# Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

EXERCISES FOR CHAPTER 21
Exercises for Addition Modela1. Can you average length by visual inspection? To find out, present two unequal lengths in 3 × 4 factorial design and judge average length of each of the 12 pairs. After practice trials, present the design twice to provide an error term for Anova. Do this experiment with two subjects, yourself and one other. Get verbal reports of how subjects think they did the task. For this exercise, use a 1–20 rating scale. To avoid end bias, use end anchors to be called 1 and 20, respectively (Note 21.6.1a). Analyze and discuss the data.a2. In a 2 × 5 design, suppose the row stimuli have values 1 and 3, and the column stimuli have values 1, 2, 4, 8, and 16.
 a. Assume an addition model, calculate the cell entries for the factorial table, and plot these values, showing that they exhibit parallelism. b. In this same 2 × 5 design, suppose the row stimuli have values a and b, and the column stimuli have values v, w, x, y, and z. Assume an addition model and write down the entry in each cell of the factorial data table. c. How does the factorial table for (b) reveal parallelism?
a3. Conclusion 2 of the parallelism theorem says that the marginal means for each factor are a linear scale of the values of that factor. Check this numerically with the column factor for the numerical example of Exercise a2.a4. With an additive model, the cell entries are completely determined by the marginal means. The formula for a two-way design is

cell mean = row mean + column mean - overall mean.

Get marginal means for the data of Exercise a2 and check that this formula is correct. (As an optional exercise, derive this formula algebraically.)a5.
 a. How, according to the parallelism theorem, do the data of Figure 20.3 relate to the subjective values of heaviness? b. The psychophysical function is the function relating the subjective value of some sensory dimension to the objective, physical magnitude. How does the measurement of (a) solve the problem of determining the psychophysical function for heaviness? c. Why go to this illusion to get subjective heaviness? Why not eliminate the illusion by concealing the weights behind a screen and ask subjects to judge heaviness of these unseen lifted weights?

a6. In Figure 21.4: a. Why is the parallelism essential to show that bimodality is real? b. Explain bimodality in terms of propensity to approach and avoid goals. c. Outline an experiment to test bipolarity with another stimulus class.

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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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