Linear Models and Analysis of Variance:

CONCEPTS, MODELS, AND APPLICATIONS

 

Volume II

 

 

 

 

 

First Edition

 

 

 

 

 

 

 

 

David W. Stockburger

 

Southwest Missouri State University

 

 

 

 

 

 

@Copyright 1993


 

                                           TABLE OF CONTENTS

 

Title                                                                                            Page

EXPERIMENTAL DESIGNS.............................................................................. 132

Notation.................................................................................................... 133

Kinds of Factors........................................................................................ 134

Treatment...................................................................................... 134

Group Factors............................................................................... 135

Trials Factors................................................................................ 135

Blocking........................................................................................ 135

Unit Factors.................................................................................. 137

Error Factors................................................................................. 137

Fixed and Random Factors........................................................................ 137

Fixed Factors................................................................................ 137

Random Factors............................................................................ 138

Relationships Between Factors................................................................... 139

Crossed........................................................................................ 139

Nested.......................................................................................... 140

An Example Design................................................................................... 142

A Second Example Design......................................................................... 144

A Third Example Design............................................................................ 146

Determining the Number of Subjects and Measures per Subject................. 148

Setting up the Data Matrix......................................................................... 148

A Note of Caution..................................................................................... 149

 

One Between Group ANOVA.............................................................................. 150

Why Multiple Comparisons Using t-tests is NOT the Analysis of Choice..... 150

The Bottom Line - Results and Interpretation of ANOVA.......................... 151

HYPOTHESIS TESTING THEORY UNDERLYING ANOVA.............. 153

The Sampling Distribution Reviewed.............................................. 153

Two Ways of Estimating the Population Parameter σX²................... 154

The F-ratio and F-distribution.................................................................... 157

Non-significant and Significant F-ratios....................................................... 159

Similarity of ANOVA and t-test................................................................. 162

EXAMPLE OF A NON-SIGNIFICANT ONE-WAY ANOVA.............. 164

EXAMPLE OF A SIGNIFICANT ONE-WAY ANOVA........................ 164

USING MANOVA.................................................................................. 164

The Data....................................................................................... 165

Example Output............................................................................. 166

Dot Notation............................................................................................. 168

POST-HOC Tests of Significance