# 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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