples	p. 406
Summary	p. 408
Epilogue: The Realm of Statistics	p. 411
Review of Basic Mathematics	p. 415
List of Symbols	p. 425
Answers to Problems	p. 429
Statistical Tables	p. 445
Areas under the Normal Curve Corresponding to Given Values of z	p. 446
The Binomial Distribution	p. 451
Random Numbers	p. 455
Student's t Distribution	p. 458
The F Distribution	p. 460
The Studentized Range Statistic	p. 464
Values of the Correlation Coefficient Required for Different Levels of Significance When H[subscript o]: p = 0	p. 465
Values of Fisher's z' for Values of r	p. 467
The X[superscript 2] Distribution	p. 468
Critical One-Tail Values of[Sigma]R[subscript X] for the Mann-Whitney U Test	p. 469
Critical Values for the Smaller of R[subscript +] or R[subscript -] for the Wilcoxon Signed-Ranks Test	p. 471
References	p. 473
Index	p. 481
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