Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

PREFACE

Prediction is the strong point of regression analysis. In admitting graduate students, some departments utilize predictive power of the GRE. Similar predictive formulas are often used to sort out those more likely to succeed in particular jobs or to benefit from certain medical treatments. These statistical prediction formulas are typically superior to expert judgment, and less costly to boot.

The term regression merely means curve fitting, usually a straight line curve. This regression exhibits the response measure, Y, as a function of the predictor variable, X. The slope of this line reflects how strongly Y depends on X, so this slope is the main concern. Thus, a slope of 0 means that X has no predictive power for Y.

Statistically, regression analysis can be seen as an extension of Anova that uses a metric predictor variable, X, in place of the experimental variable, A, of previous chapters. The slope of the regression line, which is usually the main concern, can be determined, together with its confidence interval.

The two big problems with prediction are extrastatistical: To find good predictor variables; and to find a valid measure of the criterion to be predicted. The GRE is not actually a strong predictor of success in graduate school. Moreover, success in graduate school is not easily measured, and however measured may have little relation to the final criterion—life after graduation.

Regression can also be used in experimental studies, especially when the stimulus variables are quantitative or metric. With metric stimulus variables, regression analysis offers marked simplification of factorial design. Also, linear trend analysis is markedly simpler with regression formulas than with the linear contrasts of Anova that are generally recommended.

The correlation coefficient is a byproduct of regression analysis. It can be useful in specialized domains, as in test theory. The correlation coefficient suffers surprisingly many flaws, however, that severely limit its usefulness.

Causal analysis is the weak point of regression analysis. Regression–correlation is often used to attempt causal interpretation from uncontrolled, observational data. A good deal of what is reported in the media and even in professional journals is unwarranted inference based on regression analysis of uncontrolled data. The many well-known pitfalls are glossed over with lip-service cautions or simply ignored. Causal analysis with observational data has high importance, but effective work requires unusually high expertise, both statistical and extrastatistical.

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Empirical Direction in Design and Analysis
Table of contents

Table of contents

  • Title Page iii
  • Dedication v
  • Foreword vi
  • Contents vii
  • Preface xvi
  • Chapter 1 - Scientific Inference 1
  • Preface 30
  • Chapter 2 - Statistical Inference 31
  • How to Do Exercises 54
  • Exercises for Chapter 2 54
  • Preface 58
  • Chapter 3 - Elements of Analysis of Variance I 59
  • Notes 75
  • Appendix: How to Randomize 77
  • Exercises for Chapter 3 84
  • Preface 90
  • Chapter 4 - Elements of Analysis of Variance II 91
  • Notes 111
  • Exercises for Chapter 4 113
  • Preface 118
  • Chapter 5 - Factorial Design 119
  • Notes 145
  • Appendix: Hand Calculation for Factorial Design 148
  • Exercises for Chapter 5 151
  • Preface 158
  • Chapter 6 - Repeated Measures Design 159
  • Notes 177
  • Exercises for Chapter 6 181
  • Preface 188
  • Chapter 7 - Understanding Interactions 189
  • Notes 209
  • Exercises for Chapter 7 214
  • Preface 218
  • Chapter 8 - Confounding 219
  • Notes 250
  • Preface 258
  • Chapter 9 - Regression and Correlation 259
  • Notes 280
  • Exercises for Chapter 9 282
  • Preface 286
  • Chapter 10 - Frequency Data and Chi-Square 287
  • Notes 300
  • Exercises for Chapter 10 302
  • Preface 306
  • Chapter 11 - Single Subject Design 307
  • Notes 338
  • Exercises for Chapter 11 345
  • Preface 350
  • Chapter 12 - Nonnormal Data and Unequal Variance 351
  • Notes 373
  • Exercises for Chapter 12 378
  • Preface 382
  • Chapter 13 - Analysis of Covariance 383
  • Notes 395
  • Exercises for Chapter 13 397
  • Preface 400
  • Chapter 14 - Design Topics I 401
  • Notes 431
  • Exercises for Chapter 14 437
  • Preface 442
  • Chapter 15 - Design Topics II 443
  • Notes 475
  • Exercises for Chapter 15 481
  • Preface 484
  • Chapter 16 - Multiple Regression 485
  • Notes 514
  • Exercises for Chapter 16 520
  • Preface 524
  • Chapter 17 - Multiple Comparisons 525
  • Notes 546
  • Exercises for Chapter 17 548
  • Preface 550
  • Chapter 18 - Sundry Topics 551
  • Notes 589
  • Exercises for Chapter 18 596
  • Preface 602
  • Chapter 19 - Foundations of Statistics 603
  • Notes 637
  • Preface 646
  • Chapter 20 - Mathematical Models for Process Analysis 647
  • Notes 677
  • Exercises for Chapter 20 681
  • Preface 688
  • Chapter 21 - Toward Unified Theory 689
  • Notes 729
  • Exercises for Chapter 21 742
  • Preface 750
  • Chapter 22 - Principles and Tactics of Writing Papers 751
  • Notes 761
  • Preface 764
  • Chapter 23 - Lifelong Learning 765
  • Notes 780
  • Preface 782
  • Chapter 0 - Basic Statistical Concepts 783
  • Notes 803
  • Exercises for Chapter 0 805
  • Statistical Tables 808
  • References 820
  • Author Index 847
  • Subject Index 854
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