Data analysis for experimental design:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Guilford Press
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 439 S. graph. Darst. |
| ISBN: | 9781606230176 |
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MARC
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| 100 | 1 | |a Gonzalez, Richard |d 1962- |e Verfasser |0 (DE-588)137158882 |4 aut | |
| 245 | 1 | 0 | |a Data analysis for experimental design |c Richard Gonzalez |
| 264 | 1 | |a New York |b Guilford Press |c 2009 | |
| 300 | |a XVIII, 439 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Data-analyse |2 gtt | |
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| 650 | 7 | |a Experiment - Statistik |2 idsbb | |
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| 650 | 7 | |a Psychometrie |2 idsbb | |
| 650 | 7 | |a Statistik - Experiment |2 idsbb | |
| 650 | 4 | |a Analysis of Variance | |
| 650 | 4 | |a Analysis of variance | |
| 650 | 4 | |a Experimental design | |
| 650 | 4 | |a Psychometrics | |
| 650 | 4 | |a Research Design | |
| 650 | 4 | |a Statistics as Topic | |
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Record in the Search Index
| _version_ | 1804138442547789824 |
|---|---|
| adam_text | Titel: Data analysis for experimental design
Autor: Gonzalez, Richard
Jahr: 2009
Contents
The Nature of Research 1
1.1 Introduction.......................... 1
1.2 Observations and Variables.................. 5
1.3 Behavioral Variables...................... 6
1.4 Stimulus Variables....................... 7
1.5 Individual Difference Variables................ 9
1.6 Discrete and Continuous Variables.............. 10
1.7 Levels of Measurement..................... 11
1.8 Summarizing Observations in Research ........... 14
1.9 Questions and Problems.................... 16
Principles of Experimental Design 19
2.1 The Farmer from Whidbey Island.............. 19
2.2 The Experiment........................ 20
2.3 The Question of Interest.................... 21
2.4 Sample Space and Probability ................ 22
2.5 Simulation of the Experiment................. 23
2.6 Permutations.......................... 25
2.7 Combinations.......................... 26
2.8 Probabilities of Possible Outcomes.............. 27
2.9 A Sample Space for the Experiment............. 29
2.10 Testing a Null Hypothesis................... 30
2.11 Type I and Type II Errors .................. 32
2.12 Experimental Controls..................... 34
2.13 The Importance of Randomization.............. 36
2.14 A Variation in Design..................... 38
2.15 Summary............................ 39
2.16 Questions and Problems.................... 40
Xi
xii Contents
3 The Standard Normal Distribution: An Amazing
Approximation 45
3.1 Introduction.......................... 45
3.2 Binomial Populations and Binomial Variables........ 46
3.3 Mean of a Population..................... 48
3.4 Variance and Standard Deviation of a Population ..... 49
3.5 The Average of a Sum and the Variance of a Sum..... 51
3.6 The Average and Variance of Repeated Samples...... 52
3.7 The Second Experiment with the Farmer: lit and oT ... 55
3.8 Representing Probabilities by Areas............. 57
3.9 The Standard Normal Distribution.............. 58
3.10 The Second Experiment with the Farmer: A Normal
Distribution Test........................ 60
3.11 The First Experiment with the Farmer: A Normal
Distribution Test........................ 64
3.12 Examples of Binomial Models................. 68
3.13 Populations That Have Several Possible Values....... 70
3.14 The Distribution of the Sum from a Uniform Distribution . 71
3.15 The Distribution of the Sum T from a U-Shaped Population 75
3.16 The Distribution of the Sum T from a Skewed Population . 79
3.17 Summary and Sermon..................... 82
3.18 Questions and Problems.................... 84
4 Tests for Means from Random Samples 87
4.1 Transforming a Sample Mean into a Standard Normal
Variable............................. 87
4.2 The Variance and Standard Error of the Mean When the
Population Variance a2 Is Known.............. 89
4.3 The Variance and Standard Error of the Mean When
Population er2 Is Unknown.................. 90
4.4 The t Distribution and the One-Sample t Test....... 92
4.5 Confidence Interval for a Mean................ 95
4.6 Standard Error of the Difference between Two Means ... 98
4.7 Confidence Interval for a Difference between Two Means . . 103
4.8 Test of Significance for a Difference between Two Means:
The Two-Sample t Test.................... 103
4.9 Using a Computer Program.................. 106
4.10 Returning to the Farmer Example in Chapter 2....... 107
Contents xiii
4.10.1 Methodological Issues Reiterated .......... 109
4.11 Effect Size for a Difference between Two Independent Means 110
4.12 The Null Hypothesis and Alternatives............ 112
4.13 The Power of the t Test against a Specified Alternative . . 117
4.14 Estimating the Number of Observations Needed in
Comparing Two Treatment Means.............. 122
4.15 Random Assignment of Participants............. 125
4.16 Attrition in Behavioral Science Experiments ........ 126
4.17 Summary............................ 128
4.18 Questions and Problems.................... 128
Homogeneity and Normality Assumptions 133
5.1 Introduction.......................... 133
5.2 Testing Two Variances: The F Distribution......... 134
5.3 An Example of Testing the Homogeneity of Two Variances 136
5.4 Caveats............................. 136
5.5 Boxplots ............................ 138
5.6 A t Test for Two Independent Means When the
Population Variances Are Not Equal............. 140
5.6.1 SPSS Example..................... 143
5.7 Nonrandom Assignment of Subjects............. 145
5.8 Treatments That Operate Differentially on Individual
Difference Variables...................... 145
5.9 Nonadditivity of a Treatment Effect............. 148
5.10 Transformations of Raw Data................. 149
5.10.1 Two Samples from Different Poisson Distributions . 150
5.10.2 Two Samples from Different Binomial Populations 154
5.10.3 Heterogeneity of Variance: Time as a Dependent
Variable........................ 156
5.10.4 When Means Are Proportional to Standard
Deviations: The Power Transformation....... 157
5.10.5 Transformation of Scale: General Considerations . 158
5.11 Normality............................ 160
5.12 Summary............................ 161
5.13 Questions and Problems.................... 162
The Analysis of Variance: One Between-Subjects Factor 165
6.1 Introduction.......................... 165
6.2 Notation for a One-Way Between-Subjects Design..... 167
xjv Contents
6.3 Sums of Squares for the One-Way Between-Subjects Design 169
6.4 One-Way Between-Subjects Design: An Example...... 172
6.5 Test of Significance for a One-Way Between-Subjects Design 177
6.5.1 Structural Model................... 179
6.5.2 Equality of Variance Assumption.......... 181
6.5.3 Equality between the Two-Sample t Test and the
F Test for Two Groups................ 182
6.6 Weighted Means Analysis with Unequal n s......... 183
6.7 Summary............................ 185
6.8 Questions and Problems.................... 186
7 Pairwise Comparisons 191
7.1 Introduction.......................... 191
7.2 A One-Way Between-Subjects Experiment with 4
Treatments........................... 194
7.3 Protection Levels and the Bonferroni Significant
Difference (BSD) Test..................... 197
7.4 Fisher s Significant Difference (FSD) Test.......... 200
7.5 The Tukey Significant Difference (TSD) Test........ 202
7.6 Seheffe s Significant Difference (SSD) Test.......... 203
7.7 The Four Methods: General Considerations......... 205
7.8 Questions and Problems.................... 208
8 Orthogonal, Planned and Unplanned Comparisons 211
8.1 Introduction.......................... 211
8.2 Comparisons on Treatment Means.............. 212
8.3 Standard Error of a Comparison............... 215
8.4 The t Test of Significance for a Comparison......... 216
8.5 Orthogonal Comparisons................... 218
8.6 Choosing a Set of Orthogonal Comparisons......... 219
8.7 Protection Levels with Orthogonal Comparisons...... 222
8.8 Treatments as Values of an Ordered Variable........ 222
8.9 Coefficients for Orthogonal Polynomials........... 223
8.10 Tests of Significance for Trend Comparisons......... 226
8.11 The Relation between a Set of Orthogonal Comparisons
and the Treatment Sum of Squares.............. 228
8.12 Tests of Significance for Planned Comparisons....... 230
8.13 Effect Size for Comparisons................. . 231
8.14 The Equality of Variance Assumption............ 232
Contents xv
8.15 Unequal Sample Size...................... 232
8.16 Unplanned Comparisons.................... 233
8.16.1 Some Examples of the Scheffe Test......... 233
8.16.2 The Scheffe Test for Comparisons.......... 236
8.16.3 Properties of the Scheffe Test............ 237
8.17 Summary............................ 238
8.18 Questions and Problems.................... 239
9 The 2k Between-Subjects Factorial Experiment 243
9.1 Introduction.......................... 243
9.2 An Example of a 23 Factorial Experiment.......... 244
9.3 Assumption of Homogeneity of Variance........... 247
9.4 Factorial Data as a One-Way Between-Subjects Design . . 249
9.5 Partitioning the Treatment Sum of Squares......... 251
9.6 Summary of the Analysis of Variance ............ 255
9.7 Graphs That Depict the Interactions............. 257
9.8 Other 2k Factorial Experiments................ 261
9.9 Notation and Sums of Squares for a Factorial Experiment . 263
9.10 Summary............................ 266
9.11 Questions and Problems.................... 266
10 Between-Subjects Factorial Experiments: Factors with
More Than Two Levels 269
10.1 Introduction .......................... 269
10.2 An Example of a 4 x 3 x 2 Factorial Experiment...... 270
10.3 Partitioning the Sum of Squares into Main Effects and
Interactions........................... 272
10.4 Orthogonal Partitioning for Main Effects.......... 274
10.5 Orthogonal Partitioning for Interactions........... 280
10.6 Effect Size for Comparisons in a Factorial Design...... 284
10.7 Performing Multiple Tests................... 284
10.8 The Structural Model and Nomenclature.......... 285
10.9 Summary............................ 287
10.10 Questions and Problems.................... 287
11 Between-Subjects Factorial Experiments: Further
Considerations 291
11.1 The Scheffe Test for Comparisons.............. 291
11.2 Pairwise Comparisons in Factorial Designs ......... 294
xvi Contents
11.3 Unequal Sample Sizes in a Factorial Design......... 298
11.4 Individual Difference Factors................. 301
11.5 Control Variables........................ 302
11.6 Random-Effect Factors .................... 307
11.7 Nested Factors......................... 311
11.7.1 Nested Designs in SPSS ............... 315
11.8 Homogeneity of Variance................... 316
11.9 Summary............................ 318
11.10 Questions and Problems.................... 318
12 Within-Subjects Factors: One-Way and 2* Factorial
Designs 321
12.1 Introduction .......................... 321
12.2 Example: One-Way ANOVA with a Within-Subjects Factor 322
12.3 Trend Analysis on One-Way Within-Subjects Designs . . . 327
12.4 Assumptions and Effect Size Measures............ 330
12.5 2k Factorial Designs: All Within-Subjects Factors..... 333
12.6 Multiple Tests......................... 336
12.7 Design Considerations with Within-Subjects Designs .... 338
12.8 Scheffe Test for Within-Subjects Factors........... 340
12.9 SPSS Syntax.......................... 342
12.10 Multilevel Approach to Within-Subjects Designs...... 344
12.11 Summary............................ 347
12.12 Questions and Problems.................... 347
13 Within-Subjects Factors: General Designs 349
13.1 Introduction.......................... 349
13.2 General Within-Subjects Factorial Design.......... 349
13.3 Designs Containing Both Within-Subjects
and Between-Subjects Factors ................ 357
13.3.1 Structural Model................... 361
13.3.2 SPSS Syntax...................... 363
13.4 Omnibus Tests......................... 365
13.5 Summary............................ 368
13.6 Questions and Problems.................... 368
14 Contrasts on Binomial Data: Between-Subject Designs 371
14.1 Introduction .......................... 371
14.2 Preliminaries.......................... 373
Contents xvii
14.3 Four Examples of Wald Tests................. 376
14.3.1 Comparisons on Raw Proportions.......... 376
14.3.2 The Arcsin Transformation.............. 377
14.3.3 The Logit Transformation.............. 379
14.3.4 The Probit Transformation.............. 380
14.4 Other Statistical Tests for Comparisons on Proportions . . 381
14.4.1 Contrast on Raw Proportions (Pooled Error Term) 381
14.4.2 Student s t Test and the ANOVA.......... 383
14.4.3 Comments on the t Test and the ANOVA..... 385
14.5 Numerical Examples...................... 386
14.5.1 Collapsing the k x 2 Contingency Table...... 387
14.6 How Do These Tests Differ and What Do They Test? ... 391
14.6.1 Structural Model................... 394
14.7 Summary............................ 397
14.8 Questions and Problems.................... 398
15 Debriefing 399
15.1 Introduction..........................399
15.2 Descriptive Statistics and Plotting Data...........400
15.3 Presenting Your Results....................401
15.4 Nonparametric Statistical Tests................403
15.5 Nonexperimental Controls...................404
15.6 Questions and Problems....................409
Appendix A. The Method of Least Squares 411
A.l Introduction.......................... 411
A.2 The Derivative of a Power Function............. 412
A.3 The Derivative of a Power Function with an Added Constant 412
A.4 The Derivative of a Power Function with a Multiplicative
Coefficient ........................... 413
A.5 The Method of Least Squares................. 413
A.6 Another Method for Finding the Derivative of ^T,(X ? a)2 . 415
A.7 Least Squares Estimates q2- and p for a Between-Subjects
Design with One Factor.................... 410
Appendix B. Statistical Tables 419
B.l t Table.............................420
B.2 F Tables ............................421
B.2.1 a = 0.05........................421
xviii Contents
B.2.2 a = 0.01........................422
B.3 Z Table: Standard Normal Distribution...........423
B.4 Chi-Squared Table.......................424
B.5 Table of Coefficients for Orthogonal Polynomials......425
B.6 Tukey s Studentized Range Table for a = 0.05.......426
References 427
Index 435
|
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| spelling | Gonzalez, Richard 1962- Verfasser (DE-588)137158882 aut Data analysis for experimental design Richard Gonzalez New York Guilford Press 2009 XVIII, 439 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Data-analyse gtt Datenanalyse idsbb Experiment - Statistik idsbb Experimenteel ontwerp gtt Psychometrie idsbb Statistik - Experiment idsbb Analysis of Variance Analysis of variance Experimental design Psychometrics Research Design Statistics as Topic HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017000352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gonzalez, Richard 1962- Data analysis for experimental design Data-analyse gtt Datenanalyse idsbb Experiment - Statistik idsbb Experimenteel ontwerp gtt Psychometrie idsbb Statistik - Experiment idsbb Analysis of Variance Analysis of variance Experimental design Psychometrics Research Design Statistics as Topic |
| title | Data analysis for experimental design |
| title_auth | Data analysis for experimental design |
| title_exact_search | Data analysis for experimental design |
| title_full | Data analysis for experimental design Richard Gonzalez |
| title_fullStr | Data analysis for experimental design Richard Gonzalez |
| title_full_unstemmed | Data analysis for experimental design Richard Gonzalez |
| title_short | Data analysis for experimental design |
| title_sort | data analysis for experimental design |
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