Statistics: An Introduction, 5th Edition

✍ Scribed by Roger E. Kirk

• Publisher: Wadsworth Publishing
• Year: 2007
• Tongue: English
• Leaves: 673
• Edition: 5th
• Category: Library

✦ Synopsis

Master Teacher and writer Roger E. Kirk brings two clear goals to the Fifth Edition of STATISTICS: AN INTRODUCTION: to provide a sound introduction to descriptive and inferential statistics and to help students read and understand statistical presentations in their field. Kirk provides guidelines to help you decide when to use various procedures, and how to understand the logic of the procedures. This revision includes a complete update, focusing specifically on increased coverage of effect size and power.

✦ Table of Contents

Front Cover......Page 1
Title Page......Page 6
Copyright......Page 7
Preface......Page 8
Contents......Page 14
1. Introduction to Statistics......Page 22
Some Misconceptions......Page 23
Kinds of Statisticians......Page 24
Develop Effective Study Techniques......Page 25
Master Foundation Concepts before Going on to New Material......Page 26
Population and Sample Defined......Page 27
Descriptive and Inferential Statistics......Page 28
Random Sampling......Page 29
CHECK YOUR UNDERSTANDING OF SECTIONS 1.1 TO 1.3......Page 31
Variables and Constants......Page 32
Classification of Variables in Mathematics......Page 33
Nominal Measurement......Page 35
Ordinal Measurement......Page 36
Interval Measurement......Page 37
Ratio Measurement......Page 38
Implications of the Two Ways of Thinking about Numbers......Page 40
Some Subtle Problems in Interpreting Numbers......Page 41
CHECK YOUR UNDERSTANDING OF SECTION 1.4......Page 42
Probability Theory......Page 43
Experimental Statistics......Page 44
1.6 Looking Back: What Have You Learned?......Page 45
2. Frequency Distributions and Graphs......Page 50
2.2 Frequency Distributions......Page 51
Ungrouped Frequency Distribution for Quantitative Variables......Page 52
Grouped Frequency Distribution for Quantitative Variables......Page 53
Determining the Number and Size of Class Intervals for a Quantitative Variable......Page 55
Relative Frequency Distributions......Page 57
Cumulative Frequency Distributions......Page 58
Frequency Distributions for Qualitative Variables......Page 59
CHECK YOUR UNDERSTANDING OF SECTION 2.2......Page 60
Bar Graph......Page 62
Pie Chart......Page 63
CHECK YOUR UNDERSTANDING OF SECTION 2.4......Page 64
Histogram......Page 65
Cumulative Polygon......Page 66
Stem-and-Leaf Display......Page 67
2.6 Shapes of Distributions......Page 69
Bell-Shaped Distributions......Page 70
J, U, and Rectangular Distributions......Page 71
CHECK YOUR UNDERSTANDING OF SECTION 2.6......Page 72
2.7 Misleading Graphs......Page 73
REVIEW EXERCISES FOR CHAPTER 2......Page 75
3. Measures of Central Tendency......Page 82
3.2 Mode......Page 83
Summation Notation for the Mean......Page 85
CHECK YOUR UNDERSTANDING OF SECTION 3.3......Page 87
3.4 Median......Page 89
Computing the Median from a Frequency Distribution......Page 92
CHECK YOUR UNDERSTANDING OF SECTION 3.4......Page 93
Merits of the Mean......Page 94
Merits of the Mode......Page 96
Summary of the Properties of the Mean, Median, and Mode......Page 97
3.6 Location of the Mean, Median, and Mode in a Distribution......Page 98
3.7 Mean of Two or More Means......Page 99
Summation Rules......Page 100
Proof That the Mean Is a Balance Point......Page 102
CHECK YOUR UNDERSTANDING OF SECTION 3.8......Page 103
REVIEW EXERCISES FOR CHAPTER 3......Page 104
4. Measures of Dispersion, Skewness, and Kurtosis......Page 110
What Measures of Dispersion Tell You......Page 111
Range......Page 112
Semi-Interquartile Range......Page 113
Standard Deviation......Page 116
Index of Dispersion......Page 120
CHECK YOUR UNDERSTANDING OF SECTION 4.2......Page 122
Standard Deviation......Page 126
Index of Dispersion......Page 127
Summary of the Properties of the Measures of Dispersion......Page 128
CHECK YOUR UNDERSTANDING OF SECTION 4.3......Page 129
4.5 Detecting Outliers......Page 130
Detecting Outliers with a Box Plot......Page 131
Skewness......Page 133
Kurtosis......Page 135
4.7 Looking Back: What Have You Learned?......Page 136
REVIEW EXERCISES FOR CHAPTER 4......Page 137
5. Correlation......Page 144
Correlation and Regression Distinguished......Page 145
A Bit of History......Page 146
5.2 A Numerical Index of Correlation......Page 148
CHECK YOUR UNDERSTANDING OF SECTION 5.2......Page 149
5.3 Pearson Product-Moment Correlation Coefficient......Page 150
Information Contained in the Cross Product......Page 152
CHECK YOUR UNDERSTANDING OF SECTION 5.3......Page 154
5.4 Interpretation of Correlation Coefficient: Explained and Unexplained Variation......Page 156
CHECK YOUR UNDERSTANDING OF SECTION 5.4......Page 158
Error: Interpreting r in Terms of Arbitrary Descriptive Labels......Page 159
CHECK YOUR UNDERSTANDING OF SECTION 5.5......Page 160
Nature of the Relationship Between X and Y......Page 161
Truncated Range......Page 162
Spurious Effects Due to Subgroups with Different Means or Standard Deviations......Page 163
Non-normality and Heterogeneity of Array Variances......Page 165
5.7 Spearman Rank Correlation......Page 168
CHECK YOUR UNDERSTANDING OF SECTION 5.7......Page 170
REVIEW EXERCISES FOR CHAPTER 5......Page 172
6. Regression......Page 180
An Overview of the Prediction Process......Page 181
Predicting Y from X......Page 182
Predicting X from Y......Page 187
Relationship between r and the Slopes of the Regression Lines......Page 188
CHECK YOUR UNDERSTANDING OF SECTIONS 6.1 AND 6.2......Page 189
6.3 Another Measure of Ability to Predict: The Standard Error of Estimate......Page 190
An Alternative Formula for S[sub(Y.X)]......Page 191
Descriptive Application of S[sub(Y.X)]......Page 192
6.4 Assumptions Associated with Regression and the Standard Error of Estimate......Page 193
Multiple Regression......Page 194
Multiple Correlation......Page 197
CHECK YOUR UNDERSTANDING OF SECTION 6.5......Page 198
6.6 Looking Back: What Have You Learned?......Page 199
REVIEW EXERCISES FOR CHAPTER 6......Page 200
7. Probability......Page 204
The Subjective-Personalistic View of Probability......Page 205
The Classical, or Logical, View of Probability......Page 206
CHECK YOUR UNDERSTANDING OF SECTION 7.1......Page 207
Graphing Simple and Compound Events......Page 208
CHECK YOUR UNDERSTANDING OF SECTION 7.2......Page 210
Addition Rule of Probability......Page 211
Multiplication Rule of Probability......Page 213
Multiplication Rule for Statistically Independent Events......Page 216
Common Errors in Applying the Rules of Probability......Page 217
CHECK YOUR UNDERSTANDING OF SECTION 7.3......Page 218
Fundamental Counting Rule......Page 219
Permutation of n Objects Taken r at a Time, [sub(n)]P[sub(r)]......Page 220
CHECK YOUR UNDERSTANDING OF SECTION 7.4......Page 222
7.5 Looking Back: What Have You Learned?......Page 223
REVIEW EXERCISES FOR CHAPTER 7......Page 224
8. Random Variables and Probability Distributions......Page 228
8.2 Random Sampling......Page 229
Sampling with or without Replacement......Page 230
Using a Table of Random Numbers......Page 231
CHECK YOUR UNDERSTANDING OF SECTION 8.2......Page 232
Random Variables......Page 233
Distribution of a Discrete Random Variable......Page 234
Expected Value of a Discrete Random Variable......Page 236
Expected Value of a Continuous Random Variable......Page 237
Standard Deviation of a Discrete Random Variable......Page 238
CHECK YOUR UNDERSTANDING OF SECTION 8.3......Page 239
Bernoulli Trial......Page 240
Binomial Distribution......Page 241
Expected Value and Standard Deviation of Binomial Distribution......Page 243
CHECK YOUR UNDERSTANDING OF SECTION 8.4......Page 244
8.5 Looking Back: What Have You Learned?......Page 245
REVIEW EXERCISES FOR CHAPTER 8......Page 246
9. Normal Distribution and Sampling Distributions......Page 250
9.2 The Normal Distribution......Page 251
Characteristics of the Normal Distribution......Page 252
Converting Scores to Standard Scores......Page 253
Finding Areas under the Normal Distribution......Page 254
Finding Scores When the Area Is Known......Page 256
Normal Approximation to the Binomial Distribution......Page 257
CHECK YOUR UNDERSTANDING OF SECTION 9.2......Page 258
Percentile Rank......Page 259
Relative Advantages of z Scores and Percentile Ranks......Page 260
Comparing Performance on Different Tests......Page 261
Looking Ahead to Inferential Statistics......Page 263
Sampling Distributions......Page 264
Sampling Distribution of the Mean......Page 265
Standard Error of a Statistic......Page 268
Test Statistics......Page 269
CHECK YOUR UNDERSTANDING OF SECTION 9.4......Page 270
9.5 Looking Back: What Have You Learned?......Page 271
REVIEW EXERCISES FOR CHAPTER 9......Page 272
Demonstration Showing That σ[sup(2)] and σ[sup(2)][sub(est)] Are Unbiased Estimators but S[sup(2)] Is a Biased Estimator......Page 274
10. Statistical Inference: One-Sample Hypothesis Test......Page 278
Scientific Hypotheses......Page 279
Statistical Hypotheses......Page 280
Hypothesis Testing and the Method of Indirect Proof......Page 281
Rejection or Nonrejection of H[sub(o)]: What Does It Mean?......Page 282
The Role of Logic in Evaluating a Scientific Hypothesis......Page 283
10.2 Hypothesis Testing......Page 284
Step 1: Stating the Statistical Hypotheses......Page 285
Step 2: Specifying the Test Statistic......Page 286
Step 3: Specifying n and the Sampling Distribution......Page 287
Step 4: Specifying the Significance Level, α......Page 289
Step 5: Making a Decision......Page 290
CHECK YOUR UNDERSTANDING OF SECTION 10.2......Page 291
10.3 One-Sample t Test for a Mean......Page 292
Some Experimental Design Considerations......Page 294
10.4 More about Hypothesis Testing......Page 295
One-and Two-Tailed Tests......Page 296
Type I and Type II Errors......Page 298
More about Type I and Type II Errors......Page 301
Determining the n Required to Achieve an Acceptable α, 1 – β, and μ – μ[sub(0)]......Page 302
Reporting p Values......Page 303
CHECK YOUR UNDERSTANDING OF SECTION 10.4......Page 305
10.5 Looking Back: What Have You Learned?......Page 306
REVIEW EXERCISES FOR CHAPTER 10......Page 307
11. Statistical Inference: One-Sample Confidence Interval......Page 312
Criticisms of Null Hypothesis Significance Testing......Page 313
11.2 Confidence Interval for μ......Page 314
Computation of a Two-Sided Confidence Interval for μ......Page 316
Interpretation of a Confidence Interval......Page 317
Computation of a One-Sided Confidence Interval for μ......Page 318
Interval Estimation versus Hypothesis Testing......Page 319
11.3 Practical Significance......Page 320
CHECK YOUR UNDERSTANDING OF SECTIONS 11.2 AND 11.3......Page 322
11.4 Looking Back: What Have You Learned?......Page 323
REVIEW EXERCISES FOR CHAPTER 11......Page 324
12. Statistical Inference: Other One-Sample Test Statistics......Page 328
12.2 One-Sample z Test and Confidence Interval for a Proportion......Page 329
Computational Example for z Test for a Proportion......Page 330
Confidence Interval for a Proportion......Page 331
Computational Example for Confidence Interval for a Proportion......Page 332
Choosing a Sample Size......Page 333
CHECK YOUR UNDERSTANDING OF SECTION 12.2......Page 334
Computational Example for Test of ρ = 0......Page 336
Confidence Interval for a Correlation......Page 337
Practical Significance of a Correlation......Page 338
12.4 Looking Back: What Have You Learned?......Page 339
REVIEW EXERCISES FOR CHAPTER 12......Page 341
13. Statistical Inference: Two Samples......Page 344
13.2 Two-Sample t Test and Confidence Interval for μ[sub(1)] – μ[sub(2)] Using Independent Samples......Page 345
Computational Example for t Test for μ[sub(1)] – μ[sub(2)] (Independent Samples)......Page 347
Two-Sample t’ Test for μ[sub(1)] – μ[sub(2)] with Unequal Variances (Independent Samples)......Page 351
Practical Significance......Page 352
t Confidence Interval for μ[sub(1)] – μ[sub(2)] (Independent Samples)......Page 353
t' Confidence Interval for μ[sub(1)] – μ[sub(2)] with Unequal Variances (Independent Samples)......Page 355
CHECK YOUR UNDERSTANDING OF SECTION 13.2......Page 356
13.3 Two Randomization Strategies: Random Sampling and Random Assignment......Page 358
The Strategy of Random Assignment......Page 359
Advantages and Disadvantages of the Two Research Strategies......Page 360
CHECK YOUR UNDERSTANDING OF SECTION 13.3......Page 361
Introduction to Dependent Samples......Page 362
t Test for μ[sub(1)] – μ[sub(2)] (Dependent Samples)......Page 363
Computational Example for t Test for μ[sub(1)] – μ[sub(2)] (Dependent Samples)......Page 365
Determining the Required Sample Size (Dependent Samples)......Page 367
t Confidence Interval for μ[sub(1)] – μ[sub(2)] (Dependent Samples)......Page 368
Group Matching: A Research Strategy to Be Avoided......Page 369
CHECK YOUR UNDERSTANDING OF SECTION 13.4......Page 370
13.5 Looking Back: What Have You Learned?......Page 372
REVIEW EXERCISES FOR CHAPTER 13......Page 374
14. Statistical Inference: Other Two-Sample Test Statistics......Page 382
F Test for Two Variances (Independent Samples)......Page 383
Computational Example for F Test for Two Variances (Independent Samples)......Page 385
F Confidence Interval for Two Variances (Independent Samples)......Page 387
Computational Example of Confidence Interval for Two Variances (Independent Samples)......Page 388
t Test for Two Variances (Dependent Samples)......Page 391
t Confidence Interval for Two Variances (Dependent Samples)......Page 392
CHECK YOUR UNDERSTANDING OF SECTION 14.3......Page 393
z Test for Two Proportions (Independent Samples)......Page 395
Computational Example of z Test for Two Proportions (Independent Samples)......Page 396
z Confidence Interval for Two Proportions (Independent Samples)......Page 397
Computational Example of Confidence Interval for Two Proportions (Independent Samples)......Page 398
CHECK YOUR UNDERSTANDING OF SECTION 14.4......Page 399
z Test for Two Proportions (Dependent Samples)......Page 400
z Confidence Interval for Two Proportions (Dependent Samples)......Page 401
Computational Example of Confidence Interval for Two Proportions (Dependent Samples)......Page 403
14.6 Looking Back: What Have You Learned?......Page 404
REVIEW EXERCISES FOR CHAPTER 14......Page 406
15. Introduction to the Analysis of Variance......Page 412
The Omnibus Null Hypothesis......Page 413
CHECK YOUR UNDERSTANDING OF SECTION 15.2......Page 414
The Composite Nature of a Score......Page 415
Model Equation for a Score......Page 416
Partition of the Total Sum of Squares......Page 418
Degrees of Freedom......Page 419
Mean Squares and the F Statistic......Page 420
The Nature of MSBG and MSWG......Page 421
CHECK YOUR UNDERSTANDING OF SECTION 15.3......Page 423
15.4 Completely Randomized Design......Page 424
Computational Procedures for a CR-3 Design......Page 425
CHECK YOUR UNDERSTANDING OF SECTION 15.4......Page 429
Assumption That the Model Equation X[sub(ij)] = μ + (μ[sub(j)] – μ) + (X[sub(ij)] – μ[sub(j)]) Reflects All the Sources of Variation That Affect X[sub(ij)]......Page 431
Assumption of Homogeneity of Variance......Page 432
Contrasts among Means......Page 433
Fisher-Hayter Multiple Comparison Test......Page 435
Scheffé’s Multiple Comparison Test and Confidence Interval......Page 437
Comparison of the Multiple Comparison Tests......Page 439
15.7 Practical Significance......Page 440
CHECK YOUR UNDERSTANDING OF SECTIONS 15.6 AND 15.7......Page 441
15.8 Looking Back: What Have You Learned?......Page 443
REVIEW EXERCISES FOR CHAPTER 15......Page 444
16. Other Analysis of Variance Designs......Page 450
Controlling Nuisance Variables......Page 451
Procedures for Forming Blocks......Page 454
CHECK YOUR UNDERSTANDING OF SECTION 16.2......Page 455
Model Equation for a Score......Page 456
Computational Procedures for RB-3 Design......Page 457
Multiple Comparison Procedures......Page 461
Computational Example for the Fisher-Hayter Multiple Comparison Procedure......Page 462
Practical Significance......Page 463
Assumptions Associated with a Randomized Block Design......Page 465
CHECK YOUR UNDERSTANDING OF SECTION 16.3......Page 466
Introduction to Factorial Designs......Page 467
Computational Procedures for CRF-23 Design......Page 469
Interpreting Interactions......Page 473
Multiple Comparison Procedures......Page 475
Practical Significance......Page 477
Relative Merits of Factorial Designs......Page 479
CHECK YOUR UNDERSTANDING OF SECTION 16.4......Page 480
16.5 Looking Back: What Have You Learned?......Page 482
REVIEW EXERCISES FOR CHAPTER 16......Page 483
17. Statistical Inference for Frequency Data......Page 488
17.2 Three Applications of Pearson's Chi-Square Statistic......Page 489
17.3 Testing Goodness of Fit......Page 491
Computational Example......Page 492
Characteristics of Pearson’s Statistic......Page 494
Practical Significance......Page 495
Assumptions of the Goodness-of-Fit Test......Page 496
CHECK YOUR UNDERSTANDING OF SECTIONS 17.2 AND 17.3......Page 497
Computational Example......Page 498
Degrees of Freedom for a Contingency Table......Page 500
Contingency Tables with Three or More Rows or Columns......Page 501
Practical Significance......Page 503
Assumptions of the Independence Test......Page 504
CHECK YOUR UNDERSTANDING OF SECTION 17.4......Page 505
Computational Example......Page 506
Extension of the Test of Equality to More Than Two Response Categories......Page 508
CHECK YOUR UNDERSTANDING OF SECTION 17.5......Page 509
17.6 Looking Back: What Have You Learned?......Page 511
REVIEW EXERCISES FOR CHAPTER 17......Page 513
Special Computational Procedure for a 2 × 2 Contingency Table......Page 517
18. Statistical Inference for Ranked Data......Page 520
18.2 Assumption-Freer Tests......Page 521
Computational Procedure for Small Samples......Page 523
Computational Procedures When One or Both n’s Exceed 20......Page 525
Measures of Relative Efficiency......Page 526
CHECK YOUR UNDERSTANDING OF SECTIONS 18.2 AND 18.3......Page 527
18.4 Wilcoxon T Test for Dependent Samples......Page 528
Computational Procedure for Small Samples......Page 529
Computational Procedures When n Is Greater Than 50......Page 531
CHECK YOUR UNDERSTANDING OF SECTION 18.4......Page 532
18.5 Comparison of Parametric Tests and Assumption-Freer Tests for Ranked Data......Page 533
18.6 Looking Back: What Have You Learned?......Page 535
REVIEW EXERCISES FOR CHAPTER 18......Page 536
Appendix A: Review of Basic Mathematics......Page 540
Appendix B: Glossary of Symbols......Page 554
Appendix C: Answers to Check Your Understanding Exercises......Page 562
Appendix D: Tables......Page 620
Appendix E: Student Database......Page 648
References......Page 662
Index......Page 666