ssiz 2 prop Exp

This page presents tables of sample size (per group) comparing two unpaired proportions, for the following combinations.

Powers of 0.8, 0.9, and 0.99
Probability of Type I Error (α) of 0.1, 0.05, 0.01, and 0.001
One and two tail models

Sample size calculated to be less than 1/proportion (ssiz<1/p1 or ssiz<1/p2) are not included in the table, as a single positive case in the group will then exceed the proportion being compared.

Sample size for two proportions are used mostly in the Risk Difference model, although it is also used for Risk Ratio comparisons.

The sample size from this page can be used for Odds Ratio comparison, if Odds Ratio is used in a similar manner as Risk Differences or Risk Ratio to compare two proportions. However, Odds Ratio is often used in matched pair controlled studies, and in that case the sample size is calculated as number of matched units, and a different algorithm is used. Sample size for matched paired controlled studies are available in the Sample Size for Matched Paired Controlled Studies Program Page

if a researcher wishes to use a smaller sample size than those published in these tables or calculated using the Sample Size for Comparison of Two Proportions Program Page , he/she should use either the Chi Squares Test for the 2x2 contingency table or the Fisher's Exact probability, as these do not assume a normal transformation of the difference between proportions.

The Chi Squares Test requires a minimum of 30 cases overall, and each cell in the 2x2 table should have a minimum of 5 cases.

The Fisher's Exact Probability is based on the Poisson distribution, and has no minimal sample size requirement. However, a statistically significant result (p<0.05) is unlikely whatever the data, if less than 6 cases overall are included.

In the tables

Power= 1-β, where β is the Probability of Type II Error
α is the Probability of Type I Error
p1 and p2 are the proportions in the two groups to be detected
1 tail and 2 tail are the statistical models.

Power=0.8 Power=0.9 Power=0.95

α		0.1		0.05		0.01		0.001		α		0.1		0.05		0.01		0.001
p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.05	0.1	250	343	343	435	556	647	857	946	0.05	0.15	81	111	111	141	180	209	277	306
0.05	0.2	43	60	60	76	97	113	149	165	0.05	0.25	28	39	39	49	63	73	97	108
0.05	0.3	20	28	28	36	46	53	70	78	0.05	0.35		21	21	27	35	41	54	59
0.05	0.4				22	28	32	43	47	0.05	0.45					23	26	35	39
0.05	0.5						22	29	32	0.05	0.55							25	27
0.05	0.6							21	23	0.05	0.65								20
0.05	0.7									0.05	0.75
0.05	0.8									0.05	0.85
0.05	0.9									0.05	0.95
0.1	0.15	394	540	540	686	877	1021	1352	1493	0.1	0.2	115	157	157	199	255	297	393	434
0.1	0.25	57	79	79	100	128	149	197	218	0.1	0.3	36	49	49	62	79	92	122	135
0.1	0.35	25	34	34	43	55	64	85	94	0.1	0.4	18	25	25	32	41	48	63	70
0.1	0.45	14	20	20	25	32	37	49	54	0.1	0.5	11	16	16	20	25	30	39	44
0.1	0.55		13	13	16	21	24	32	36	0.1	0.6		11	11	14	17	20	27	30
0.1	0.65				11	15	17	23	25	0.1	0.7				10	12	15	19	21
0.1	0.75					11	12	17	18	0.1	0.8						11	14	16
0.1	0.85							12	14	0.1	0.9							11	12
0.1	0.95								10	0.15	0.2	520	714	714	906	1158	1348	1784	1971
0.15	0.25	144	197	197	250	320	373	494	545	0.15	0.3	69	95	95	121	155	180	238	263
0.15	0.35	42	57	57	73	93	109	144	159	0.15	0.4	28	39	39	49	63	74	97	108
α		0.1		0.05		0.01		0.001		α		0.1		0.05		0.01		0.001
p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.15	0.45	21	28	28	36	46	54	71	78	0.15	0.5	16	22	22	27	35	41	54	60
0.15	0.55	12	17	17	22	28	32	43	47	0.15	0.6	10	14	14	17	22	26	35	38
0.15	0.65	8	11	11	14	18	21	28	31	0.15	0.7	7	9	9	12	15	18	24	26
0.15	0.75	6	8	8	10	13	15	20	22	0.15	0.8		7	7	8	11	13	17	19
0.15	0.85		6	6	7	9	11	14	16	0.15	0.9				6	8	9	12	14
0.15	0.95					7	8	10	12	0.2	0.25	628	862	862	1094	1399	1628	2155	2381
0.2	0.3	169	231	231	294	376	437	579	639	0.2	0.35	79	109	109	138	177	206	273	301
0.2	0.4	47	64	64	82	105	122	161	178	0.2	0.45	31	43	43	54	70	81	107	119
0.2	0.5	22	31	31	39	50	58	77	85	0.2	0.55	17	23	23	29	38	44	58	64
0.2	0.6	13	18	18	23	29	34	45	50	0.2	0.65	10	14	14	18	23	27	36	40
0.2	0.7	8	12	12	15	19	22	29	32	0.2	0.75	7	10	10	12	16	18	24	27
0.2	0.8	6	8	8	10	13	15	20	22	0.2	0.85	5	7	7	8	11	13	17	19
0.2	0.9		6	6	7	9	11	14	16	0.2	0.95		5	5	6	8	9	12	13
0.25	0.3	719	986	986	1251	1600	1862	2465	2722	0.25	0.35	189	259	259	329	421	490	648	716
0.25	0.4	88	120	120	152	195	227	300	332	0.25	0.45	51	70	70	89	113	132	175	193
0.25	0.5	33	46	46	58	74	87	115	127	0.25	0.55	24	32	32	41	53	61	81	90
0.25	0.6	18	24	24	31	39	46	60	67	0.25	0.65	14	19	19	24	30	35	47	52
0.25	0.7	11	15	15	19	24	28	37	41	0.25	0.75	9	12	12	15	19	22	30	33
0.25	0.8	7	10	10	12	16	18	24	27	0.25	0.85	6	8	8	10	13	15	20	22
0.25	0.9	5	7	7	8	11	12	17	18	0.25	0.95	4	5	5	7	9	10	14	15
0.3	0.35	791	1084	1084	1377	1760	2049	2712	2995	0.3	0.4	205	281	281	356	456	530	702	776
0.3	0.45	94	128	128	163	208	242	321	354	0.3	0.5	54	74	74	93	120	139	184	204
α		0.1		0.05		0.01		0.001		α		0.1		0.05		0.01		0.001
p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.3	0.55	35	48	48	61	78	90	120	132	0.3	0.6	24	33	33	42	54	63	84	93
0.3	0.65	18	25	25	31	40	47	62	68	0.3	0.7	14	19	19	24	30	36	47	52
0.3	0.75	11	15	15	19	24	28	37	41	0.3	0.8	8	12	12	15	19	22	29	32
0.3	0.85	7	9	9	12	15	18	24	26	0.3	0.9	6	8	8	10	12	15	19	21
0.3	0.95	5	6	6	8	10	12	16	17	0.35	0.4	845	1159	1159	1471	1881	2189	2897	3200
0.35	0.45	216	296	296	376	481	560	741	818	0.35	0.5	98	134	134	170	217	253	335	370
0.35	0.55	55	76	76	96	123	144	190	210	0.35	0.6	36	49	49	62	79	92	122	135
0.35	0.65	25	34	34	43	55	64	85	94	0.35	0.7	18	25	25	31	40	47	62	68
0.35	0.75	14	19	19	24	30	35	47	52	0.35	0.8	10	14	14	18	23	27	36	40
0.35	0.85	8	11	11	14	18	21	28	31	0.35	0.9	7	9	9	11	15	17	23	25
0.35	0.95	5	7	7	9	12	14	18	20	0.4	0.45	881	1208	1208	1534	1961	2282	3021	3337
0.4	0.5	223	305	305	388	496	577	764	844	0.4	0.55	100	136	136	173	222	258	342	377
0.4	0.6	56	77	77	97	125	145	192	212	0.4	0.65	36	49	49	62	79	92	122	135
0.4	0.7	24	33	33	42	54	63	84	93	0.4	0.75	18	24	24	31	39	46	60	67
0.4	0.8	13	18	18	23	29	34	45	50	0.4	0.85	10	14	14	17	22	26	35	38
0.4	0.9	8	11	11	14	17	20	27	30	0.4	0.95	6	8	8	11	14	16	21	23
0.45	0.5	899	1233	1233	1565	2001	2329	3083	3405	0.45	0.55	225	309	309	392	501	583	772	852
0.45	0.6	100	136	136	173	222	258	342	377	0.45	0.65	55	76	76	96	123	144	190	210
0.45	0.7	35	48	48	61	78	90	120	132	0.45	0.75	24	32	32	41	53	61	81	90
0.45	0.8	17	23	23	29	38	44	58	64	0.45	0.85	12	17	17	22	28	32	43	47
0.45	0.9	9	13	13	16	21	24	32	36	0.45	0.95	7	10	10	12	16	19	25	27
0.5	0.55	899	1233	1233	1565	2001	2329	3083	3405	0.5	0.6	223	305	305	388	496	577	764	844
α		0.1		0.05		0.01		0.001		α		0.1		0.05		0.01		0.001
p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	p1	p2	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.5	0.65	98	134	134	170	217	253	335	370	0.5	0.7	54	74	74	93	120	139	184	204
0.5	0.75	33	46	46	58	74	87	115	127	0.5	0.8	22	31	31	39	50	58	77	85
0.5	0.85	16	22	22	27	35	41	54	60	0.5	0.9	11	16	16	20	25	30	39	44
0.5	0.95	8	12	12	15	19	22	29	32	0.55	0.6	881	1208	1208	1534	1961	2282	3021	3337
0.55	0.65	216	296	296	376	481	560	741	818	0.55	0.7	94	128	128	163	208	242	321	354
0.55	0.75	51	70	70	89	113	132	175	193	0.55	0.8	31	43	43	54	70	81	107	119
0.55	0.85	21	28	28	36	46	54	71	78	0.55	0.9	14	20	20	25	32	37	49	54
0.55	0.95	10	14	14	18	23	26	35	39	0.6	0.65	845	1159	1159	1471	1881	2189	2897	3200
0.6	0.7	205	281	281	356	456	530	702	776	0.6	0.75	88	120	120	152	195	227	300	332
0.6	0.8	47	64	64	82	105	122	161	178	0.6	0.85	28	39	39	49	63	74	97	108
0.6	0.9	18	25	25	32	41	48	63	70	0.6	0.95	12	17	17	22	28	32	43	47
0.65	0.7	791	1084	1084	1377	1760	2049	2712	2995	0.65	0.75	189	259	259	329	421	490	648	716
0.65	0.8	79	109	109	138	177	206	273	301	0.65	0.85	42	57	57	73	93	109	144	159
0.65	0.9	25	34	34	43	55	64	85	94	0.65	0.95	16	21	21	27	35	41	54	59
0.7	0.75	719	986	986	1251	1600	1862	2465	2722	0.7	0.8	169	231	231	294	376	437	579	639
0.7	0.85	69	95	95	121	155	180	238	263	0.7	0.9	36	49	49	62	79	92	122	135
0.7	0.95	20	28	28	36	46	53	70	78	0.75	0.8	628	862	862	1094	1399	1628	2155	2381
0.75	0.85	144	197	197	250	320	373	494	545	0.75	0.9	57	79	79	100	128	149	197	218
0.75	0.95	28	39	39	49	63	73	97	108	0.8	0.85	520	714	714	906	1158	1348	1784	1971
0.8	0.9	115	157	157	199	255	297	393	434	0.8	0.95	43	60	60	76	97	113	149	165
0.85	0.9	394	540	540	686	877	1021	1352	1493	0.85	0.95	81	111	111	141	180	209	277	306
0.9	0.95	250	343	343	435	556	647	857	946

Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for Clinical Studies. Second Ed. Blackwell Science IBSN 0-86542-870-0 p. 18-20