Bayesian updating: increasing sample size during the course of a study

Table 4 Percentage error and mean sample size for the equal variances t-test \(\left( {N_{{min}} = 20,N_{{max}} = 50000} \right)\)

			BF_target = 3		BF_target = 5		BF_target = 10		BF_target = 20
HypSet	ES	Fraction	% error	Mean N	% error	Mean N	% error	Mean N	% error	Mean N
1	0	1b	5.1	22	4.1	29	2.5	70	1.5	296
1	0	2b	7.2	24	5.7	36	3.7	123	2.3	523
1	0	3b	9.1	26	7.1	47	4.4	179	3.1	799
1	0.2	1b	78.9	25	72.1	49	47.0	171	13.6	406
1	0.2	2b	70.8	29	61.3	69	27.3	238	3.6	451
1	0.2	3b	65.2	32	51.3	79	19.0	268	1.5	435
1	0.5	1b	35.0	26	19.9	37	4.3	58	0.2	74
1	0.5	2b	24.7	27	10.7	39	0.8	56	0.0	68
1	0.5	3b	17.9	28	6.5	40	0.2	54	0.0	63
1	0.8	1b	6.1	22	1.9	25	0.1	28	0.0	31
1	0.8	2b	3.2	22	1.0	24	0.0	27	0.0	30
1	0.8	3b	1.8	22	0.5	24	0.0	26	0.0	29
2	0	1b	5.0	22	3.9	27	3.8	92	2.1	380
2	0	2b	7.4	23	6.3	42	4.2	180	2.8	758
2	0	3b	9.8	26	7.7	62	5.3	265	3.5	1114
2	0.2	1b	88.3	23	84.7	34	56.6	170	10.1	512
2	0.2	2b	82.4	25	73.3	56	30.0	282	1.1	543
2	0.2	3b	78.9	28	62.2	83	17.2	342	0.0	531
2	0.5	1b	50.5	24	34.7	35	2.5	70	0.0	85
2	0.5	2b	39.8	26	15.4	44	0.1	67	0.0	78
2	0.5	3b	31.9	28	6.3	48	0.0	64	0.0	75
2	0.8	1b	13.9	23	4.7	26	0.0	31	0.0	34
2	0.8	2b	7.7	23	1.1	26	0.0	29	0.0	33
2	0.8	3b	5.6	23	0.1	26	0.0	29	0.0	32
3	0.2	1b	19.2	26	12.8	41	7.0	71	3.8	114
3	0.2	2b	18.5	26	13.1	40	7.3	71	3.3	114
3	0.2	3b	19.8	26	13.3	39	7.4	70	3.4	113
3	0.5	1b	2.1	21	0.8	23	0.3	26	0.2	31
3	0.5	2b	2.0	21	1.1	23	0.3	26	0.1	31
3	0.5	3b	2.4	21	0.7	23	0.4	26	0.3	31
3	0.8	1b	0.1	20	0.0	20	0.0	21	0.0	21
3	0.8	2b	0.2	20	0.0	20	0.0	21	0.0	21
3	0.8	3b	0.1	20	0.1	20	0.0	21	0.0	21

Hyp Set 1: \({H}_{0}:{\mu }_{1}={\mu }_{2}\) and \({H}_{1}:{\mu }_{1}<{\mu }_{2}\); Hyp Set 2: \({H}_{0}:{\mu }_{1}={\mu }_{2}\) and \({H}_{1}:{\mu }_{1}\ne {\mu }_{2}\)
Hyp Set 3: \({H}_{1}:{\mu }_{1}>{\mu }_{2}\) and \({H}_{2}:{\mu }_{1}<{\mu }_{2}\). Underline: scenarios with one replication inconclusive