Confidence and Tolerance Intervals

Exact Binomial Confidence Intervals (Clopper-Pearson Table)

Exact confidence limits for a proportion, the standard choice for response rates in small single-arm trials.

n = 1 to 30
90%, 95% and 99%
Calculator for any n

Clopper-Pearson Exact CI

Jump to a sample size below. Rows: number of successes x · Columns: observed proportion and lower/upper limits.

n = 1

n = 1
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.9500	0.0000	0.9750	0.0000	0.9950
1	1.000	0.0500	1.0000	0.0250	1.0000	0.0050	1.0000

n = 2

n = 2
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.7764	0.0000	0.8419	0.0000	0.9293
1	0.500	0.0253	0.9747	0.0126	0.9874	0.0025	0.9975
2	1.000	0.2236	1.0000	0.1581	1.0000	0.0707	1.0000

n = 3

n = 3
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.6316	0.0000	0.7076	0.0000	0.8290
1	0.333	0.0170	0.8646	0.0084	0.9057	0.0017	0.9586
2	0.667	0.1354	0.9830	0.0943	0.9916	0.0414	0.9983
3	1.000	0.3684	1.0000	0.2924	1.0000	0.1710	1.0000

n = 4

n = 4
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.5271	0.0000	0.6024	0.0000	0.7341
1	0.250	0.0127	0.7514	0.0063	0.8059	0.0013	0.8891
2	0.500	0.0976	0.9024	0.0676	0.9324	0.0294	0.9706
3	0.750	0.2486	0.9873	0.1941	0.9937	0.1109	0.9987
4	1.000	0.4729	1.0000	0.3976	1.0000	0.2659	1.0000

n = 5

n = 5
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.4507	0.0000	0.5218	0.0000	0.6534
1	0.200	0.0102	0.6574	0.0051	0.7164	0.0010	0.8149
2	0.400	0.0764	0.8107	0.0527	0.8534	0.0229	0.9172
3	0.600	0.1893	0.9236	0.1466	0.9473	0.0828	0.9771
4	0.800	0.3426	0.9898	0.2836	0.9949	0.1851	0.9990
5	1.000	0.5493	1.0000	0.4782	1.0000	0.3466	1.0000

n = 6

n = 6
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.3930	0.0000	0.4593	0.0000	0.5865
1	0.167	0.0085	0.5818	0.0042	0.6412	0.0008	0.7460
2	0.333	0.0628	0.7287	0.0433	0.7772	0.0187	0.8564
3	0.500	0.1532	0.8468	0.1181	0.8819	0.0663	0.9337
4	0.667	0.2713	0.9372	0.2228	0.9567	0.1436	0.9813
5	0.833	0.4182	0.9915	0.3588	0.9958	0.2540	0.9992
6	1.000	0.6070	1.0000	0.5407	1.0000	0.4135	1.0000

n = 7

n = 7
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.3482	0.0000	0.4096	0.0000	0.5309
1	0.143	0.0073	0.5207	0.0036	0.5787	0.0007	0.6849
2	0.286	0.0534	0.6587	0.0367	0.7096	0.0158	0.7970
3	0.429	0.1288	0.7747	0.0990	0.8159	0.0553	0.8823
4	0.571	0.2253	0.8712	0.1841	0.9010	0.1177	0.9447
5	0.714	0.3413	0.9466	0.2904	0.9633	0.2030	0.9842
6	0.857	0.4793	0.9927	0.4213	0.9964	0.3151	0.9993
7	1.000	0.6518	1.0000	0.5904	1.0000	0.4691	1.0000

n = 8

n = 8
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.3123	0.0000	0.3694	0.0000	0.4843
1	0.125	0.0064	0.4707	0.0032	0.5265	0.0006	0.6315
2	0.250	0.0464	0.5997	0.0319	0.6509	0.0137	0.7422
3	0.375	0.1111	0.7108	0.0852	0.7551	0.0475	0.8303
4	0.500	0.1929	0.8071	0.1570	0.8430	0.0999	0.9001
5	0.625	0.2892	0.8889	0.2449	0.9148	0.1697	0.9525
6	0.750	0.4003	0.9536	0.3491	0.9681	0.2578	0.9863
7	0.875	0.5293	0.9936	0.4735	0.9968	0.3685	0.9994
8	1.000	0.6877	1.0000	0.6306	1.0000	0.5157	1.0000

n = 9

n = 9
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.2831	0.0000	0.3363	0.0000	0.4450
1	0.111	0.0057	0.4291	0.0028	0.4825	0.0006	0.5850
2	0.222	0.0410	0.5496	0.0281	0.6001	0.0121	0.6926
3	0.333	0.0977	0.6551	0.0749	0.7007	0.0416	0.7809
4	0.444	0.1688	0.7486	0.1370	0.7880	0.0868	0.8539
5	0.556	0.2514	0.8312	0.2120	0.8630	0.1461	0.9132
6	0.667	0.3449	0.9023	0.2993	0.9251	0.2191	0.9584
7	0.778	0.4504	0.9590	0.3999	0.9719	0.3074	0.9879
8	0.889	0.5709	0.9943	0.5175	0.9972	0.4150	0.9994
9	1.000	0.7169	1.0000	0.6637	1.0000	0.5550	1.0000

n = 10

n = 10
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.2589	0.0000	0.3085	0.0000	0.4113
1	0.100	0.0051	0.3942	0.0025	0.4450	0.0005	0.5443
2	0.200	0.0368	0.5069	0.0252	0.5561	0.0109	0.6482
3	0.300	0.0873	0.6066	0.0667	0.6525	0.0370	0.7351
4	0.400	0.1500	0.6965	0.1216	0.7376	0.0768	0.8091
5	0.500	0.2224	0.7776	0.1871	0.8129	0.1283	0.8717
6	0.600	0.3035	0.8500	0.2624	0.8784	0.1909	0.9232
7	0.700	0.3934	0.9127	0.3475	0.9333	0.2649	0.9630
8	0.800	0.4931	0.9632	0.4439	0.9748	0.3518	0.9891
9	0.900	0.6058	0.9949	0.5550	0.9975	0.4557	0.9995
10	1.000	0.7411	1.0000	0.6915	1.0000	0.5887	1.0000

n = 11

n = 11
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.2384	0.0000	0.2849	0.0000	0.3822
1	0.091	0.0047	0.3644	0.0023	0.4128	0.0005	0.5086
2	0.182	0.0333	0.4701	0.0228	0.5178	0.0098	0.6085
3	0.273	0.0788	0.5644	0.0602	0.6097	0.0333	0.6933
4	0.364	0.1351	0.6502	0.1093	0.6921	0.0688	0.7668
5	0.455	0.1996	0.7288	0.1675	0.7662	0.1145	0.8307
6	0.545	0.2712	0.8004	0.2338	0.8325	0.1693	0.8855
7	0.636	0.3498	0.8649	0.3079	0.8907	0.2332	0.9312
8	0.727	0.4356	0.9212	0.3903	0.9398	0.3067	0.9667
9	0.818	0.5299	0.9667	0.4822	0.9772	0.3915	0.9902
10	0.909	0.6356	0.9953	0.5872	0.9977	0.4914	0.9995
11	1.000	0.7616	1.0000	0.7151	1.0000	0.6178	1.0000

n = 12

n = 12
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.2209	0.0000	0.2646	0.0000	0.3569
1	0.083	0.0043	0.3387	0.0021	0.3848	0.0004	0.4770
2	0.167	0.0305	0.4381	0.0209	0.4841	0.0090	0.5729
3	0.250	0.0719	0.5273	0.0549	0.5719	0.0303	0.6552
4	0.333	0.1229	0.6091	0.0992	0.6511	0.0624	0.7275
5	0.417	0.1810	0.6848	0.1517	0.7233	0.1034	0.7915
6	0.500	0.2453	0.7547	0.2109	0.7891	0.1522	0.8478
7	0.583	0.3152	0.8190	0.2767	0.8483	0.2085	0.8966
8	0.667	0.3909	0.8771	0.3489	0.9008	0.2725	0.9376
9	0.750	0.4727	0.9281	0.4281	0.9451	0.3448	0.9697
10	0.833	0.5619	0.9695	0.5159	0.9791	0.4271	0.9910
11	0.917	0.6613	0.9957	0.6152	0.9979	0.5230	0.9996
12	1.000	0.7791	1.0000	0.7354	1.0000	0.6431	1.0000

n = 13

n = 13
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.2058	0.0000	0.2471	0.0000	0.3347
1	0.077	0.0039	0.3163	0.0019	0.3603	0.0004	0.4490
2	0.154	0.0281	0.4101	0.0192	0.4545	0.0083	0.5410
3	0.231	0.0660	0.4946	0.0504	0.5381	0.0278	0.6206
4	0.308	0.1127	0.5726	0.0909	0.6143	0.0571	0.6913
5	0.385	0.1657	0.6452	0.1386	0.6842	0.0942	0.7546
6	0.462	0.2240	0.7130	0.1922	0.7487	0.1383	0.8113
7	0.538	0.2870	0.7760	0.2513	0.8078	0.1887	0.8617
8	0.615	0.3548	0.8343	0.3158	0.8614	0.2454	0.9058
9	0.692	0.4274	0.8873	0.3857	0.9091	0.3087	0.9429
10	0.769	0.5054	0.9340	0.4619	0.9496	0.3794	0.9722
11	0.846	0.5899	0.9719	0.5455	0.9808	0.4590	0.9917
12	0.923	0.6837	0.9961	0.6397	0.9981	0.5510	0.9996
13	1.000	0.7942	1.0000	0.7529	1.0000	0.6653	1.0000

n = 14

n = 14
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1926	0.0000	0.2316	0.0000	0.3151
1	0.071	0.0037	0.2967	0.0018	0.3387	0.0004	0.4240
2	0.143	0.0260	0.3854	0.0178	0.4281	0.0076	0.5123
3	0.214	0.0611	0.4657	0.0466	0.5080	0.0257	0.5892
4	0.286	0.1040	0.5400	0.0839	0.5810	0.0526	0.6579
5	0.357	0.1527	0.6096	0.1276	0.6486	0.0866	0.7201
6	0.429	0.2061	0.6750	0.1766	0.7114	0.1267	0.7766
7	0.500	0.2636	0.7364	0.2304	0.7696	0.1724	0.8276
8	0.571	0.3250	0.7939	0.2886	0.8234	0.2234	0.8733
9	0.643	0.3904	0.8473	0.3514	0.8724	0.2799	0.9134
10	0.714	0.4600	0.8960	0.4190	0.9161	0.3421	0.9474
11	0.786	0.5343	0.9389	0.4920	0.9534	0.4108	0.9743
12	0.857	0.6146	0.9740	0.5719	0.9822	0.4877	0.9924
13	0.929	0.7033	0.9963	0.6613	0.9982	0.5760	0.9996
14	1.000	0.8074	1.0000	0.7684	1.0000	0.6849	1.0000

n = 15

n = 15
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1810	0.0000	0.2180	0.0000	0.2976
1	0.067	0.0034	0.2794	0.0017	0.3195	0.0003	0.4016
2	0.133	0.0242	0.3634	0.0166	0.4046	0.0071	0.4863
3	0.200	0.0568	0.4398	0.0433	0.4809	0.0239	0.5605
4	0.267	0.0967	0.5108	0.0779	0.5510	0.0488	0.6273
5	0.333	0.1417	0.5774	0.1182	0.6162	0.0801	0.6882
6	0.400	0.1909	0.6404	0.1634	0.6771	0.1170	0.7439
7	0.467	0.2437	0.7000	0.2127	0.7341	0.1587	0.7949
8	0.533	0.3000	0.7563	0.2659	0.7873	0.2051	0.8413
9	0.600	0.3596	0.8091	0.3229	0.8366	0.2561	0.8830
10	0.667	0.4226	0.8583	0.3838	0.8818	0.3118	0.9199
11	0.733	0.4892	0.9033	0.4490	0.9221	0.3727	0.9512
12	0.800	0.5602	0.9432	0.5191	0.9567	0.4395	0.9761
13	0.867	0.6366	0.9758	0.5954	0.9834	0.5137	0.9929
14	0.933	0.7206	0.9966	0.6805	0.9983	0.5984	0.9997
15	1.000	0.8190	1.0000	0.7820	1.0000	0.7024	1.0000

n = 16

n = 16
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1707	0.0000	0.2059	0.0000	0.2819
1	0.062	0.0032	0.2640	0.0016	0.3023	0.0003	0.3814
2	0.125	0.0227	0.3438	0.0155	0.3835	0.0067	0.4628
3	0.188	0.0531	0.4166	0.0405	0.4565	0.0223	0.5344
4	0.250	0.0903	0.4844	0.0727	0.5238	0.0455	0.5991
5	0.312	0.1321	0.5483	0.1102	0.5866	0.0745	0.6585
6	0.375	0.1778	0.6090	0.1520	0.6457	0.1086	0.7132
7	0.438	0.2267	0.6666	0.1975	0.7012	0.1471	0.7638
8	0.500	0.2786	0.7214	0.2465	0.7535	0.1897	0.8103
9	0.562	0.3334	0.7733	0.2988	0.8025	0.2362	0.8529
10	0.625	0.3910	0.8222	0.3543	0.8480	0.2868	0.8914
11	0.688	0.4517	0.8679	0.4134	0.8898	0.3415	0.9255
12	0.750	0.5156	0.9097	0.4762	0.9273	0.4009	0.9545
13	0.812	0.5834	0.9469	0.5435	0.9595	0.4656	0.9777
14	0.875	0.6562	0.9773	0.6165	0.9845	0.5372	0.9933
15	0.938	0.7360	0.9968	0.6977	0.9984	0.6186	0.9997
16	1.000	0.8293	1.0000	0.7941	1.0000	0.7181	1.0000

n = 17

n = 17
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1616	0.0000	0.1951	0.0000	0.2678
1	0.059	0.0030	0.2501	0.0015	0.2869	0.0003	0.3630
2	0.118	0.0213	0.3262	0.0146	0.3644	0.0063	0.4413
3	0.176	0.0499	0.3956	0.0380	0.4343	0.0209	0.5104
4	0.235	0.0846	0.4605	0.0681	0.4990	0.0426	0.5732
5	0.294	0.1238	0.5219	0.1031	0.5596	0.0697	0.6310
6	0.353	0.1664	0.5803	0.1421	0.6167	0.1014	0.6846
7	0.412	0.2119	0.6360	0.1844	0.6708	0.1371	0.7344
8	0.471	0.2601	0.6892	0.2298	0.7219	0.1764	0.7807
9	0.529	0.3108	0.7399	0.2781	0.7702	0.2193	0.8236
10	0.588	0.3640	0.7881	0.3292	0.8156	0.2656	0.8629
11	0.647	0.4197	0.8336	0.3833	0.8579	0.3154	0.8986
12	0.706	0.4781	0.8762	0.4404	0.8969	0.3690	0.9303
13	0.765	0.5395	0.9154	0.5010	0.9319	0.4268	0.9574
14	0.824	0.6044	0.9501	0.5657	0.9620	0.4896	0.9791
15	0.882	0.6738	0.9787	0.6356	0.9854	0.5587	0.9937
16	0.941	0.7499	0.9970	0.7131	0.9985	0.6370	0.9997
17	1.000	0.8384	1.0000	0.8049	1.0000	0.7322	1.0000

n = 18

n = 18
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1533	0.0000	0.1853	0.0000	0.2550
1	0.056	0.0028	0.2377	0.0014	0.2729	0.0003	0.3463
2	0.111	0.0201	0.3103	0.0138	0.3471	0.0059	0.4217
3	0.167	0.0470	0.3767	0.0358	0.4142	0.0197	0.4884
4	0.222	0.0797	0.4389	0.0641	0.4764	0.0400	0.5492
5	0.278	0.1164	0.4978	0.0969	0.5348	0.0654	0.6055
6	0.333	0.1563	0.5540	0.1334	0.5901	0.0951	0.6579
7	0.389	0.1990	0.6078	0.1730	0.6425	0.1284	0.7068
8	0.444	0.2440	0.6594	0.2153	0.6924	0.1649	0.7526
9	0.500	0.2912	0.7088	0.2602	0.7398	0.2047	0.7953
10	0.556	0.3406	0.7560	0.3076	0.7847	0.2474	0.8351
11	0.611	0.3922	0.8010	0.3575	0.8270	0.2932	0.8716
12	0.667	0.4460	0.8437	0.4099	0.8666	0.3421	0.9049
13	0.722	0.5022	0.8836	0.4652	0.9031	0.3945	0.9346
14	0.778	0.5611	0.9203	0.5236	0.9359	0.4508	0.9600
15	0.833	0.6233	0.9530	0.5858	0.9642	0.5116	0.9803
16	0.889	0.6897	0.9799	0.6529	0.9862	0.5783	0.9941
17	0.944	0.7623	0.9972	0.7271	0.9986	0.6537	0.9997
18	1.000	0.8467	1.0000	0.8147	1.0000	0.7450	1.0000

n = 19

n = 19
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1459	0.0000	0.1765	0.0000	0.2434
1	0.053	0.0027	0.2264	0.0013	0.2603	0.0003	0.3311
2	0.105	0.0190	0.2958	0.0130	0.3314	0.0056	0.4037
3	0.158	0.0445	0.3594	0.0338	0.3958	0.0186	0.4682
4	0.211	0.0753	0.4191	0.0605	0.4557	0.0378	0.5271
5	0.263	0.1099	0.4758	0.0915	0.5120	0.0617	0.5818
6	0.316	0.1475	0.5300	0.1258	0.5655	0.0895	0.6329
7	0.368	0.1875	0.5819	0.1629	0.6164	0.1207	0.6809
8	0.421	0.2297	0.6319	0.2025	0.6650	0.1549	0.7260
9	0.474	0.2739	0.6799	0.2445	0.7114	0.1919	0.7684
10	0.526	0.3201	0.7261	0.2886	0.7555	0.2316	0.8081
11	0.579	0.3681	0.7703	0.3350	0.7975	0.2740	0.8451
12	0.632	0.4181	0.8125	0.3836	0.8371	0.3191	0.8793
13	0.684	0.4700	0.8525	0.4345	0.8742	0.3671	0.9105
14	0.737	0.5242	0.8901	0.4880	0.9085	0.4182	0.9383
15	0.789	0.5809	0.9247	0.5443	0.9395	0.4729	0.9622
16	0.842	0.6406	0.9555	0.6042	0.9662	0.5318	0.9814
17	0.895	0.7042	0.9810	0.6686	0.9870	0.5963	0.9944
18	0.947	0.7736	0.9973	0.7397	0.9987	0.6689	0.9997
19	1.000	0.8541	1.0000	0.8235	1.0000	0.7566	1.0000

n = 20

n = 20
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1391	0.0000	0.1684	0.0000	0.2327
1	0.050	0.0026	0.2161	0.0013	0.2487	0.0003	0.3171
2	0.100	0.0181	0.2826	0.0123	0.3170	0.0053	0.3871
3	0.150	0.0422	0.3437	0.0321	0.3789	0.0176	0.4495
4	0.200	0.0714	0.4010	0.0573	0.4366	0.0358	0.5066
5	0.250	0.1041	0.4556	0.0866	0.4910	0.0583	0.5598
6	0.300	0.1396	0.5078	0.1189	0.5428	0.0846	0.6096
7	0.350	0.1773	0.5580	0.1539	0.5922	0.1139	0.6566
8	0.400	0.2171	0.6064	0.1912	0.6395	0.1460	0.7009
9	0.450	0.2587	0.6531	0.2306	0.6847	0.1806	0.7428
10	0.500	0.3020	0.6980	0.2720	0.7280	0.2177	0.7823
11	0.550	0.3469	0.7413	0.3153	0.7694	0.2572	0.8194
12	0.600	0.3936	0.7829	0.3605	0.8088	0.2991	0.8540
13	0.650	0.4420	0.8227	0.4078	0.8461	0.3434	0.8861
14	0.700	0.4922	0.8604	0.4572	0.8811	0.3904	0.9154
15	0.750	0.5444	0.8959	0.5090	0.9134	0.4402	0.9417
16	0.800	0.5990	0.9286	0.5634	0.9427	0.4934	0.9642
17	0.850	0.6563	0.9578	0.6211	0.9679	0.5505	0.9824
18	0.900	0.7174	0.9819	0.6830	0.9877	0.6129	0.9947
19	0.950	0.7839	0.9974	0.7513	0.9987	0.6829	0.9997
20	1.000	0.8609	1.0000	0.8316	1.0000	0.7673	1.0000

n = 21

n = 21
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1329	0.0000	0.1611	0.0000	0.2230
1	0.048	0.0024	0.2067	0.0012	0.2382	0.0002	0.3043
2	0.095	0.0172	0.2706	0.0117	0.3038	0.0050	0.3718
3	0.143	0.0401	0.3292	0.0305	0.3634	0.0168	0.4322
4	0.190	0.0678	0.3844	0.0545	0.4191	0.0339	0.4876
5	0.238	0.0988	0.4370	0.0822	0.4717	0.0553	0.5392
6	0.286	0.1324	0.4874	0.1128	0.5218	0.0801	0.5878
7	0.333	0.1682	0.5359	0.1459	0.5697	0.1078	0.6337
8	0.381	0.2057	0.5828	0.1811	0.6156	0.1381	0.6772
9	0.429	0.2450	0.6281	0.2182	0.6598	0.1707	0.7185
10	0.476	0.2858	0.6719	0.2571	0.7022	0.2055	0.7576
11	0.524	0.3281	0.7142	0.2978	0.7429	0.2424	0.7945
12	0.571	0.3719	0.7550	0.3402	0.7818	0.2815	0.8293
13	0.619	0.4172	0.7943	0.3844	0.8189	0.3228	0.8619
14	0.667	0.4641	0.8318	0.4303	0.8541	0.3663	0.8922
15	0.714	0.5126	0.8676	0.4782	0.8872	0.4122	0.9199
16	0.762	0.5630	0.9012	0.5283	0.9178	0.4608	0.9447
17	0.810	0.6156	0.9322	0.5809	0.9455	0.5124	0.9661
18	0.857	0.6708	0.9599	0.6366	0.9695	0.5678	0.9832
19	0.905	0.7294	0.9828	0.6962	0.9883	0.6282	0.9950
20	0.952	0.7933	0.9976	0.7618	0.9988	0.6957	0.9998
21	1.000	0.8671	1.0000	0.8389	1.0000	0.7770	1.0000

n = 22

n = 22
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1273	0.0000	0.1544	0.0000	0.2140
1	0.045	0.0023	0.1981	0.0012	0.2284	0.0002	0.2924
2	0.091	0.0164	0.2595	0.0112	0.2916	0.0048	0.3577
3	0.136	0.0382	0.3159	0.0291	0.3491	0.0160	0.4161
4	0.182	0.0646	0.3691	0.0519	0.4028	0.0323	0.4699
5	0.227	0.0941	0.4198	0.0782	0.4537	0.0526	0.5201
6	0.273	0.1260	0.4685	0.1073	0.5022	0.0761	0.5674
7	0.318	0.1599	0.5155	0.1386	0.5487	0.1024	0.6123
8	0.364	0.1956	0.5609	0.1720	0.5934	0.1310	0.6549
9	0.409	0.2327	0.6048	0.2071	0.6365	0.1618	0.6954
10	0.455	0.2713	0.6475	0.2439	0.6779	0.1946	0.7340
11	0.500	0.3113	0.6887	0.2822	0.7178	0.2293	0.7707
12	0.545	0.3525	0.7287	0.3221	0.7561	0.2660	0.8054
13	0.591	0.3952	0.7673	0.3635	0.7929	0.3046	0.8382
14	0.636	0.4391	0.8044	0.4066	0.8280	0.3451	0.8690
15	0.682	0.4845	0.8401	0.4513	0.8614	0.3877	0.8976
16	0.727	0.5315	0.8740	0.4978	0.8927	0.4326	0.9239
17	0.773	0.5802	0.9059	0.5463	0.9218	0.4799	0.9474
18	0.818	0.6309	0.9354	0.5972	0.9481	0.5301	0.9677
19	0.864	0.6841	0.9618	0.6509	0.9709	0.5839	0.9840
20	0.909	0.7405	0.9836	0.7084	0.9888	0.6423	0.9952
21	0.955	0.8019	0.9977	0.7716	0.9988	0.7076	0.9998
22	1.000	0.8727	1.0000	0.8456	1.0000	0.7860	1.0000

n = 23

n = 23
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1221	0.0000	0.1482	0.0000	0.2058
1	0.043	0.0022	0.1902	0.0011	0.2195	0.0002	0.2814
2	0.087	0.0157	0.2492	0.0107	0.2804	0.0046	0.3446
3	0.130	0.0365	0.3036	0.0278	0.3359	0.0153	0.4012
4	0.174	0.0617	0.3549	0.0495	0.3878	0.0308	0.4534
5	0.217	0.0898	0.4039	0.0746	0.4370	0.0502	0.5022
6	0.261	0.1202	0.4510	0.1023	0.4841	0.0725	0.5483
7	0.304	0.1525	0.4964	0.1321	0.5292	0.0974	0.5921
8	0.348	0.1863	0.5405	0.1638	0.5727	0.1246	0.6338
9	0.391	0.2216	0.5832	0.1971	0.6146	0.1537	0.6736
10	0.435	0.2582	0.6246	0.2319	0.6551	0.1848	0.7116
11	0.478	0.2961	0.6649	0.2682	0.6941	0.2176	0.7479
12	0.522	0.3351	0.7039	0.3059	0.7318	0.2521	0.7824
13	0.565	0.3754	0.7418	0.3449	0.7681	0.2884	0.8152
14	0.609	0.4168	0.7784	0.3854	0.8029	0.3264	0.8463
15	0.652	0.4595	0.8137	0.4273	0.8362	0.3662	0.8754
16	0.696	0.5036	0.8475	0.4708	0.8679	0.4079	0.9026
17	0.739	0.5490	0.8798	0.5159	0.8977	0.4517	0.9275
18	0.783	0.5961	0.9102	0.5630	0.9254	0.4978	0.9498
19	0.826	0.6451	0.9383	0.6122	0.9505	0.5466	0.9692
20	0.870	0.6964	0.9635	0.6641	0.9722	0.5988	0.9847
21	0.913	0.7508	0.9843	0.7196	0.9893	0.6554	0.9954
22	0.957	0.8098	0.9978	0.7805	0.9989	0.7186	0.9998
23	1.000	0.8779	1.0000	0.8518	1.0000	0.7942	1.0000

n = 24

n = 24
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1173	0.0000	0.1425	0.0000	0.1981
1	0.042	0.0021	0.1829	0.0011	0.2112	0.0002	0.2713
2	0.083	0.0150	0.2398	0.0103	0.2700	0.0044	0.3324
3	0.125	0.0350	0.2923	0.0266	0.3236	0.0146	0.3873
4	0.167	0.0590	0.3418	0.0474	0.3738	0.0295	0.4379
5	0.208	0.0859	0.3891	0.0713	0.4215	0.0479	0.4855
6	0.250	0.1149	0.4347	0.0977	0.4671	0.0692	0.5304
7	0.292	0.1457	0.4787	0.1262	0.5109	0.0930	0.5732
8	0.333	0.1780	0.5214	0.1563	0.5532	0.1188	0.6140
9	0.375	0.2116	0.5629	0.1880	0.5941	0.1465	0.6530
10	0.417	0.2464	0.6032	0.2211	0.6336	0.1759	0.6904
11	0.458	0.2824	0.6424	0.2555	0.6718	0.2070	0.7262
12	0.500	0.3194	0.6806	0.2912	0.7088	0.2396	0.7604
13	0.542	0.3576	0.7176	0.3282	0.7445	0.2738	0.7930
14	0.583	0.3968	0.7536	0.3664	0.7789	0.3096	0.8241
15	0.625	0.4371	0.7884	0.4059	0.8120	0.3470	0.8535
16	0.667	0.4786	0.8220	0.4468	0.8437	0.3860	0.8812
17	0.708	0.5213	0.8543	0.4891	0.8738	0.4268	0.9070
18	0.750	0.5653	0.8851	0.5329	0.9023	0.4696	0.9308
19	0.792	0.6109	0.9141	0.5785	0.9287	0.5145	0.9521
20	0.833	0.6582	0.9410	0.6262	0.9526	0.5621	0.9705
21	0.875	0.7077	0.9650	0.6764	0.9734	0.6127	0.9854
22	0.917	0.7602	0.9850	0.7300	0.9897	0.6676	0.9956
23	0.958	0.8171	0.9979	0.7888	0.9989	0.7287	0.9998
24	1.000	0.8827	1.0000	0.8575	1.0000	0.8019	1.0000

n = 25

n = 25
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1129	0.0000	0.1372	0.0000	0.1910
1	0.040	0.0020	0.1761	0.0010	0.2035	0.0002	0.2618
2	0.080	0.0144	0.2310	0.0098	0.2603	0.0042	0.3210
3	0.120	0.0335	0.2817	0.0255	0.3122	0.0140	0.3743
4	0.160	0.0566	0.3296	0.0454	0.3608	0.0282	0.4235
5	0.200	0.0823	0.3754	0.0683	0.4070	0.0459	0.4698
6	0.240	0.1101	0.4195	0.0936	0.4513	0.0663	0.5136
7	0.280	0.1395	0.4622	0.1207	0.4939	0.0889	0.5553
8	0.320	0.1703	0.5036	0.1495	0.5350	0.1135	0.5952
9	0.360	0.2024	0.5439	0.1797	0.5748	0.1399	0.6335
10	0.400	0.2356	0.5832	0.2113	0.6133	0.1679	0.6702
11	0.440	0.2699	0.6214	0.2440	0.6507	0.1974	0.7054
12	0.480	0.3051	0.6586	0.2780	0.6869	0.2283	0.7393
13	0.520	0.3414	0.6949	0.3131	0.7220	0.2607	0.7717
14	0.560	0.3786	0.7301	0.3493	0.7560	0.2946	0.8026
15	0.600	0.4168	0.7644	0.3867	0.7887	0.3298	0.8321
16	0.640	0.4561	0.7976	0.4252	0.8203	0.3665	0.8601
17	0.680	0.4964	0.8297	0.4650	0.8505	0.4048	0.8865
18	0.720	0.5378	0.8605	0.5061	0.8793	0.4447	0.9111
19	0.760	0.5805	0.8899	0.5487	0.9064	0.4864	0.9337
20	0.800	0.6246	0.9177	0.5930	0.9317	0.5302	0.9541
21	0.840	0.6704	0.9434	0.6392	0.9546	0.5765	0.9718
22	0.880	0.7183	0.9665	0.6878	0.9745	0.6257	0.9860
23	0.920	0.7690	0.9856	0.7397	0.9902	0.6790	0.9958
24	0.960	0.8239	0.9980	0.7965	0.9990	0.7382	0.9998
25	1.000	0.8871	1.0000	0.8628	1.0000	0.8090	1.0000

n = 26

n = 26
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1088	0.0000	0.1323	0.0000	0.1844
1	0.038	0.0020	0.1698	0.0010	0.1964	0.0002	0.2529
2	0.077	0.0138	0.2229	0.0095	0.2513	0.0041	0.3104
3	0.115	0.0322	0.2719	0.0245	0.3015	0.0134	0.3621
4	0.154	0.0543	0.3182	0.0436	0.3487	0.0271	0.4100
5	0.192	0.0790	0.3626	0.0655	0.3935	0.0440	0.4550
6	0.231	0.1056	0.4054	0.0897	0.4365	0.0635	0.4977
7	0.269	0.1338	0.4468	0.1157	0.4779	0.0852	0.5385
8	0.308	0.1633	0.4870	0.1433	0.5179	0.1087	0.5775
9	0.346	0.1940	0.5262	0.1721	0.5567	0.1338	0.6150
10	0.385	0.2257	0.5643	0.2023	0.5943	0.1605	0.6510
11	0.423	0.2584	0.6016	0.2335	0.6308	0.1886	0.6857
12	0.462	0.2921	0.6379	0.2659	0.6663	0.2181	0.7191
13	0.500	0.3266	0.6734	0.2993	0.7007	0.2489	0.7511
14	0.538	0.3621	0.7079	0.3337	0.7341	0.2809	0.7819
15	0.577	0.3984	0.7416	0.3692	0.7665	0.3143	0.8114
16	0.615	0.4357	0.7743	0.4057	0.7977	0.3490	0.8395
17	0.654	0.4738	0.8060	0.4433	0.8279	0.3850	0.8662
18	0.692	0.5130	0.8367	0.4821	0.8567	0.4225	0.8913
19	0.731	0.5532	0.8662	0.5221	0.8843	0.4615	0.9148
20	0.769	0.5946	0.8944	0.5635	0.9103	0.5023	0.9365
21	0.808	0.6374	0.9210	0.6065	0.9345	0.5450	0.9560
22	0.846	0.6818	0.9457	0.6513	0.9564	0.5900	0.9729
23	0.885	0.7281	0.9678	0.6985	0.9755	0.6379	0.9866
24	0.923	0.7771	0.9862	0.7487	0.9905	0.6896	0.9959
25	0.962	0.8302	0.9980	0.8036	0.9990	0.7471	0.9998
26	1.000	0.8912	1.0000	0.8677	1.0000	0.8156	1.0000

n = 27

n = 27
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1050	0.0000	0.1277	0.0000	0.1782
1	0.037	0.0019	0.1640	0.0009	0.1897	0.0002	0.2446
2	0.074	0.0133	0.2153	0.0091	0.2429	0.0039	0.3004
3	0.111	0.0310	0.2627	0.0235	0.2916	0.0129	0.3507
4	0.148	0.0522	0.3076	0.0419	0.3373	0.0260	0.3973
5	0.185	0.0759	0.3506	0.0630	0.3808	0.0423	0.4411
6	0.222	0.1015	0.3921	0.0862	0.4226	0.0610	0.4828
7	0.259	0.1285	0.4323	0.1111	0.4628	0.0817	0.5226
8	0.296	0.1568	0.4714	0.1375	0.5018	0.1042	0.5608
9	0.333	0.1862	0.5095	0.1652	0.5396	0.1283	0.5975
10	0.370	0.2166	0.5466	0.1940	0.5763	0.1538	0.6328
11	0.407	0.2479	0.5829	0.2239	0.6120	0.1807	0.6669
12	0.444	0.2801	0.6184	0.2548	0.6467	0.2088	0.6998
13	0.481	0.3131	0.6530	0.2867	0.6805	0.2381	0.7314
14	0.519	0.3470	0.6869	0.3195	0.7133	0.2686	0.7619
15	0.556	0.3816	0.7199	0.3533	0.7452	0.3002	0.7912
16	0.593	0.4171	0.7521	0.3880	0.7761	0.3331	0.8193
17	0.630	0.4534	0.7834	0.4237	0.8060	0.3672	0.8462
18	0.667	0.4905	0.8138	0.4604	0.8348	0.4025	0.8717
19	0.704	0.5286	0.8432	0.4982	0.8625	0.4392	0.8958
20	0.741	0.5677	0.8715	0.5372	0.8889	0.4774	0.9183
21	0.778	0.6079	0.8985	0.5774	0.9138	0.5172	0.9390
22	0.815	0.6494	0.9241	0.6192	0.9370	0.5589	0.9577
23	0.852	0.6924	0.9478	0.6627	0.9581	0.6027	0.9740
24	0.889	0.7373	0.9690	0.7084	0.9765	0.6493	0.9871
25	0.926	0.7847	0.9867	0.7571	0.9909	0.6996	0.9961
26	0.963	0.8360	0.9981	0.8103	0.9991	0.7554	0.9998
27	1.000	0.8950	1.0000	0.8723	1.0000	0.8218	1.0000

n = 28

n = 28
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.1015	0.0000	0.1234	0.0000	0.1724
1	0.036	0.0018	0.1585	0.0009	0.1835	0.0002	0.2369
2	0.071	0.0128	0.2082	0.0088	0.2350	0.0038	0.2911
3	0.107	0.0298	0.2542	0.0227	0.2823	0.0124	0.3399
4	0.143	0.0503	0.2977	0.0403	0.3267	0.0251	0.3853
5	0.179	0.0731	0.3394	0.0606	0.3689	0.0407	0.4280
6	0.214	0.0977	0.3797	0.0830	0.4095	0.0586	0.4687
7	0.250	0.1237	0.4187	0.1069	0.4487	0.0786	0.5076
8	0.286	0.1509	0.4567	0.1322	0.4867	0.1002	0.5449
9	0.321	0.1791	0.4938	0.1588	0.5235	0.1232	0.5808
10	0.357	0.2082	0.5300	0.1864	0.5593	0.1477	0.6155
11	0.393	0.2383	0.5654	0.2150	0.5942	0.1733	0.6490
12	0.429	0.2691	0.6000	0.2446	0.6282	0.2002	0.6814
13	0.464	0.3007	0.6338	0.2751	0.6613	0.2282	0.7126
14	0.500	0.3331	0.6669	0.3065	0.6935	0.2572	0.7428
15	0.536	0.3662	0.6993	0.3387	0.7249	0.2874	0.7718
16	0.571	0.4000	0.7309	0.3718	0.7554	0.3186	0.7998
17	0.607	0.4346	0.7617	0.4058	0.7850	0.3510	0.8267
18	0.643	0.4700	0.7918	0.4407	0.8136	0.3845	0.8523
19	0.679	0.5062	0.8209	0.4765	0.8412	0.4192	0.8768
20	0.714	0.5433	0.8491	0.5133	0.8678	0.4551	0.8998
21	0.750	0.5813	0.8763	0.5513	0.8931	0.4924	0.9214
22	0.786	0.6203	0.9023	0.5905	0.9170	0.5313	0.9414
23	0.821	0.6606	0.9269	0.6311	0.9394	0.5720	0.9593
24	0.857	0.7023	0.9497	0.6733	0.9597	0.6147	0.9749
25	0.893	0.7458	0.9702	0.7177	0.9773	0.6601	0.9876
26	0.929	0.7918	0.9872	0.7650	0.9912	0.7089	0.9962
27	0.964	0.8415	0.9982	0.8165	0.9991	0.7631	0.9998
28	1.000	0.8985	1.0000	0.8766	1.0000	0.8276	1.0000

n = 29

n = 29
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.0981	0.0000	0.1194	0.0000	0.1670
1	0.034	0.0018	0.1534	0.0009	0.1776	0.0002	0.2296
2	0.069	0.0124	0.2016	0.0085	0.2277	0.0036	0.2823
3	0.103	0.0288	0.2461	0.0219	0.2735	0.0120	0.3298
4	0.138	0.0485	0.2884	0.0389	0.3166	0.0242	0.3740
5	0.172	0.0705	0.3289	0.0585	0.3577	0.0392	0.4157
6	0.207	0.0942	0.3680	0.0799	0.3972	0.0565	0.4554
7	0.241	0.1192	0.4060	0.1030	0.4354	0.0756	0.4933
8	0.276	0.1453	0.4429	0.1273	0.4724	0.0964	0.5299
9	0.310	0.1725	0.4790	0.1528	0.5083	0.1185	0.5651
10	0.345	0.2005	0.5143	0.1794	0.5433	0.1420	0.5991
11	0.379	0.2293	0.5488	0.2069	0.5774	0.1666	0.6320
12	0.414	0.2589	0.5825	0.2352	0.6106	0.1923	0.6638
13	0.448	0.2893	0.6156	0.2645	0.6431	0.2191	0.6946
14	0.483	0.3203	0.6480	0.2945	0.6747	0.2469	0.7243
15	0.517	0.3520	0.6797	0.3253	0.7055	0.2757	0.7531
16	0.552	0.3844	0.7107	0.3569	0.7355	0.3054	0.7809
17	0.586	0.4175	0.7411	0.3894	0.7648	0.3362	0.8077
18	0.621	0.4512	0.7707	0.4226	0.7931	0.3680	0.8334
19	0.655	0.4857	0.7995	0.4567	0.8206	0.4009	0.8580
20	0.690	0.5210	0.8275	0.4917	0.8472	0.4349	0.8815
21	0.724	0.5571	0.8547	0.5276	0.8727	0.4701	0.9036
22	0.759	0.5940	0.8808	0.5646	0.8970	0.5067	0.9244
23	0.793	0.6320	0.9058	0.6028	0.9201	0.5446	0.9435
24	0.828	0.6711	0.9295	0.6423	0.9415	0.5843	0.9608
25	0.862	0.7116	0.9515	0.6834	0.9611	0.6260	0.9758
26	0.897	0.7539	0.9712	0.7265	0.9781	0.6702	0.9880
27	0.931	0.7984	0.9876	0.7723	0.9915	0.7177	0.9964
28	0.966	0.8466	0.9982	0.8224	0.9991	0.7704	0.9998
29	1.000	0.9019	1.0000	0.8806	1.0000	0.8330	1.0000

n = 30

n = 30
		90% CI		95% CI		99% CI
x	p̂ = x/n	Lower	Upper	Lower	Upper	Lower	Upper
0	0.000	0.0000	0.0950	0.0000	0.1157	0.0000	0.1619
1	0.033	0.0017	0.1486	0.0008	0.1722	0.0002	0.2228
2	0.067	0.0120	0.1953	0.0082	0.2207	0.0035	0.2740
3	0.100	0.0278	0.2386	0.0211	0.2653	0.0116	0.3203
4	0.133	0.0469	0.2796	0.0376	0.3072	0.0233	0.3634
5	0.167	0.0681	0.3190	0.0564	0.3472	0.0378	0.4040
6	0.200	0.0909	0.3570	0.0771	0.3857	0.0545	0.4428
7	0.233	0.1150	0.3939	0.0993	0.4228	0.0729	0.4799
8	0.267	0.1402	0.4299	0.1228	0.4589	0.0929	0.5156
9	0.300	0.1663	0.4651	0.1473	0.4940	0.1142	0.5501
10	0.333	0.1933	0.4994	0.1729	0.5281	0.1367	0.5834
11	0.367	0.2211	0.5331	0.1993	0.5614	0.1604	0.6157
12	0.400	0.2495	0.5661	0.2266	0.5940	0.1850	0.6470
13	0.433	0.2787	0.5984	0.2546	0.6257	0.2107	0.6773
14	0.467	0.3085	0.6301	0.2834	0.6567	0.2373	0.7067
15	0.500	0.3389	0.6611	0.3130	0.6870	0.2648	0.7352
16	0.533	0.3699	0.6915	0.3433	0.7166	0.2933	0.7627
17	0.567	0.4016	0.7213	0.3743	0.7454	0.3227	0.7893
18	0.600	0.4339	0.7505	0.4060	0.7734	0.3530	0.8150
19	0.633	0.4669	0.7789	0.4386	0.8007	0.3843	0.8396
20	0.667	0.5006	0.8067	0.4719	0.8271	0.4166	0.8633
21	0.700	0.5349	0.8337	0.5060	0.8527	0.4499	0.8858
22	0.733	0.5701	0.8598	0.5411	0.8772	0.4844	0.9071
23	0.767	0.6061	0.8850	0.5772	0.9007	0.5201	0.9271
24	0.800	0.6430	0.9091	0.6143	0.9229	0.5572	0.9455
25	0.833	0.6810	0.9319	0.6528	0.9436	0.5960	0.9622
26	0.867	0.7204	0.9531	0.6928	0.9624	0.6366	0.9767
27	0.900	0.7614	0.9722	0.7347	0.9789	0.6797	0.9884
28	0.933	0.8047	0.9880	0.7793	0.9918	0.7260	0.9965
29	0.967	0.8514	0.9983	0.8278	0.9992	0.7772	0.9998
30	1.000	0.9050	1.0000	0.8843	1.0000	0.8381	1.0000

Tip: click any value to highlight its row and column.

How to read this table

Find the block for your sample size n.
Go to the row for the observed number of successes x.
Read the lower and upper limits for your confidence level. They are proportions: multiply by 100 for percentages.

Worked example

A single-arm Phase II trial observes 3 responses in 20 patients (15%). In the n = 20 block, row x = 3, 95% columns gives a 95% confidence interval of 0.0321 to 0.3789, or about 3.2% to 37.9%. Even a 15% observed response rate is consistent with a true rate as low as 3% or as high as 38%, which is why small trials are usually treated as screening studies.

With 0 responses in 20, row x = 0 gives an upper 95% limit of 0.1684. The quick "rule of three" approximation, 3/n = 0.15, is slightly smaller.

Click the underlined links to highlight the value in the table.

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Formula and how the values were computed

Lower = B(α/2; x, n − x + 1) · Upper = B(1 − α/2; x + 1, n − x), where B is the beta quantile

Limits are computed exactly from the beta distribution (equivalently, by inverting two one-sided binomial tests) and rounded to four decimals. When x = 0 the lower limit is 0, and when x = n the upper limit is 1.

Frequently asked questions

Why use the exact interval instead of p̂ ± 1.96 SE?

The simple Wald interval can extend below 0 or above 1 and has poor coverage for small n or proportions near 0 or 1. The Clopper-Pearson interval always covers the true proportion at least as often as stated.

Is the exact interval too wide?

It is conservative: its actual coverage is at least the stated level, so it can be wider than necessary. The Wilson and Jeffreys intervals are narrower alternatives with close to nominal coverage.

Exact Binomial Confidence Intervals (Clopper-Pearson Table)

Clopper-Pearson Exact CI

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7

n = 8

n = 9

n = 10

n = 11

n = 12

n = 13

n = 14

n = 15

n = 16

n = 17

n = 18

n = 19

n = 20

n = 21

n = 22

n = 23

n = 24

n = 25

n = 26

n = 27

n = 28

n = 29

n = 30

How to read this table

Worked example

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Formula and how the values were computed

Frequently asked questions

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