Testing Normal Means: The Reconcilability of the 𝑃 Value and the Bayesian Evidence

Table 2

𝑃 value and lim𝑃(𝐻₀∣𝑥) for testing the Behrens-Fisher problem for different 𝜈₀₁ and 𝜈₀₂.

	𝜈01=0.5, 𝜈02=0.5
𝑐−(𝑥−𝑦)	−2.5000	−2.1000	−1.8000	−1.6000	−1.3000	−0.9000	−0.5000	−0.3000	−0.1000
𝑝(𝑥)	0.0030	0.0080	0.0130	0.0240	0.0490	0.1310	0.2720	0.3495	0.4565
lim𝑃(𝐻0∣𝑥)	0.0010	0.0035	0.0060	0.0135	0.0280	0.1030	0.2245	0.3375	0.4410
	𝜈01=2, 𝜈02=2
𝑐−(𝑥−𝑦)	−2.5000	−2.1000	−1.8000	−1.6000	−1.3000	−0.9000	−0.5000	−0.3000	−0.1000
𝑝(𝑥)	0.0025	0.0045	0.0165	0.0270	0.0545	0.1130	0.2550	0.3480	0.4595
lim𝑃(𝐻0∣𝑥)	0.0005	0.0015	0.0050	0.0080	0.0245	0.1000	0.2125	0.3155	0.4345
	𝜈01=0.2, 𝜈02=0.5
𝑐−(𝑥−𝑦)	−2.5000	−2.1000	−1.8000	−1.6000	−1.3000	−0.9000	−0.5000	−0.3000	−0.1000
𝑝(𝑥)	0.0025	0.0085	0.0145	0.0295	0.0470	0.1225	0.2550	0.3400	0.4610
lim𝑃(𝐻0∣𝑥)	0.0015	0.0030	0.0045	0.0130	0.0275	0.1055	0.2215	0.3245	0.4455
	𝜈01=0.5, 𝜈02=0.2
𝑐−(𝑥−𝑦)	−2.5000	−2.1000	−1.8000	−1.6000	−1.3000	−0.9000	−0.5000	−0.3000	−0.1000
𝑝(𝑥)	0.0055	0.0070	0.0170	0.0265	0.0545	0.1215	0.2485	0.3535	0.4650
lim𝑃(𝐻0∣𝑥)	0.0010	0.0055	0.0070	0.0125	0.0440	0.1085	0.2500	0.3285	0.4300
	𝜈01=5, 𝜈02=0.5
𝑐−(𝑥−𝑦)	−2.5000	−2.1000	−1.8000	−1.6000	−1.3000	−0.9000	−0.5000	−0.3000	−0.1000
𝑝(𝑥)	0.0025	0.0060	0.0150	0.0230	0.0570	0.1145	0.2645	0.3685	0.4460
lim𝑃(𝐻0∣𝑥)	0.0020	0.0025	0.0065	0.0095	0.0330	0.0890	0.2205	0.3105	0.4305