Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

PREFACE

Five issues in experimental design are considered in this chapter.

15.1. Nested Factors and Natural Groups. In one typical nested design, treatments are given to subjects in natural groups, as with classroom groups in education or hospital wards in medical science. Correct analysis requires that the error term be calculated from differences between group means. The practice of calculating the error term from differences between subjects is not valid because subjects within groups are not generally independent.

15.2. Random Factors. With a random factor, the factor levels are chosen at random from some population, of stimulus materials, for example, or therapists, or classroom groups. This helps obtain generality across the random factor. Indeed, random factor Anova can provide a statistical generalization from the random sample to the population, although this benefit may have unacceptable cost. It may usually be preferable, therefore, to use standard fixed factor Anova.

15.3. Reducing Design Size. Multiple factors must sometimes be included in a design, but multifactor designs tend to be large and costly, even infeasible. Fractional replication can reduce design size by using only a well-chosen fraction of the conditions in the complete factorial design. Fractional design, extensively developed by statisticians, has been underutilized by psychologists. The rationale is shown for a simple case and illustrated with an empirical study of serial belief integration.

For single subject analysis, Latin squares have unrecognized potential for reducing design size while balancing multiple variables. For independent groups, however, Latin square designs have limited usefulness.

15.4. Unequaln. When a factorial design has unequal n in different cells, the simple formulas of Chapter 5 are not applicable. This once confused issue is no longer a big problem because the complicated calculations for unequal n are now done by computer. It is suggested, however, that primary use be made of two-mean comparisons with confidence intervals instead of overall Anova.

15.5. Quasi-Experimental Design. In quasi-experimental design, treatments are given to groups that differ preexperimentally. Treatment effects are thus confounded with uncontrolled/unknown differences between groups. Common methods to “control for” or “partial out” uncontrolled variables are seldom justified. Field science with nonrandomized groups has high importance, but it requires high expertise.

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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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