Journal of Probability and Statistics / 2011 / Article / Tab 1

Research Article

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 sizeEqual variancesUnequal 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

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