ANOVA and ANCOVA : a GLM approach / Andrew Rutherford
- Author
- Rutherford, Andrew, 1958-
- Published
- Hoboken, N.J. : Wiley, [2011]
- Copyright Date
- ©2011
- Edition
- 2nd ed.
- Physical Description
- xiii, 344 pages : illustrations ; 25 cm
- Contents
- Machine generated contents note: 1.1.Regression, Analysis of Variance, and Analysis of Covariance -- 1.2.A Pocket History of Regression, ANOVA, and ANCOVA -- 1.3.An Outline of General Linear Models (GLMs) -- 1.3.1.Regression -- 1.3.2.Analysis of Variance -- 1.3.3.Analysis of Covariance -- 1.4.The "General" in GLM -- 1.5.The "Linear" in GLM -- 1.6.Least Squares Estimates -- 1.7.Fixed, Random, and Mixed Effects Analyses -- 1.8.The Benefits of a GLM Approach to ANOVA and ANCOVA -- 1.9.The GLM Presentation -- 1.10.Statistical Packages for Computers -- 2.1.Independent Measures Designs -- 2.2.Balanced Data Designs -- 2.3.Factors and Independent Variables -- 2.4.An Outline of Traditional ANOVA for Single Factor Designs -- 2.5.Variance -- 2.6.Traditional ANOVA Calculations for Single Factor Designs -- 2.7.Confidence Intervals -- 2.8.GLM Approaches to Single Factor ANOVA -- 2.8.1.Experimental Design GLMs -- 2.8.2.Estimating Effects by Comparing Full and Reduced Experimental Design GLMs -- 2.8.3.Regression GLMs -- 2.8.4.Schemes for Coding Experimental Conditions -- 2.8.4.1.Dummy Coding -- 2.8.4.2.Why Only (p - 1) Variables Are Used to Represent All Experimental Conditions? -- 2.8.4.3.Effect Coding -- 2.8.5.Coding Scheme Solutions to the Overparameterization Problem -- 2.8.6.Cell Mean GLMs -- 2.8.7.Experimental Design Regression and Cell Mean GLMs -- 3.1.Introduction -- 3.2.Comparisons Between Experimental Condition Means -- 3.3.Linear Contrasts -- 3.4.Comparison Sum of Squares -- 3.5.Orthogonal Contrasts -- 3.6.Testing Multiple Hypotheses -- 3.6.1.Type 1 and Type 2 Errors -- 3.6.2.Type 1 Error Rate Inflation with Multiple Hypothesis Testing -- 3.6.3.Type 1 Error Rate Control and Analysis Power -- 3.6.4.Different Conceptions of Type 1 Error Rate -- 3.6.4.1.Testwise Type 1 Error Rate -- 3.6.4.2.Familywise Type 1 Error Rate -- 3.6.4.3.Experimentwise Type 1 Error Rate -- 3.6.4.4.False Discovery Rate -- 3.6.5.Identifying the "Family" in Familywise Type 1 Error Rate Control -- 3.6.6.Logical and Empirical Relations -- 3.6.6.1.Logical Relations -- 3.6.6.2.Empirical Relations -- 3.7.Planned and Unplanned Comparisons -- 3.7.1.Direct Assessment of Planned Comparisons -- 3.7.2.Contradictory Results with ANOVA Omnibus F-tests and Direct Planned Comparisons -- 3.8.A Basic Data Analysis Strategy -- 3.8.1.ANOVA First? -- 3.8.2.Strong and Weak Type 1 Error Control -- 3.8.3.Stepwise Tests -- 3.8.4.Test Power -- 3.9.The Three Basic Stages of Data Analysis -- 3.9.1.Stage 1 -- 3.9.2.Stage 2 -- 3.9.2.1.Rom's Test -- 3.9.2.2.Shaffer's R Test -- 3.9.2.3.Applying Shaffer's R Test After a Significant F-test -- 3.9.3.Stage 3 -- 3.10.The Role of the Omnibus F-Test -- 4.1.Introduction -- 4.2.Effect Size as a Standardized Mean Difference -- 4.3.Effect Size as Strength of Association (SOA) -- 4.3.1.SOA for Specific Comparisons -- 4.4.Small, Medium, and Large Effect Sizes -- 4.5.Effect Size in Related Measures Designs -- 4.6.Overview of Standardized Mean Difference and SOA Measures of Effect Size -- 4.7.Power -- 4.7.1.Influences on Power -- 4.7.2.Uses of Power Analysis -- 4.7.3.Determining the Sample Size Needed to Detect the Omnibus Effect -- 4.7.4.Determining the Sample Size Needed to Detect Specific Effects -- 4.7.5.Determining the Power Level of a Planned or Completed Study -- 4.7.6.The Fallacy of Observed Power -- 5.1.Factorial Designs -- 5.2.Factor Main Effects and Factor Interactions -- 5.2.1.Estimating Effects by Comparing Full and Reduced Experimental Design GLMs -- 5.3.Regression GLMs for Factorial ANOVA -- 5.4.Estimating Effects with Incremental Analysis -- 5.4.1.Incremental Regression Analysis -- 5.4.1.1.Step 1 -- 5.4.1.2.Step 2 -- 5.4.1.3.Step 3 -- 5.5.Effect Size Estimation -- 5.5.1.SOA for Omnibus Main and Interaction Effects -- 5.5.1.1.Complete ω2 for Main and Interaction Effects -- 5.5.1.2.Partial ω2 for Main and Interaction Effects -- 5.5.2.Partial ω2 for Specific Comparisons -- 5.6.Further Analyses -- 5.6.1.Main Effects: Encoding Instructions and Study Time -- 5.6.2.Interaction Effect: Encoding Instructions x Study Time -- 5.6.2.1.Simple Effects: Comparing the Three Levels of Factor B at a1, and at a2 -- 5.6.2.2.Simple Effects: Comparing the Two Levels of Factor A at b1, at b2, and at b3 -- 5.7.Power -- 5.7.1.Determining the Sample Size Needed to Detect Omnibus Main Effects and Interactions -- 5.7.2.Determining the Sample Size Needed to Detect Specific Effects -- 6.1.Introduction -- 6.1.1.Randomized Block Designs -- 6.1.2.Matched Sample Designs -- 6.1.3.Repeated Measures Designs -- 6.2.Order Effect Controls in Repeated Measures Designs -- 6.2.1.Randomization -- 6.2.2.Counterbalancing -- 6.2.2.1.Crossover Designs -- 6.2.2.2.Latin Square Designs -- 6.3.The GLM Approach to Single Factor Repeated Measures Designs -- 6.4.Estimating Effects by Comparing Full and Reduced Repeated Measures Design GLMs -- 6.5.Regression GLMs for Single Factor Repeated Measures Designs -- 6.6.Effect Size Estimation -- 6.6.1.A Complete ω2 SOA for the Omnibus Effect Comparable Across Repeated and Independent Measures Designs -- 6.6.2.A Partial ω2 SOA for the Omnibus Effect Appropriate for Repeated Measures Designs -- 6.6.3.A Partial ω2 SOA for Specific Comparisons Appropriate for Repeated Measures Designs -- 6.7.Further Analyses -- 6.8.Power -- 6.8.1.Determining the Sample Size Needed to Detect the Omnibus Effect -- 6.8.2.Determining the Sample Size Needed to Detect Specific Effects -- 7.1.Factorial Related and Repeated Measures Designs -- 7.2.Fully Repeated Measures Factorial Designs -- 7.3.Estimating Effects by Comparing Full and Reduced Experimental Design GLMs -- 7.4.Regression GLMs for the Fully Repeated Measures Factorial ANOVA -- 7.5.Effect Size Estimation -- 7.5.1.A Complete ω2 SOA for Main and Interaction Omnibus Effects Comparable Across Repeated Measures and Independent Designs -- 7.5.2.A Partial ω2 SOA for the Main and Interaction Omnibus Effects Appropriate for Repeated Measures Designs -- 7.5.3.A Partial ω2 SOA for Specific Comparisons Appropriate for Repeated Measures Designs -- 7.6.Further Analyses -- 7.6.1.Main Effects: Encoding Instructions and Study Time -- 7.6.2.Interaction Effect: Encoding Instructions x Study Time -- 7.6.2.1.Simple Effects: Comparison of Differences Between the Three Levels of Factor B (Study Time) at Each Level of Factor A (Encoding Instructions) -- 7.6.2.2.Simple Effects: Comparison of Differences Between the Two Levels of Factor A (Encoding Instructions) at Each Level of Factor B (Study Time) -- 7.7.Power -- 8.1.Mixed Measures and Split-Plot Designs -- 8.2.Factorial Mixed Measures Designs -- 8.3.Estimating Effects by Comparing Full and Reduced Experimental Design GLMs -- 8.4.Regression GLM for the Two-Factor Mixed Measures ANOVA -- 8.5.Effect Size Estimation -- 8.6.Further Analyses -- 8.6.1.Main Effects: Independent Factor-Encoding Instructions -- 8.6.2.Main Effects: Related Factor-Study Time -- 8.6.3.Interaction Effect: Encoding Instructions x Study Time -- 8.6.3.1.Simple Effects: Comparing Differences Between the Three Levels of Factor B (Study Time) at Each Level of Factor A (Encoding Instructions) -- 8.6.3.2.Simple Effects: Comparing Differences Between the Two Levels of Factor A (Encoding Instructions) at Each Level of Factor B (Study Time) -- 8.7.Power -- 9.1.The Nature of ANCOVA -- 9.2.Single Factor Independent Measures ANCOVA Designs -- 9.3.Estimating Effects by Comparing Full and Reduced ANCOVA GLMs -- 9.4.Regression GLMs for the Single Factor, Single-Covariate ANCOVA -- 9.5.Further Analyses -- 9.6.Effect Size Estimation -- 9.6.1.A Partial ω2 SOA for the Omnibus Effect -- 9.6.2.A Partial *omega;2 SOA for Specific Comparisons -- 9.7.Power -- 9.8.Other ANCOVA Designs -- 9.8.1.Single Factor and Fully Repeated Measures Factorial ANCOVA Designs -- 9.8.2.Mixed Measures Factorial ANCOVA -- 10.1.Introduction 23. -- 10.2.ANOVA and GLM Assumptions -- 10.2.1.Independent Measures Designs -- 10.2.2.Related Measures -- 10.2.2.1.Assessing and Dealing with Sphericity Violations -- 10.2.3.Traditional ANCOVA -- 10.3.A Strategy for Checking GLM and Traditional ANCOVA Assumptions -- 10.4.Assumption Checks and Some Assumption Violation Consequences -- 10.4.1.Independent Measures ANOVA and ANCOVA Designs -- 10.4.1.1.Random Sampling -- 10.4.1.2.Independence -- 10.4.1.3.Normality -- 10.4.1.4.Homoscedasticity: Homogeneity of Variance -- 10.4.2.Traditional ANCOVA Designs -- 10.4.2.1.Covariate Independent of Experimental Conditions -- 10.4.2.2.Linear Regression -- 10.4.2.3.Homogeneous Regression -- 10.5.Should Assumptions be Checked? -- 11.1.Alternatives to Traditional ANCOVA -- 11.2.The Heterogeneous Regression Problem -- 11.3.The Heterogeneous Regression ANCOVA GLM -- 11.4.Single Factor Independent Measures Heterogeneous Regression ANCOVA -- 11.5.Estimating Heterogeneous Regression ANCOVA Effects -- 11.6.Regression GLMs for Heterogeneous Regression ANCOVA -- 11.7.Covariate-Experimental Condition Relations -- 11.7.1.Adjustments Based on the General Covariate Mean -- 11.7.2.Multicolinearity -- 11.8.Other Alternatives -- 11.8.1.Stratification (Blocking) -- 11.8.2.Replacing the Experimental Conditions with the Covariate -- 11.9.The Role of Heterogeneous Regression ANCOVA -- 12.1.Introduction -- 12.2.Review of the Single Factor Repeated Measures Experimental Design GLM and ANOVA -- 12.3.The Multilevel Approach to the Single Factor Repeated Measures Experimental Design -- 12.4.Parameter Estimation in Multilevel Analysis -- 12.5.Applying Multilevel Models with Different Covariance Structures -- 12.5.1.Using SYSTAT to Apply the Multilevel GLM of the Repeated Measures Experimental Design GLM -- 12.5.1.1.The Linear Mixed Model -- 12.5.1.2.The Hierarchical Linear Mixed Model -- 12.5.2.Applying Alternative Multilevel GLMs to the Repeated Measures Data -- 12.6.Empirically Assessing Different Multilevel Models.
- Subject(s)
- ISBN
- 9780470385555 (cloth)
0470385553 (cloth) - Bibliography Note
- Includes bibliographical references and index.
View MARC record | catkey: 7541762