Confidence Intervals on Variance Components Book

	Preface
1	Introduction	1
1.1	Background	1
1.2	Scope of Book	7
2	General Concepts	9
2.1	Introduction	9
2.2	Variance Component Models	9
2.3	Point Estimation, Confidence Intervals, and Tests of Hypotheses	13
2.4	Simultaneous Confidence Intervals	18
2.5	Notation and Use of Tables	20
2.6	Confidence Intervals on the Variance of a Normal Population	25
2.7	Confidence Intervals on the Ratio of Variances From Two Normal Populations	26
2.8	Summary	27
3	General Results for Balanced Designs	28
3.1	Introduction	28
3.2	Intervals on Sums of Expected Mean Squares	29
3.3	Confidence Intervals on Linear Combinations of Expected Mean Squares with Different Signs	36
3.4	Confidence Intervals on Ratios of Expected Mean Squares	43
3.5	Simultaneous Confidence Intervals	51
3.6	Summary	57
4	The One-Fold Nested Design	58
4.1	Introduction	58
4.2	The Balanced One-Fold Random Model	60
4.3	The Unbalanced One-Fold Model	68
4.4	Summary	77
5	The Two-Fold and (Q-1)-Fold Nested Designs	78
5.1	Introduction	78
5.2	The Balanced Two-Fold Nested Random Model	79
5.3	Balanced (Q-1)-Fold Nested Random Models	91
5.4	The Unbalanced Two-Fold Nested Random Model	96
5.5	Unbalanced (Q-1)-Fold Nested Designs	109
5.6	Summary	116
6	Crossed Random Designs	117
6.1	Introduction	117
6.2	The Balanced Two-Factor Crossed Random Model with Interaction	118
6.3	The Balanced Two-Factor Crossed Random Model without Interaction	126
6.4	The Balanced Three-Factor Crossed Random Model with Interaction	131
6.5	Unbalanced Two-Factor Crossed Random Models with Interaction	136
6.6	Unbalanced Two-Factor Crossed Random Models without Interaction	142
6.7	Balanced Incomplete Block Random Models	145
6.8	Summary	149
7	Mixed Models	150
7.1	Introduction	150
7.2	Balanced Two-Factor Crossed Mixed Models	151
7.3	A Balanced Three-Factor Crossed Mixed Model with Interaction	156
7.4	Balanced Nested Mixed Models	160
7.5	Balanced Mixed Models with Both Crossed and Nested Effects: A Split-Plot Design	163
7.6	Regression Models with Nested Error Structure	167
7.7	Unbalanced Mixed Models	170
7.8	Summary	173
	Appendix A: F-Tables	175
	Appendix B: Wald's Confidence Interval on a Ratio of Two Variance Components	186
	References	193
	Index	209