Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

PREFACE

Nonnormality is likely to widen confidence intervals and decrease power. The robustness of Anova applies mainly to the false alarm parameter, α. Power, in contrast, can be seriously affected by nonnormality.

The real trouble is extreme scores; they contribute disproportionately to error variance. Nonnormality is a problem mainly because it is usually accompanied by extreme scores. Distributions that have longer or heavier tails than the normal distribution are common in practice; these tail scores increase the error variance disproportionately.

Avoiding extreme scores depends first on empirics: experimental task, experimental procedure, and response measure. Better instructions, for example, will reduce the likelihood that an occasional subject will misunderstand the task and yield an extreme score. Similar considerations apply to every aspect of experimental procedure. Choice of response measure can have marked effects on the shape of the data distribution—which should be a primary concern in planning any investigation.

After the data are in, the shape of their distribution can still be changed statistically. Trimming seems the most useful statistical technique to deal with extreme scores. This is one of numerous “robust” techniques, distinguished from the others by a formula for the variance that makes for easy use.

Three alternatives to trimming are also considered: response transformation, outlier methods, and distribution-free rank tests. Time scores, for example, often have long right tails; transforming time to speed tends to normalize the data and increase power. Statistical tests for outliers are nonrobust, useful only in very special situations. Distribution-free tests of the ranked data appear inferior to Anova of these same ranks.

Unequal variance can have adverse effects on overall Anova, especially if coupled with unequal n. Available evidence suggests that extensions of Anova to handle unequal variance with more than two groups are sensitive to nonnormality and so not very useful. Even when applicable, moreover, overall Anova does little to localize the effects and explicate the data pattern.

Accordingly, an alternative to overall Anova with unequal variance is advocated in this book: Focus on two-mean comparisons at the outset. To this end, formulas are given for confidence intervals that allow unequal variance and unequal n as well.

-350-

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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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