Final Outline

Topics outline

General Linear Model (GLM)
 

Common to all

Matrix form of the model, meaning of the parts

Design (variables and coefficients) vs. noise

Assumptions

Underlying Normal distribution - what is normally distributed? Mean = ? Variance = ?

Estimation - what is estimated? Using what method?

General matrix solution for the normal equations. What are they?

Plots: visualize the data, assess normality, assess homoscedasticity

 

Regression

Models

Simple Linear Regression (SLR)

Multiple Regression

Designs with replicates

Pure error and Tests of Fit

SLR - Simple Linear Regression

Model

Parameters, parameter estimation formulas

Predicted Ys, residuals

Hypotheses

t-tests for β₀, β₁

Test of Regression

Pure error and Test of Fit

Coefficient of Determination

Multiple Regression

Various models

Tests of individual βs

Test of "Regression"

Pure error and Test of Fit

Coefficient of Determination

 

Analysis of Variance (ANOVA)

Designs

Completely randomized single-factor design (CR-SF)

Randomized complete-block single-factor design (RCB-SF) (Example was one blocking factor, one treatment factor)

Randomized block incomplete factorial (RB-IF) (Example was the Latin Square design with 2 blocking factors, one treatment factor.)

CR-CF 2-way and 3-way designs

Randomized complete block design (one blocking factor, two treatment factors)

2^k complete and n > 1 (replicated design)

2^k complete and n = 1 (non-replicated design)

2^k incomplete, n > 1 or n = 1

ANOVA topics:

The statistical model (GLM)

Means coding, effects coding

Estimation, what is estimated

Purposes of DOE

Elimination of systematic bias

Increasing statistical precision

Hypotheses

Hypotheses in means coding: matrices/vectors and the Kronecker product, later the 2^k trick

Hypotheses in effects coding: when are interactions assumed = 0?

Comparisons other than the major effects

Single-df contrasts/comparisons

Multiple comparisons

Experimentwise error and methods to deal with it

Bonferroni

Tukey

Dunnett

Calculating SSsand dfs, then MS and F

Why the F test, which compares variances, tests means/effects

"G" (replicated) vs. "S" (non-replicated) designs, and the consequences

"G" designs

Residual = score - group mean

SS_E = sum of squared residuals (or other SS formula)

"S" designs

Special formula for residuals, or no formula

Assume certain interactions = 0

"Pool" SS and df; then SS_E = SS_T - SS_{all included effects}

Incomplete 2^k designs

Patterns of confounding

Orthogonal contrasts

Completely confounded contrasts

Partially confounded contrasts

Reducing the number of observations without reducing the number of factors, in a principled way that produces favorable patterns of confounding. Use of the generating function to choose cells to eliminate and to predict confounds.

Introducing blocking factors without raising the number of observations, in a principled way that produces favorable patterns of confounding. Use of the generating function to predict confounds and to form the blocks.

Useful plots

Plotting the means of groups

Sorted residuals vs. Normal quantiles: assess normality

Residuals vs. group membership or group means: assess equality of variance

In 2^k designs, Effect size vs. Normal quantiles: determine which effects are likely = 0, with their variance reflecting only noise, and so are candidates for pooling into the error term

 

Statistical control charts

X-bar chart

R chart

Class Home