Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

PREFACE

Every investigation with more than two conditions faces two linked hazards: escalation of false alarm and loss of power. Each comparison of two means is an opportunity for false alarm. Four conditions yield six two-mean comparisons—six opportunities for false alarms. Hence the effective α for this family of six comparisons is greater than the α used for each single test—not.05 but.20. This familywise α escalates rapidly with more conditions.

You can hold α down to whatever you want—at a price. The price is loss of power, that is, β increase. This is the α-β tradeoff dilemma of Chapter 2.

Two polarized philosophies have developed for dealing with this α–β trade–off dilemma. Each philosophy is mainly concerned with avoiding one of the two hazards. The familywise philosophy postulates that α should be set at some fixed value, regardless of the number of conditions. Necessarily, therefore, power decreases with more conditions. The per comparison philosophy, seeking to lessen such loss of power, allows larger α with more conditions.

The per comparison philosophy is advocated in this chapter for most work in experimental psychology. Current texts, in contrast, increasingly follow the familywise philosophy. But although some situations do require familywise analysis, these are not common in experimental psychology. The per comparison philosophy is founded on empirical common sense, as shown in the Parable of the Two Philosophies.

Extrastatistical considerations have an essential role with multiple comparisons. Among these are the guideline of planned comparisons and the principle of replication, which do much to provide reasonable control of α and β. This guideline and this principle are accepted by most empirical investigators.

Empirical judgment is the primary basis for handling multiple comparisons, not statistical techniques. Empirical judgment underlies the cost–benefit analysis necessary to deal with the α–β tradeoff dilemma. Above all, empirical judgment is needed in planning the design and analysis, especially in relation to the guideline of planned tests and the principle of replication. This chapter, accordingly, sets the issue of multiple comparisons within the framework of the Experimental Pyramid of Chapter 1.

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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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