GLM UNIVARIATE, ANOVA, ANCOVA
Overview
Univariate GLM is the general linear model now often used to implement such long-established statistical procedures as regression and members of the anova family. It is "general" in the sense that one may implement both regression and anova models. One may also have fixed factors, random factors, and covariates as predictors. Also, in GLM one may have multiple dependent variables, as discussed in a separate section on multivariate GLM and one may have linear transformations and/or linear combinations of dependent variables. Moreover, one can apply multivariate tests of significance when modeling correlated dependent variables, not relying on individual univariate tests as in multiple regression. GLM also handles repeated measures designs. Finally, because GLM uses a generalized inverse of the matrix of independent variables' correlations with each other, it can handle redundant independents which would prevent solution in ordinary regression models.
The full content is now available from Statistical Associates Publishers. http://www.statisticalassociates.com
Below is the unformatted table of contents.
GLM UNIVARIATE
Table of Contents
Overview 4
Key Concepts 8
Why testing means is related to variance in analysis of variance 8
One-way anova 9
Simple one-way anova in SPSS 9
Simple one-way anova in SAS 13
Two-way anova 16
Two-way anova in SPSS 17
Two-way anova in SAS 20
Multivariate or n-way anova 22
Regression models 22
Parameter estimates (b coefficients) for factor levels 24
Parameter estimates for dichotomies 25
Significance of parameter estimates 25
Research designs 25
Between-groups anova design 25
Completely randomized design 27
Full factorial anova 27
Balanced designs 28
Latin square designs 29
Graeco-Latin square designs 30
Randomized Complete Block Design (RCBD anova) 30
Split plot designs 32
Mixed design models 32
Random v. fixed effects models 34
In SPSS 34
In SAS 35
Linear mixed models (LMM) vs. general linear models (GLM) 36
Effects 36
Treating a random factor as a fixed factor 36
Mixed effects models 37
Nested designs 37
Nested designs 38
In SPSS 39
In SAS 42
Treatment by replication design 42
Within-groups (repeated measures) anova designs 42
Counterbalancing 43
Reliability procedure 44
Repeated measures GLM in SPSS 44
Repeated measures GLM in SAS 44
Interpreting repeated measures output 45
Variables 46
Types of variables 46
Dependent variable 46
Fixed and random factors 47
Covariates 47
WLS weights 47
Models and types of effects 48
Full factorial models 48
Effects 49
Main effects 49
Interaction effects 49
Residual effects 52
Effect size measures 53
Effect size coefficients based on percent of variance explained 53
Partial eta-squared 53
Omega-squared 54
Herzberg's R2 55
Intraclass correlation 55
Effect size coefficients based on standardized mean differences 55
Cohen's d 55
Glass's delta 57
Hedge's g 58
Significance tests 58
F-test 58
Reading the F value 58
Example 1 59
Example 2 59
Significance in two-way anova 60
Computation of F 60
F-test assumptions 60
Adjusted means 61
Lack of fit test 61
Power level and noncentrality parameter 62
Hotelling's T-Square 63
Planned multiple comparison t-tests 63
Simple t-test difference of means 65
Bonferroni-adjusted t-test 65
Sidak test 67
Dunnett's test 67
HSU's multiple comparison with the best (MCB) test 67
Post-hoc multiple comparison tests 67
The q-statistic 68
Output formats: pairwise vs. multiple range 69
Tests assuming equal variances 69
Least significant difference (LSD) test 69
The Fisher-Hayter test 70
Tukey's test, a.k.a. Tukey honestly significant difference (HSD) test 71
Tukey-b test, a.k.a. Tukey's wholly significant difference (WSD) test 72
S-N-K or Student-Newman-Keuls test 73
Duncan test 74
Ryan test (REGWQ) 74
The Shaffer-Ryan test 76
The Scheffé test 76
Hochberg GT2 test 78
Gabriel test 80
Waller-Duncan test 80
Tests not assuming equal variances 80
Tamhane's T2 test 80
and 80 more pages of GLM Univariate topics
Overview
Univariate GLM is the general linear model now often used to implement such long-established statistical procedures as regression and members of the anova family. It is "general" in the sense that one may implement both regression and anova models. One may also have fixed factors, random factors, and covariates as predictors. Also, in GLM one may have multiple dependent variables, as discussed in a separate section on multivariate GLM and one may have linear transformations and/or linear combinations of dependent variables. Moreover, one can apply multivariate tests of significance when modeling correlated dependent variables, not relying on individual univariate tests as in multiple regression. GLM also handles repeated measures designs. Finally, because GLM uses a generalized inverse of the matrix of independent variables' correlations with each other, it can handle redundant independents which would prevent solution in ordinary regression models.
The full content is now available from Statistical Associates Publishers. http://www.statisticalassociates.com
Below is the unformatted table of contents.
GLM UNIVARIATE
Table of Contents
Overview 4
Key Concepts 8
Why testing means is related to variance in analysis of variance 8
One-way anova 9
Simple one-way anova in SPSS 9
Simple one-way anova in SAS 13
Two-way anova 16
Two-way anova in SPSS 17
Two-way anova in SAS 20
Multivariate or n-way anova 22
Regression models 22
Parameter estimates (b coefficients) for factor levels 24
Parameter estimates for dichotomies 25
Significance of parameter estimates 25
Research designs 25
Between-groups anova design 25
Completely randomized design 27
Full factorial anova 27
Balanced designs 28
Latin square designs 29
Graeco-Latin square designs 30
Randomized Complete Block Design (RCBD anova) 30
Split plot designs 32
Mixed design models 32
Random v. fixed effects models 34
In SPSS 34
In SAS 35
Linear mixed models (LMM) vs. general linear models (GLM) 36
Effects 36
Treating a random factor as a fixed factor 36
Mixed effects models 37
Nested designs 37
Nested designs 38
In SPSS 39
In SAS 42
Treatment by replication design 42
Within-groups (repeated measures) anova designs 42
Counterbalancing 43
Reliability procedure 44
Repeated measures GLM in SPSS 44
Repeated measures GLM in SAS 44
Interpreting repeated measures output 45
Variables 46
Types of variables 46
Dependent variable 46
Fixed and random factors 47
Covariates 47
WLS weights 47
Models and types of effects 48
Full factorial models 48
Effects 49
Main effects 49
Interaction effects 49
Residual effects 52
Effect size measures 53
Effect size coefficients based on percent of variance explained 53
Partial eta-squared 53
Omega-squared 54
Herzberg's R2 55
Intraclass correlation 55
Effect size coefficients based on standardized mean differences 55
Cohen's d 55
Glass's delta 57
Hedge's g 58
Significance tests 58
F-test 58
Reading the F value 58
Example 1 59
Example 2 59
Significance in two-way anova 60
Computation of F 60
F-test assumptions 60
Adjusted means 61
Lack of fit test 61
Power level and noncentrality parameter 62
Hotelling's T-Square 63
Planned multiple comparison t-tests 63
Simple t-test difference of means 65
Bonferroni-adjusted t-test 65
Sidak test 67
Dunnett's test 67
HSU's multiple comparison with the best (MCB) test 67
Post-hoc multiple comparison tests 67
The q-statistic 68
Output formats: pairwise vs. multiple range 69
Tests assuming equal variances 69
Least significant difference (LSD) test 69
The Fisher-Hayter test 70
Tukey's test, a.k.a. Tukey honestly significant difference (HSD) test 71
Tukey-b test, a.k.a. Tukey's wholly significant difference (WSD) test 72
S-N-K or Student-Newman-Keuls test 73
Duncan test 74
Ryan test (REGWQ) 74
The Shaffer-Ryan test 76
The Scheffé test 76
Hochberg GT2 test 78
Gabriel test 80
Waller-Duncan test 80
Tests not assuming equal variances 80
Tamhane's T2 test 80
and 80 more pages of GLM Univariate topics
