This course covers the design of experiments using General Linear Models. The learning outcomes include understanding necessary and sufficient conditions for estimability, estimating error variance, developing ANOVA models, partitioning sum of squares, conducting F tests, working with contrasts, and using R software for analysis. The course teaches skills such as model development, parameter estimation, orthogonal contrasts, and deriving least squares estimates. The teaching method involves theoretical explanations, examples, derivations, and software illustrations. The intended audience for this course includes statisticians, data analysts, researchers, and anyone interested in experimental design and analysis.
General Linear Models - Design of Experiments
Overview
Syllabus
Design of Experiments: Models Introduction.
Design of Experiments: Projection Matrix onto c(X).
Design of Experiments: Projection Matrix onto c(X) Example.
Design of Experiments: Least Square Estimator of Beta.
Estimability (part 1/4): Necessary and Sufficient Conditions.
Estimability (part 2/4): Unique Unbiased Estimator.
Estimability (part 3/4): Gauss Markov Theorem.
Estimability (part 4/4): Generating Estimable Functions.
Design of Experiments: Estimating the Error Variance.
1-way fixed-effects ANOVA (part 1/10): Model Development.
1-way fixed-effects ANOVA (part 1/10): (Example) Model Development.
1-way fixed-effects ANOVA (part 2/10): Estimating Parameters.
1-way fixed-effects ANOVA (part 2/10): (Example) Estimating Parameters.
1-way fixed-effects ANOVA (part 3/10): Partitioning the Sum of Squares.
1-way fixed-effects ANOVA (part 3/10): (Example) Partitioning the Sum of Squares.
1-way fixed-effects ANOVA (part 4/10): Sum of Squares Derivations.
1-way fixed-effects ANOVA (part 4/10): (Example) Sum of Squares Derivations.
1-way fixed-effects ANOVA (part 5/10): F Test and C.I.'s.
1-way fixed-effects ANOVA (part 5/10): (Example) F Test and C.I.'s.
1-way fixed-effects ANOVA (part 6/10): Unbalanced Case.
1-way fixed-effects ANOVA (part 7/10): Contrasts.
1-way fixed-effects ANOVA (part 7/10): (Example) Contrasts.
1-way fixed-effects ANOVA (part 8/10): Contrasts with Normal Assumptions.
1-way fixed-effects ANOVA (part 8/10): (Example) Contrasts with Normal Assumptions.
1-way fixed-effects ANOVA (part 9/10): Orthogonal Contrasts.
1-way fixed-effects ANOVA (part 9/10): (Example) Orthogonal Contrasts.
1-way fixed-effects ANOVA (part 10/10): Partitioning SS(trt).
1-way fixed-effects ANOVA (part 10/10): (Example) Partitioning SS(trt).
1-way fixed-effects ANOVA (part 11/10): Residuals.
1-way fixed-effects ANOVA (part 11/10): (Example) Residuals.
1-way Random-Effects ANOVA(part 1/6): Model Development.
1-way Random-Effects ANOVA(part 2/6): Distributional Properties of SS.
1-way Random-Effects ANOVA(part 3/6): Another Proof for the Distribution for SS(trt).
1-way Random-Effects ANOVA(part 4/6): Variance Components Estimation.
1-way Random-Effects ANOVA(part 5/6): F Test & C I's.
1-way Random-Effects ANOVA(part 6/6): R Software.
Repeated Measures 1-way fixed effects ANOVA (part 1/7): Model Development.
Repeated Measures 1-way fixed effects ANOVA (part 2/7): Perpendicular Projection Matrices.
Repeated Measures 1-way fixed effects ANOVA (part 3/7): Column Space of the Design Matrix.
Repeated Measures 1-way fixed effects ANOVA (part 4/7): Partitioning the Sum of Squares.
Repeated Measures 1-way fixed effects ANOVA (part 5/7): Distributional Properties of the SS..
Repeated Measures 1-way fixed effects ANOVA (part 6/7): Contrasts.
Repeated Measures 1-way fixed effects ANOVA (part 7/7): R Software Illustrating Parts 1-6.
Randomized Complete Blocks ANOVA (part 1/6): Model Development.
Randomized Complete Blocks ANOVA (part 2/6): Projection Matrices and Column Spaces.
Randomized Complete Blocks ANOVA (part 3/6): Sum of Squares and F-Test.
Randomized Complete Blocks ANOVA (part 4/6): Estimability and Treatment Contrasts.
Randomized Complete Blocks ANOVA (part 5/6): Random Treatment Effects.
Randomized Complete Blocks ANOVA (part 6/6): R Software Illustration.
The Regression Approach to ANOVA (part 1/4): Partial F Test.
The Regression Approach to ANOVA (part 2/4): Type I, II, III, IV Sum of Squares.
The Regression Approach to ANOVA (part 3/4): Balanced Designs.
The Regression Approach to ANOVA (part 4/4): R Software Illustration.
Balanced Incomplete Block Design (part 0/8): Rough Draft.
Balanced Incomplete Block Design (part 1/8): Model Development.
Balanced Incomplete Block Design (part 2/8): Column Spaces of the Design Matrix.
Balanced Incomplete Block Design (part 3/8): Deriving the Least Squares Estimates.
Balanced Incomplete Block Design (part 4/8): Sum of Squares Error and Partial F Test.
Balanced Incomplete Block Design (part 5/8): Notation and Properties for Upcoming Contrast Videos.
Balanced Incomplete Block Design (part 6/8): Estimability and Treatment Contrasts.
Balanced Incomplete Block Design (part 7/8): Partitioning SS(trt) with Orthogonal Contrasts.
Balanced Incomplete Block Design (part 8/8): R Software Illustration.
Analysis of Covariance (part 1/9): Model Development.
Analysis of Covariance (part 2/9): Column Spaces of the Design Matrix.
Analysis of Covariance (part 3/9): Deriving the Least Squares Estimates.
Analysis of Covariance (part 4/9): Sum of Squared Error and Partial F Tests.
Analysis of Covariance (part 5/9): Estimability and Treatment Contrasts.
Analysis of Covariance (part 6/9): Balanced 1-way fixed-effects ANOVA with 1 Covariate.
Analysis of Covariance (part 7/9): Balanced Randomized Complete Block Design ANOVA with 1 Covariate.
Analysis of Covariance (part 8/9): 1-way fixed-effects ANOVA w/ 1covariate.
Analysis of Covariance (part 9/9): 2 Factor ANOVA w/ 2 covariate (NoInteraction).
Balanced 2 Factor Factorial Design without Interaction (part 1/7): Model Development.
Balance 2 Factor Factorial Design without Interaction (part 2/7):Column Spaces of the Design Matrix.
Balanced 2 Factor Factorial Design without Interaction (part 3/7): Partitioning the SS.
Balanced 2 Factor Factorial Design without Interaction (part 4/7): Distribution of Sum of Squares.
Balanced 2 Factor Factorial Design without Interaction (part 5/7): F Tests for Factor Effects.
Balanced 2 Factor Factorial Design without Interaction (part 6/7): Contrasts.
Balanced 2 Factor Factorial Design without Interaction (part 7/7): R Software Illustration.
Balanced 2 Factor Factorial Design with Interaction (part 1/8): Model Development.
Balanced 2 Factor Factorial Design with Interaction (part 2/8): Column Spaces of the Design Matrix.
Balanced 2 Factor Factorial Design with Interaction (part 3/8): Partitioning the SS.
Balanced 2 Factor Factorial Design with Interaction (part 4/8): Distribution of SS and F Tests.
Balanced 2 Factor Factorial Design with Interaction (part 5/8): Contrasts.
Balanced 2 Factor Factorial Design with Interaction (part 6/8): Random Effects Model.
Balanced 2 Factor Factorial Design with Interaction (part 7/8): Random Effects Model F Tests.
Balanced 2 Factor Factorial Design with Interaction (part 8/8): R Software Illustration.
Hierarchical Designs (part 1/11): Model Development.
Hierarchical Designs (part 2/11): Columns Spaces of the Design Matrix.
Hierarchical Designs (part 3/11): Partitioning the SS.
Hierarchical Designs (part 4/11): Distribution of SS and F Tests.
Hierarchical Designs (part 5/11): Contrasts.
Hierarchical Designs (part 6/11): Random Effects.
Hierarchical Designs (part 7/11): Variance Components Estimation.
Hierarchical Designs (part 8/11): 3 Stage Nested.
Hierarchical Designs (part 9/11): Nested and Crossed.
Hierarchical Designs (part 10/11): R Illustration of 2-Stage Nested Design.
Hierarchical Designs (part 11/11): R Illustration of a Nested and Crossed Design.
Split Plot Design (part1/10): Model Development.
Split Plot Design (part 2/10): Design Matrix.
Split Plot Design (part 3/10): Perpendicular Projection Matrices.
Split Plot Design (part 4/10): Column Spaces of the Design Matrix.
Split Plot Design (part 5/10): Best Linear Unbiased Estimate.
Split Plot Design (part 6/10): Partitioning the Total SS.
Split Plot Design (part 7/10): Expected SS.
Split Plot Design (part 8/10): Distribution of SS.
Split Plot Design (part 9/10): F Tests.
Split Plot Design (part 10/10): R Illustration / Example.
Taught by
statisticsmatt
