Critical Values of the t Distribution

df	Proportion in One Tail
	.10	.05	.025	.01	.005	.001	.0005
	Proportion in Two Tails
	.20	.10	.05	.02	.01	.002	.001
1	3.078	6.314	12.706	31.821	63.657	318.309	636.619
2	1.886	2.920	4.303	6.964	9.925	22.327	31.599
3	1.638	2.353	3.182	4.541	5.841	10.214	12.924
4	1.533	2.132	2.776	3.747	4.604	7.173	8.610
5	1.476	2.015	2.570	3.365	4.032	5.893	6.869
6	1.440	1.943	2.447	3.143	3.707	5.208	5.959
7	1.415	1.895	2.365	2.998	3.499	4.785	5.408
8	1.397	1.860	2.306	2.896	3.355	4.501	5.041
9	1.383	1.833	2.262	2.821	3.250	4.297	4.781
10	1.372	1.812	2.228	2.764	3.169	4.144	4.587
11	1.363	1.796	2.201	2.718	3.106	4.025	4.437
12	1.356	1.782	2.179	2.681	3.054	3.930	4.318
13	1.350	1.771	2.160	2.650	3.012	3.852	4.221
14	1.345	1.761	2.145	2.624	2.977	3.787	4.140
15	1.341	1.753	2.131	2.602	2.947	3.733	4.073
16	1.337	1.746	2.120	2.583	2.921	3.686	4.015
17	1.333	1.740	2.110	2.567	2.898	3.646	3.965
18	1.330	1.734	2.101	2.552	2.878	3.610	3.922
19	1.328	1.729	2.093	2.539	2.861	3.579	3.883
20	1.325	1.725	2.086	2.528	2.845	3.552	3.849
df	Proportion in One Tail
	.10	.05	.025	.01	.005	.001	.0005
	Proportion in Two Tails
	.20	.10	.05	.02	.01	.002	.001
21	1.323	1.721	2.080	2.518	2.831	3.527	3.819
22	1.321	1.717	2.074	2.508	2.819	3.505	3.792
23	1.319	1.714	2.069	2.500	2.807	3.485	3.768
24	1.318	1.711	2.064	2.492	2.797	3.467	3.745
25	1.316	1.708	2.060	2.485	2.787	3.450	3.725
26	1.315	1.706	2.056	2.479	2.779	3.435	3.707
27	1.314	1.703	2.052	2.473	2.771	3.421	3.689
28	1.313	1.701	2.048	2.467	2.763	3.408	3.674
29	1.311	1.699	2.045	2.462	2.756	3.396	3.659
30	1.310	1.697	2.042	2.457	2.750	3.385	3.646
31	1.309	1.696	2.040	2.453	2.744	3.375	3.633
32	1.309	1.694	2.037	2.449	2.738	3.365	3.622
33	1.308	1.692	2.035	2.445	2.733	3.356	3.611
34	1.307	1.691	2.032	2.441	2.728	3.348	3.601
35	1.306	1.690	2.030	2.438	2.724	3.340	3.591
36	1.306	1.688	2.028	2.434	2.719	3.333	3.582
37	1.305	1.687	2.026	2.431	2.715	3.326	3.574
38	1.304	1.686	2.024	2.428	2.711	3.319	3.566
39	1.304	1.685	2.023	2.426	2.708	3.313	3.558
40	1.303	1.684	2.021	2.423	2.704	3.307	3.551
df	Proportion in One Tail
	.10	.05	.025	.01	.005	.001	.0005
	Proportion in Two Tails
	.20	.10	.05	.02	.01	.002	.001
41	1.303	1.683	2.020	2.421	2.701	3.301	3.544
42	1.302	1.682	2.018	2.418	2.698	3.296	3.538
43	1.302	1.681	2.017	2.416	2.695	3.291	3.532
44	1.301	1.680	2.015	2.414	2.692	3.286	3.526
45	1.301	1.679	2.014	2.412	2.689	3.281	3.520
46	1.300	1.679	2.013	2.410	2.687	3.277	3.515
47	1.300	1.678	2.012	2.408	2.684	3.273	3.510
48	1.299	1.677	2.011	2.406	2.682	3.269	3.505
49	1.299	1.677	2.010	2.405	2.680	3.265	3.500
50	1.299	1.676	2.009	2.403	2.678	3.261	3.496
51	1.298	1.675	2.008	2.402	2.676	3.258	3.492
52	1.298	1.675	2.007	2.400	2.674	3.254	3.488
53	1.298	1.674	2.006	2.399	2.672	3.251	3.484
54	1.297	1.674	2.005	2.397	2.670	3.248	3.480
55	1.297	1.673	2.004	2.396	2.668	3.245	3.476
56	1.297	1.673	2.003	2.395	2.666	3.242	3.473
57	1.297	1.672	2.002	2.393	2.665	3.239	3.469
58	1.296	1.672	2.002	2.392	2.663	3.237	3.466
59	1.296	1.671	2.001	2.391	2.662	3.234	3.463
60	1.296	1.671	2.000	2.390	2.660	3.232	3.460
df	Proportion in One Tail
	.10	.05	.025	.01	.005	.001	.0005
	Proportion in Two Tails
	.20	.10	.05	.02	.01	.002	.001
61	1.296	1.670	2.000	2.389	2.659	3.229	3.457
62	1.295	1.670	1.999	2.388	2.657	3.227	3.454
63	1.295	1.669	1.998	2.387	2.656	3.225	3.452
64	1.295	1.669	1.998	2.386	2.655	3.222	3.449
65	1.295	1.669	1.997	2.385	2.654	3.220	3.446
66	1.295	1.668	1.997	2.384	2.652	3.218	3.444
67	1.294	1.668	1.996	2.383	2.651	3.216	3.442
68	1.294	1.668	1.995	2.382	2.650	3.214	3.439
69	1.294	1.667	1.995	2.382	2.649	3.212	3.437
70	1.294	1.667	1.994	2.381	2.648	3.211	3.435
71	1.294	1.667	1.994	2.380	2.647	3.209	3.433
72	1.293	1.666	1.993	2.379	2.646	3.207	3.431
73	1.293	1.666	1.993	2.378	2.645	3.206	3.429
74	1.293	1.666	1.993	2.378	2.644	3.204	3.427
75	1.293	1.665	1.992	2.377	2.643	3.202	3.425
76	1.293	1.665	1.992	2.376	2.642	3.201	3.423
77	1.293	1.665	1.991	2.376	2.641	3.199	3.421
78	1.292	1.665	1.991	2.375	2.640	3.198	3.420
79	1.292	1.664	1.990	2.374	2.639	3.197	3.418
80	1.292	1.664	1.990	2.374	2.639	3.195	3.416
df	Proportion in One Tail
	.10	.05	.025	.01	.005	.001	.0005
	Proportion in Two Tails
	.20	.10	.05	.02	.01	.002	.001
81	1.292	1.664	1.990	2.373	2.638	3.194	3.415
82	1.292	1.664	1.989	2.373	2.637	3.193	3.413
83	1.292	1.663	1.989	2.372	2.636	3.191	3.412
84	1.292	1.663	1.989	2.371	2.636	3.190	3.410
85	1.292	1.663	1.988	2.371	2.635	3.189	3.409
86	1.291	1.663	1.988	2.370	2.634	3.188	3.407
87	1.291	1.663	1.988	2.370	2.633	3.186	3.406
88	1.291	1.662	1.987	2.369	2.633	3.185	3.404
89	1.291	1.662	1.987	2.369	2.632	3.184	3.403
90	1.291	1.662	1.987	2.368	2.631	3.183	3.402
91	1.291	1.662	1.986	2.368	2.631	3.182	3.401
92	1.291	1.662	1.986	2.367	2.630	3.181	3.399
93	1.291	1.661	1.986	2.367	2.630	3.180	3.398
94	1.291	1.661	1.986	2.367	2.629	3.179	3.397
95	1.291	1.661	1.985	2.366	2.628	3.178	3.396
96	1.290	1.661	1.985	2.366	2.628	3.177	3.395
97	1.290	1.661	1.985	2.365	2.627	3.176	3.394
98	1.290	1.661	1.984	2.365	2.627	3.175	3.392
99	1.290	1.660	1.984	2.365	2.626	3.175	3.391
100	1.290	1.660	1.984	2.364	2.626	3.174	3.390
df	Proportion in One Tail
	.10	.05	.025	.01	.005	.001	.0005
	Proportion in Two Tails
	.20	.10	.05	.02	.01	.002	.001
101	1.290	1.660	1.984	2.364	2.625	3.173	3.389
102	1.290	1.660	1.983	2.363	2.625	3.172	3.388
103	1.290	1.660	1.983	2.363	2.624	3.171	3.387
104	1.290	1.660	1.983	2.363	2.624	3.170	3.386
105	1.290	1.659	1.983	2.362	2.623	3.170	3.386
106	1.290	1.659	1.983	2.362	2.623	3.169	3.385
107	1.290	1.659	1.982	2.362	2.622	3.168	3.384
108	1.289	1.659	1.982	2.361	2.622	3.167	3.383
109	1.289	1.659	1.982	2.361	2.622	3.167	3.382
110	1.289	1.659	1.982	2.361	2.621	3.166	3.381
111	1.289	1.659	1.982	2.360	2.621	3.165	3.380
112	1.289	1.659	1.981	2.360	2.620	3.164	3.379
113	1.289	1.658	1.981	2.360	2.620	3.164	3.379
114	1.289	1.658	1.981	2.359	2.620	3.163	3.378
115	1.289	1.658	1.981	2.359	2.619	3.163	3.377
116	1.289	1.658	1.981	2.359	2.619	3.162	3.376
117	1.289	1.658	1.980	2.359	2.618	3.161	3.376
118	1.289	1.658	1.980	2.358	2.618	3.161	3.375
119	1.289	1.658	1.980	2.358	2.618	3.160	3.374
120	1.289	1.658	1.980	2.358	2.617	3.159	3.373

Critical Values of the t Distribution

p From t_Observed

Critical t

Critical Values of the t Distribution

p From tObserved

Critical t

p From t_Observed