Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

NOTES

Information integration theory (IIT) has been developed in collaboration with many students and colleagues. I wish to express my heartfelt appreciation to these men and women (see Anderson, 1996a, p. v) for their dedicated labors, and to compliment them for their enduring contributions to psychological science.

21.2a
“The uniqueness of FM [functional measurement] is in its realization that the hypothesized integration function could itself be used as the base and frame for scaling subjective values” (Budescu & Wallsten, 1979, p. 307).

Also unique to functional measurement is its extensive empirical foundation. When I introduced this functional approach (Anderson, 1962a, b), I realized that making measurement theory an integral part of substantive investigation represented a 180° conceptual shift from traditional approaches, which had viewed measurement as a preliminary to substantive inquiry. I also realized that the worth of this functional approach depended on establishing empirical validity of algebraic laws. With the blessing of Nature, such laws have been established. The true foundation of psychological measurement theory lies in such empirical investigations.

The necessity of empirical foundation is underscored by the averaging model, unexpectedly found to be the main integration rule in the empirical analyses. The traditional conception of measurement in terms of the single dimension of scale value was inherently too narrow. Measurement theory must recognize the coequal status of two scales of measurement—of weight and value.

21.2.1a
Proportional scales, which are needed in some applications (e.g., Exercise a7), are linear scales with a known zero. Linearity is the critical element; a needed zero can then often be estimated from the data.
21.2.2a
A validity criterion to assess whether magnitude estimation or rating yields a true linear scale has been provided by the parallelism theorem (pages 697 ff).

In the experiment of Figure 21.8 (next page), subjects were shown two Munsell gray chips from Figure 21.1 and instructed to judge their average grayness. This prescribed averaging model, seemingly prosaic and uninteresting, has an important function—as a validity criterion for response linearity. Since subjects are told to average, the factorial plot may be expected to exhibit parallelism—if the response is a linear scale.

Judgments with magnitude estimation are shown in the right panel; these are radically nonparallel, as shown by the two equal-length vertical bars. Judgments with ratings are shown in the left panel; these are roughly parallel.

As far as one experiment may go, this one implies that magnitude estimation is biased and invalid (see further Notes 21.6.3g, h). Rating and magnitude estimation had equal opportunity; the parallelism theorem acted as an impartial judge of both methods. Magnitude estimation could have succeeded, but it failed. The rating method could have failed, but it succeeded.

21.3.3a
This and other applications of information integration theory to language processing are discussed in Anderson (1996a, Chapter 12).

-729-

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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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