. Author manuscript; available in PMC: 2023 Jul 20.

Published in final edited form as: Stat Interface. 2016 Oct 31;10(2):313–341. doi: 10.4310/sii.2017.v10.n2.a13

Table 7.

The power estimates for pairwise tests based on Monte Carlo simulation of normal data under the given alternatives N2 and N4 with samples $𝒳$ , $𝒴$ , and $𝒵$ each with size n_x, n_y, and n_z, respectively, with N_mc = 10000 Monte Carlo replicates.

Normal Data
N2 : μ_x = 3.35, μ_y = 3.39, μ_z = 3.40; σ_x = σ_y = σ_z = 2.28
$𝒳 < 𝒴$
(n_x, n_y, n_z)	${\hat{β}}_{B F}$	${\hat{β}}_{W}$	${\hat{β}}_{t}$	${\hat{β}}_{K S}$
(1000,1000,1000)	.0501^b	.1008^a	.1070^a	.0942^a
(5000,5000,10000)	.0519^c	.2081^a	.2144^a	.1772^b
(5000,7500,10000)	.0497^c	.2435^a	.2484^a	.2062^b
(10000,10000,10000)	.0516^c	.3325^a	.3455^a	.2790^b
$𝒳 < 𝒵$
(1000,1000,1000)	.0523^c	.1225^a	.1236^a	.1121^b
(5000,5000,10000)	.0478^c	.3430^a	.3546^a	.2867^b
(5000,7500,10000)	.0482^c	.3463^a	.3562^a	.2972^b
(10000,10000,10000)	.0507^c	.4547^a	.4660^a	.3790^b
$𝒴 < 𝒵$
(1000,1000,1000)	.0529^b	.0619^a	.0636^a	.0574^ab
(5000,5000,10000)	.0477^c	.0869^a	.0884^a	.0766^b
(5000,7500,10000)	.0479^b	.0869^a	.0872^a	.0825^a
(10000,10000,10000)	.0458^c	.0919^a	.0935^a	.0827^b
N4 : μ_x = 3.35, μ_y = 3.39, μ_z = 3.42; σ_x = 2.28, σ_y = 2.33, σ_z = 2.37
$𝒳 < 𝒴$
(1000,1000,1000)	.1535^a	.1001^b	.1064^b	.0997^b
(5000,5000,10000)	.4160^a	.2054^c	.2128^b	.2198^b
(5000,7500,10000)	.4694^a	.2400^c	.2468^c	.2642^b
(10000,10000,10000)	.6550^a	.3280^c	.3397^c	.3861^b
$𝒳 < 𝒵$
(1000,1000,1000)	.3149^a	.1592^b	.1650^b	.1635^b
(5000,5000,10000)	.9057^a	.5258^d	.5451^c	.6696^b
(5000,7500,10000)	.9074^a	.5271^d	.5480^c	.6768^b
(10000,10000,10000)	.9767^a	.6722^d	.6913^c	.8385^b
$𝒴 < 𝒵$
(1000,1000,1000)	.1303^a	.0866^bc	.0910^b	.0822^c
(5000,5000,10000)	.3615^a	.1847^bc	.1930^b	.1981^b
(5000,7500,10000)	.4287^a	.2070^c	.2106^c	.2255^b
(10000,10000,10000)	.4688^a	.2302^c	.2323^c	.2496^b

The superscripts are as in Table 3