Empirical Direction in Design and Analysis

By Norman H. Anderson | Go to book overview

EXERCISES FOR CHAPTER 17
1. How can a single experiment produce multiple false alarms? Multiple false alarms and multiple misses?
2. In the numerical example of Student–Newman range test, verify that the final outcome is the separation of the means into the following three subsets, each of which contains means that are not statsig different.

{A, B}, {B, C, D}, and {C, D, E}.

a. Which two-mean comparisons are statsig?
b. You notice that the means seem to fall into two clusters, {A, B} and {C, D, E}. Use the formula in Note 4.1.1b to get 14.83 ± 7.38 as a 95% confidence interval for the difference between the means of the two clusters. How much confidence do you have that this clustering is real?
3. You test four experimental conditions but the overall Anova falls somewhat short of statsig. However, your research assistant points out that your four experimental conditions form a clear a priori rank order and suggests that a linear trend test would be most effective. What do you do?
4. a. Show that the one-for-two rule of Section 17.3.2 yields α3 =.074 for a = 3 conditions. Compare with Student–Newman procedure.
5. In the familywise test of inverted-U shape (Section 17.4.2):
a. What is the null hypothesis? Why is this null hypothesis appropriate?
b. What is the familywise α if H0 is true?
c. Suppose the expected maximum condition had not been specified beforehand, but selected by inspection of the data. Why exactly would this invalidate the analysis? What modification is needed in this case?
d. Would you have any preference between Newman–Ryan and Tukey procedures for this question of inverted U shape?
6. With one-way design, a statsig range always demonstrates a two-mean difference, whereas a statsig F says only that not all true means are equal with little information about which means differ from which. Hence a range procedure such as Student–Newman might seem preferable to the overall F. Although the range procedures may have a little less power in most situations, they go beyond the overall F to say which means differ from which.

So: Why not make range procedures standard and forget about overall Anova? As a bonus, much material of previous chapters could be omitted; learning statistics would be much easier. What reason can you see for retaining the overall F for one-way designs?

-548-

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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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