Table 5.

When effect size d = 0.8, the sample size N, the corresponding probabilities P(BF_0i > BF_thresh|H₀) and P(BF_i0 > BF_thresh|H_i) for the t test ¹ and Welch’s test ²

			type	t test				Welch’s test
			η	0.80		0.90		0.80		0.90
			output	N	P(BF > BFthresh)	N	P(BF > BFthresh)	N	P(BF > BFthresh)	N	P(BF > BFthresh)
b	BFthresh = 1	two-sided	H0	25	0.95	36	0.96	26	0.95	35	0.96
			H1		0.80		0.91		0.81		0.90
		one-sided	H0	18	0.93	27	0.95	18	0.93	27	0.95
			H2		0.81		0.90		0.81		0.90
	BFthresh = 3	two-sided	H0	36	0.85	72	0.90	36	0.85	73	0.90
			H1		0.80		0.98		0.80		0.98
		one-sided	H0	30	0.82	81	0.91	30	0.82	79	0.90
			H2		0.81		1.00		0.81		0.99
	BFthresh = 5	two-sided	H0	67	0.80	191	0.91	66	0.80	191	0.91
			H1		0.96		1.00		0.96		1.00
		one-sided	H0	67	0.80	207	0.90	67	0.80	209	0.90
			H2		0.98		1.00		0.98		1.00
2b	BFthresh = 1	two-sided	H0	21	0.91	31	0.93	21	0.91	31	0.93
			H1		0.80		0.90		0.80		0.90
		one-sided	H0	14	0.88	23	0.91	14	0.88	23	0.91
			H2		0.82		0.90		0.82		0.90
	BFthresh = 3	two-sided	H0	48	0.80	130	0.90	48	0.80	139	0.90
			H1		0.93		1.00		0.92		1.00
		one-sided	H0	48	0.80	158	0.90	46	0.80	156	0.90
			H2		0.96		1.00		0.95		1.00
	BFthresh = 5	two-sided	H0	128	0.80	369	0.90	127	0.80	379	0.90
			H1		1.00		1.00		1.00		1.00
		one-sided	H0	134	0.81	420	0.90	134	0.80	422	0.90
			H2		1.00		1.00		1.00		1.00
3b	BFthresh = 1	two-sided	H0	19	0.88	29	0.91	19	0.87	29	0.91
			H1		0.80		0.91		0.81		0.91
		one-sided	H0	10	0.82	26	0.90	10	0.80	26	0.91
			H2		0.80		0.94		1.01		0.94
	BFthresh = 3	two-sided	H0	73	0.81	196	0.90	73	0.80	208	0.91
			H1		0.99		1.00		0.99		1.00
		one-sided	H0	70	0.81	230	0.90	73	0.81	226	0.90
			H2		0.99		1.00		1.00		1.00
	BFthresh = 5	two-sided	H0	191	0.81	551	0.90	196	0.80	580	0.91
			H1		1.00		1.00		1.00		1.00
		one-sided	H0	199	0.80	608	0.90	200	0.80	622	0.90
			H2		1.00		1.00		1.00		1.00

¹ the means μ₁ = 0.8, μ₂ = 0 and the variance σ² = 1

² the means μ₁ = 0.8, μ₂ = 0 and the variances ${\sigma }_1^2=1.33$, ${\sigma }_2^2=0.67$