Introducing anova and ancova: a GLM approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
SAGE Publ.
2001
|
| Edition: | 1. publ. |
| Series: | ISM Introducing statistical methods
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 182 S. |
| ISBN: | 0761951601 076195161X |
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MARC
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| 245 | 1 | 0 | |a Introducing anova and ancova |b a GLM approach |c Andrew Rutherford |
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Record in the Search Index
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| adam_text | CONTENTS
1 AN INTRODUCTION TO GENERAL LINEAR MODELS: REGRESSION, ANALYSIS
OF VARIANCE AND ANALYSIS OF COVARIANCE
1.1 Regression, analysis of variance and analysis of covariance 1
1.2 A pocket history of regression, ANOVA and ANCOVA 2
1.3 An outline of general linear models (GLAAs) 3
1.3.1 Regression analysis 4
1.3.2 Analysis of variance 4
1.3.3 Analysis of covariance 5
1.4 The general in GLM 5
1.5 The linear in GLM 8
1.6 Least squares estimates 10
1.7 Fixed, random and mixed effects analyses 10
1.8 The benefits of a GLM approach to ANOVA and ANCOVA 1 2
1.9 The GLM presentation 1 3
1.10 Statistical packages for computers 13
2 TRADITIONAL AND GLM APPROACHES TO INDEPENDENT MEASURES SINGLE
FACTOR ANOVA DESIGNS
2.1 Independent measures designs 15
2.1.1 Factors and independent variables 1 7
2.2 Traditional ANOVA for single factor designs 18
2.2.1 Variance 18
2.2.2 Example 19
2.3 GLM approaches to single factor ANOVA 24
2.3.1 Experimental design GLMs 24
2.3.2 Estimating effects by comparing full and reduced experimental
design GLMs 29
2.3.3 Regression GLMs 32
2.3.4 Cell mean GLMs 41
2.3.5 Cell mean, regression and experimental design GLMs 42
3 GLM APPROACHES TO INDEPENDENT MEASURES FACTORIAL ANOVA
DESIGNS
3.1 Factorial designs 43
3.2 Factor main effects and factor interactions 43
3.2.1 Estimating effects by comparing full and reduced experimental
design GLMs 49
viii CONTENTS
3.3 Regression GLMs for factorial ANOVA 56
3.3.1 Estimating main and interaction effects with regression GLMs 57
A GLM APPROACHES TO REPEATED MEASURES DESIGNS
4.1 Related measures designs 60
4.2 Repeated measures designs 61
4.3 Order effect controls 6 3
4.3.1 Counterbalancing 63
4.3.2 Randomization 65
4.4 The GLM approach to single factor repeated measures designs 65
4.5 Estimating effects by comparing full and reduced single factor repeated
measures design GLMs 71
4.6 Regression GLMs for single factor repeated measures designs 74
5 GLM APPROACHES TO FACTORIAL REPEATED MEASURES DESIGNS
5.1 Factorial related measures designs 78
5.2 The fully related factorial design GLM 79
5.3 Estimating effects by comparing full and reduced fully related factorial
experimental design GLMs 85
5.4 Regression GLMs for the fully related factorial ANOVA 88
5.5 Mixed factorial ANOVA 94
5.6 Estimating effects by comparing full and reduced mixed factorial
experimental design GLMs 98
5.7 Regression GLM for the mixed factorial ANOVA 99
6 THE GLM APPROACH TO ANCOVA
6.1 The nature of ANCOVA 105
6.2 Single factor independent measures ANCOVA designs 106
6.3 Estimating effects by comparing full and reduced single factor
independent measures ANCOVA GLMs 1 1 1
6.4 Regression GLMs for the single factor independent measures
ANCOVA 1 14
6.5 Other ANCOVA designs 120
6.5.1 Related measures ANCOVA designs 121
6.5.2 Mixed measures factorial ANCOVA 121
7 ASSUMPTIONS UNDERLYING ANOVA, TRADITIONAL ANCOVA AND GLMS
7.1 ANOVA and GLM assumptions 123
7.1.1 Independent measures 123
7.1.2 Related measures 1 25
7.1.3 Traditional ANCOVA 126
7.2 A strategy for checking ANOVA and traditional ANCOVA assumptions 1 27
7.3 Assumption checks and some assumption violation consequences 128
7.3.1 ANOVA and ANCOVA # 129
7.3.2 Traditional ANCOVA 136
CONTENTS ix
8 SOME ALTERNATIVES TO TRADITIONAL ANCOVA
8.1 Alternatives to traditional ANCOVA 145
8.2 The heterogeneous regression problem 145
8.3 The heterogeneous regression ANCOVA GLM 146
8.4 Single factor independent measures heterogeneous regression
ANCOVA 148
8.5 Estimating heterogeneous regression ANCOVA effects 150
8.6 Regression GLMs for heterogeneous ANCOVA 154
8.7 Covariate experimental condition relations 157
8.7.1 Multicollinearity 158
8.8 Other alternatives 161
8.8.1 Stratification (blocking) 161
8.8.2 Replacing the experimental conditions with the covariate 162
8.9 The role of ANCOVA 162
9 FURTHER ISSUES IN ANOVA AND ANCOVA
9.1 Power 164
9.1.1 Optimal experimental designs 165
9.1.2 Normality violations 166
9.1.3 Main effects and interactions 167
9.2 Error rate and the omnibus F tests 168
9.3 Error rate and multiple comparisons 169
9.4 The role of the omnibus Rest 171
REFERENCES 173
INDEX 179
|
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| author | Rutherford, Andrew 1958- |
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| author_facet | Rutherford, Andrew 1958- |
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| dewey-full | 519.53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.53 |
| dewey-search | 519.53 |
| dewey-sort | 3519.53 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV014345064 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:01:58Z |
| institution | BVB |
| isbn | 0761951601 076195161X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009837241 |
| oclc_num | 44185265 |
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| owner | DE-29 DE-11 DE-188 |
| owner_facet | DE-29 DE-11 DE-188 |
| physical | IX, 182 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | SAGE Publ. |
| record_format | marc |
| series2 | ISM Introducing statistical methods |
| spelling | Rutherford, Andrew 1958- Verfasser (DE-588)1017602883 aut Introducing anova and ancova a GLM approach Andrew Rutherford 1. publ. London [u.a.] SAGE Publ. 2001 IX, 182 S. txt rdacontent n rdamedia nc rdacarrier ISM Introducing statistical methods Analysis of covariance Analysis of variance HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009837241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rutherford, Andrew 1958- Introducing anova and ancova a GLM approach Analysis of covariance Analysis of variance |
| title | Introducing anova and ancova a GLM approach |
| title_auth | Introducing anova and ancova a GLM approach |
| title_exact_search | Introducing anova and ancova a GLM approach |
| title_full | Introducing anova and ancova a GLM approach Andrew Rutherford |
| title_fullStr | Introducing anova and ancova a GLM approach Andrew Rutherford |
| title_full_unstemmed | Introducing anova and ancova a GLM approach Andrew Rutherford |
| title_short | Introducing anova and ancova |
| title_sort | introducing anova and ancova a glm approach |
| title_sub | a GLM approach |
| topic | Analysis of covariance Analysis of variance |
| topic_facet | Analysis of covariance Analysis of variance |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009837241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rutherfordandrew introducinganovaandancovaaglmapproach |