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