# Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

NOTES
20.1a
For convenience, the term addition will be taken to include both addition and subtraction operations; mathematically, subtraction is addition of a negative number. This usage does not imply psychological equivalence. The term adding-type will also include averaging models, although averaging differs from adding both mathematically and psychologically (Section 21.4, pages 705 ff).
20.1.2a
This contrast between stimulus measurement in regression and in Anova illustrates a general problem in model analysis. A test of goodness of fit usually depends on securing the values of certain parameters in the model. These parameter values may be obtained in two ways: from the data at hand or from separate data. The first way is used in Anova, the second in regression. The first is usually preferable.

It might instead seem that separate parameter values would be superior; estimating parameters from the data and then using these parameters to “predict” those same data seems dubious. In fact, however, separate parameters suffers two shortcomings—invalidity and unreliability—both likely to be serious.

Invalidity can be avoided by estimating parameter values from the data at hand. This gives the model its best opportunity to fit the data. This is done in Anova, which avoids the ambiguity that troubles the regression analysis and provides a valid test of goodness of fit. A statsig discrepancy can thus be unambiguously attributed to the model itself.

Unreliability in the separate parameter values will generally introduce bias. This bias problem was illustrated with Ancova for nonrandom groups (Section 13.2). Without working familiarity with statistical theory of “errors in variables, ” reliance on separate predictor values is dangerous. Other difficulties with regression analysis of substantive models are noted in Section 20.2 and in Anderson (1982, Sections 4.3 and 6.1.1).

Regression analysis can be extended to estimate stimulus values in the same way as Anova, as noted in Chapters 9 and 16. Bogartz put this approach to good use in the study of infant perception/cognition of Note 8.1.2d. The present criticism concerns use of prior stimulus metrics without allowance for unreliability or invalidity.

20.1.3a
Except for Bogartz (1994a), the role of Anova for analysis of mathematical process models is completely ignored in statistics texts. This reflects the traditional focus on statistics to the neglect of empirics.
20.1.3b
What is most remarkable is that children can do these time judgments at all. This requires a complex assemblage: the imagined animal fleeing from the imagined dog across an imagined bridge at some imagined speed, and so on. This mental assemblage must be distilled into a quantitative judgment using an unfamiliar, symbolic response mode. The conceptual implications cited in the text are only one aspect of a fundamental issue of assemblage integration. One value of algebraic rules is potential for assemblage analysis (see Assemblage Theory in Anderson & Wilkening, 1991, pp. 20 ff).
20.1.3c
The experiment of Figure 20.2 reaffirmed the long-known fallibility of verbal report, that people “tell more than they know.” But contrary to Nisbett and Wilson (1977), individuals can give veridical self-reports. One illustration comes from Wright (1996), who used functional measurement theory to resolve two difficulties that had nullified previous attempts to disprove the thesis of Nisbett and Wilson that verbal reports

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Empirical Direction in Design and Analysis

• 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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