# Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

EXERCISES FOR CHAPTER 20
a. Exercises on Addition Modela1. How can you test goodness of fit for Piaget' s centration hypothesis for the time judgments of Equation lc of Section 20.1 (see Exercise 5.2):
 1 with Anova? 2 with standard regression analysis of Chapter 9 or 16? 3 Which seems preferable?
a2. In Figure 20.3 on the size–weight illusion:
 1 Why would it be gauche to report the F for gram weight? 2 Would it be gauche to report the F for size? 3 Suppose the main effect for size was not statsig. How would this bear on the purposes of the experiment?
a3. Restate in your own words the reasoning of the last paragraph of Cognitive Development in Section 20.1.3, beginning “The conceptual implications of this result are more important than the algebraic rule itself.”a4. For the 3 × 3, Distance × Speed experiment considered in Section 20.1:
 1 Make up hypothetical data for a single subject that follow the postulated subtraction model exactly. Add an error of ± c in each cell, where c is a constant equal to about 10% of the range of data, choosing the ± sign at random for each cell. Make two replications. Apply Anova and comment. 2 Make similar data for the physically correct division model and compare the factorial graphs for both sets of data by graphical inspection. 3 Test the subtraction model with the data generated by the division model using visual inspection and also Anova. Comment. 4 The cell means predicted by the subtraction model are equal to (row mean + column mean − overall meanl. Apply this subtraction model to the division data of (b). Graph these predicted values as a function of the observed values and compute the correlation. Discuss in relation to Figure 20.5 and your analysis in (c).

a5. Serial belief integration can be studied using serial-factor design, in which each serial position constitutes a factor in the design. The main effect of each factor then measures the effect of the informer stimulus at the corresponding position. To illustrate the idea, consider three serial positions, each of which may present an informer of value 0 or 100, that is, against or for some belief issue. Subjects judge their belief only once, after all three informers have been presented, based on all the given information. Asssume that the response to

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