Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

Table 1

Coverage rates of 95% Scheffé’s intervals (S) and generalized Scheffé (GS) intervals: two sets of inferences are considered, the population means and pairwise mean differences.

Sample size	Equal variances				Unequal variances
	(0.1, 0.1, 0.1, 0.1)		(1, 1, 1, 1)		(0.3, 0.3, 0.1, 0.1)		(3, 3, 1, 1)
Balanced	S	GS	S	GS	S	GS	S	GS
(5, 5, 5, 5)	98.00	98.60	98.45	99.00	93.60	96.85	94.05	97.35
(10, 10, 10, 10)	97.90	98.45	98.20	98.65	94.75	97.10	95.10	97.30
(20, 20, 20, 20)	97.70	97.90	98.20	98.35	93.90	96.25	94.80	96.45
(50, 50, 50, 50)	97.90	97.95	98.35	98.35	94.35	96.75	94.55	96.60
Unbalanced
(5, 5, 10, 10)	98.20	98.75	98.20	98.70	87.70	97.50	87.20	97.40
(5, 5, 20, 20)	98.40	99.10	97.90	98.45	73.00	96.20	76.50	96.65
(10, 10, 20, 20)	97.95	98.05	98.35	98.35	88.40	97.30	87.05	96.65
(10, 10, 50, 50)	98.60	98.80	98.70	98.65	73.95	96.70	72.55	97.10