Table 4.

Average power multiplied by 1000 over intervals for ρ when testing ρ = 0 vs ρ > 0 at the 0.05 significance level based on one million simulated data sets. For the non-Bayesian estimators, the significance test bounds found in Table 2 were used. The Bayesian tests were based on the Bayes factors using the value of c listed in Table 3. The tests with the largest power are shown in bold for each sample size and each correlation interval.

n	Test Based on	ρ
		[0,1]	[0,.25]	[.25,.50]	[.50,.75]	[.75,1]
5	Sample Correlation Coeff	383	81	187	423	839
	Emp w/ Known Var	288	89	198	348	517
	Trunc Emp w/ Known Var	288	89	198	348	517
	MLE	356	69	141	352	862
	Sampson’s MLE Approx	355	69	140	350	861
	Uniform Prior	397	82	196	442	869
	Arc-sine Prior	397	81	192	440	875
10	Sample Correlation Coeff	529	106	326	708	977
	Emp w/ Known Var	441	110	302	562	793
	Trunc Emp w/ Known Var	441	110	302	562	793
	MLE	505	88	262	682	990
	Sampson’s MLE Approx	505	88	260	680	990
	Uniform Prior	534	105	325	722	985
	Arc-sine Prior	534	104	323	723	987
50	Sample Correlation Coeff	770	250	833	998	1000
	Emp w/ Known Var	759	245	800	993	1000
	Trunc Emp w/ Known Var	759	245	800	993	1000
	MLE	768	238	834	999	1000
	Sampson’s MLE Approx	768	238	834	999	1000
	Uniform Prior	772	250	838	998	1000
	Arc-sine Prior	772	250	838	999	1000