確率分布表

正規分布表Ⅰ

\(\displaystyle P=P_r(Z≧u)= \frac{1}{\sqrt{2π}}\int_{u}^∞e^{\frac{-u^2}{2}du}\)

u	*=0	1	2	3	4	5	6	7	8	9
0.0.*	0.500	0.496	0.492	0.488	0.484	0.480	0.476	0.47	0.468	0.46
0.1.*	0.460	0.456	0.452	0.448	0.444	0.44	0.436	0.432	0.428	0.424
0.2.*	0.420	0.416	0.412	0.409	0.405	0.401	0.397	0.393	0.389	0.385
0.3.*	0.382	0.378	0.374	0.370	0.366	0.363	0.359	0.355	0.351	0.348
0.4.*	0.344	0.340	0.337	0.333	0.329	0.326	0.32	0.319	0.315	0.312
0.5.*	0.308	0.305	0.301	0.298	0.294	0.291	0.287	0.284	0.280	0.277
0.6*	0.274	0.270	0.267	0.264	0.261	0.257	0.254	0.251	0.248	0.245
0.7*	0.241	0.238	0.235	0.232	0.229	0.226	0.223	0.220	0.217	0.214
0.8*	0.211	0.208	0.206	0.203	0.200	0.197	0.194	0.192	0.189	0.186
0.9*	0.184	0.181	0.178	0.176	0.173	0.171	0.168	0.166	0.163	0.161
1.0*	0.158	0.156	0.153	0.151	0.149	0.146	0.144	0.142	0.140	0.137
1.1*	0.135	0.133	0.131	0.129	0.127	0.125	0.123	0.121	0.119	0.117
1.2*	0.115	0.113	0.111	0.109	0.107	0.105	0.103	0.102	0.100	0.098
1.3*	0.096	0.095	0.093	0.091	0.090	0.088	0.086	0.085	0.083	0.082
1.4*	0.080	0.079	0.077	0.076	0.074	0.073	0.072	0.070	0.069	0.068
1.5*	0.066	0.065	0.064	0.063	0.061	0.060	0.059	0.058	0.057	0.055
1.6*	0.054	0.053	0.052	0.051	0.050	0.049	0.048	0.047	0.046	0.045
1.7*	0.044	0.043	0.042	0.041	0.040	0.040	0.039	0.038	0.037	0.036
1.8*	0.035	0.035	0.034	0.033	0.032	0.032	0.031	0.030	0.030	0.029
1.9*	0.028	0.028	0.027	0.026	0.026	0.025	0.025	0.024	0.023	0.023
2.0*	0.022	0.022	0.021	0.021	0.020	0.020	0.019	0.019	0.018	0.018
2.1*	0.017	0.017	0.017	0.016	0.016	0.015	0.015	0.015	0.014	0.014
2.2*	0.013	0.013	0.013	0.012	0.012	0.012	0.011	0.011	0.011	0.011
2.3*	0.01	0.01	0.01	0.009	0.009	0.009	0.009	0.008	0.008	0.008
2.4*	0.008	0.007	0.007	0.007	0.007	0.007	0.006	0.006	0.006	0.006
2.5*	0.006	0.006	0.005	0.005	0.005	0.005	0.005	0.005	0.004	0.004
2.6*	0.004	0.004	0.004	0.004	0.004	0.004	0.003	0.003	0.003	0.003
2.7*	0.003	0.003	0.003	0.003	0.003	0.002	0.002	0.002	0.002	0.002
2.8*	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.001	0.001
2.9*	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001
3.0*	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001
4.0*	0.00003	0.00003	0.00003	0.00003	0.00003	0.00002	0.00002	0.00002	0.00002	0.00002

正規分布表Ⅱ

P	0.001	0.005	0.01	0.025	0.05	0.1	0.2	0.3	0.4
u	3.09	2.576	2.376	1.96	1.645	1.282	0.845	0.524	0.253

\(χ^2\)表

\(自由度Φ,片側上限確率Pからχ^2(Φ,P)\)を求める表

Φ/P	0.995	0.99	0.975	0.95	0.5	0.1	0.05	0.025	0.01	0.005
1	0.00004	0.0002	0.001	0.0039	0.455	2.710	3.84	5.02	6.63	7.88
2	0.01003	0.02010	0.0506	0.1026	1.386	4.61	5.99	7.38	9.21	10.6
3	0.07172	0.1148	0.2158	0.352	2.37	6.25	7.81	9.35	11.3	12.8
4	0.2070	0.2971	0.484	0.711	3.36	7.78	9.49	11.1	13.3	14.9
5	0.4117	0.554	0.831	1.15	4.35	9.24	11.07	12.8	15.1	16.8
6	0.676	0.872	1.24	1.64	5.35	10.64	12.6	14.5	16.8	18.6
7	0.989	1.24	1.69	2.17	6.35	12.02	14.1	16.0	18.5	20.3
8	1.34	1.65	2.18	2.73	7.34	13.4	15.5	17.5	20.1	22.0
9	1.73	2.09	2.70	3.33	8.34	14.7	16.9	19.0	21.7	23.6
10	2.16	2.56	3.25	3.94	9.34	16.0	18.3	20.5	23.2	25.2
11	2.60	3.05	3.82	4.57	10.3	17.3	19.7	21.9	24.7	26.8
12	3.07	3.57	4.40	5.23	11.3	18.6	21.0	23.3	26.2	28.3
13	3.57	4.11	5.01	5.89	12.3	19.8	22.4	24.7	27.7	29.8
14	4.07	4.66	5.63	6.57	13.3	21.1	23.7	26.1	29.1	31.3
15	4.60	5.23	6.26	7.26	14.3	22.3	25.0	27.5	30.6	32.8
16	5.14	5.81	6.91	7.96	15.3	23.5	26.3	28.9	32.0	34.3
17	5.70	6.41	7.56	8.67	16.3	24.8	27.6	30.2	33.4	35.7
18	6.26	7.01	8.23	9.39	17.3	26.0	28.9	31.5	34.8	37.2
19	6.84	7.63	8.91	10.1	18.3	27.2	30.1	32.9	36.2	38.6
20	7.43	8.26	9.59	10.9	19.3	28.4	31.4	34.2	37.6	40.0
21	8.03	8.90	10.3	11.6	20.3	29.6	32.7	35.5	38.9	41.4
22	8.64	9.54	11.0	12.3	21.3	30.8	33.9	36.8	40.3	42.8
23	9.26	10.2	11.7	13.1	22.3	32.0	35.2	38.1	41.6	44.2
24	9.89	10.9	12.4	13.9	23.3	33.2	36.4	39.4	43.0	45.6
25	10.5	11.5	13.1	14.6	24.3	34.4	37.7	40.7	44.3	46.9
26	11.2	12.2	13.8	15.4	25.3	35.6	38.9	41.9	45.6	48.3
27	11.8	12.9	14.6	16.2	26.3	36.7	40.1	43.2	47.0	49.6
28	12.5	13.6	15.3	16.9	27.3	37.9	41.3	44.5	48.3	51.0
29	13.1	14.3	16.1	17.7	28.3	39.1	42.6	45.7	49.6	52.3
30	13.8	15.0	16.8	18.5	29.3	40.3	43.8	47.0	50.9	53.7
40	20.7	22.2	24.4	26.5	39.3	51.8	55.8	59.3	63.7	66.8
50	28.0	29.7	32.4	34.8	49.3	63.2	67.5	71.4	76.2	79.5
60	35.5	37.5	40.5	43.2	59.3	74.4	79.1	83.3	88.4	92.0
80	51.2	53.5	57.2	60.4	79.3	96.6	101.9	106.6	112.3	116.3
100	67.3	70.1	74.2	77.9	99.3	118.5	124.3	129.6	135.8	140.2

t　表

\(t(Φ,P)\)

\(自由度Φと両側確率Pからtを求める表\)

Φ/P	0.5	0.4	0.3	0.2	0.1	0.05	0.02	0.01	0.001
1	1.000	1.376	1.963	3.078	6.314	12.706	31.821	63.657	636.619
2	0.816	1.0061	1.386	1.886	2.920	4.303	6.965	9.925	31.599
3	0.765	0.978	1.25	1.638	2.353	3.182	4.541	5.841	12.924
4	0.741	0.941	1.190	1.533	2.132	2.776	3.747	4.604	8.610
5	0.727	0.920	1.156	1.476	2.015	2.571	3.365	4.032	6.869
6	0.718	0.906	1.134	1.440	1.943	2.447	3.143	3.707	5.959
7	0.711	0.896	1.119	1.415	1.895	2.365	2.998	3.499	5.408
8	0.706	0.889	1.108	1.397	1.860	2.306	2.896	3.355	5.041
9	0.703	0.883	1.100	1.383	1.833	2.262	2.821	3.250	4.781
10	0.700	0.879	1.093	1.372	1.812	2.228	2.764	3.169	4.587
11	0.697	0.876	1.088	1.363	1.796	2.201	2.718	3.106	4.437
12	0.695	0.873	1.083	1.356	1.782	2.179	2.681	3.055	4.318
13	0.694	0.870	1.079	1.350	1.771	2.160	2.650	3.012	4.221
14	0.692	0.868	1.076	1.345	1.761	2.145	2.624	2.977	4.140
15	0.691	0.866	1.074	1.341	1.753	2.131	2.602	2.947	4.073
16	0.69	0.865	1.071	1.337	1.746	2.120	2.583	2.921	4.015
17	0.689	0.863	1.069	1.333	1.740	2.110	2.567	2.898	3.965
18	0.688	0.862	1.067	1.330	1.734	2.101	2.552	2.878	3.922
19	0.688	0.861	1.066	1.328	1.729	2.093	2.539	2.861	3.883
20	0.687	0.860	1.064	1.325	1.725	2.086	2.528	2.845	3.850
21	0.686	0.859	1.063	1.323	1.721	2.080	2.518	2.831	2.819
22	0.686	0.858	1.061	1.321	1.717	2.074	2.508	2.819	3.792
23	0.685	0.858	1.060	1.319	1.714	2.069	2.500	2.807	3.768
24	0.685	0.857	1.059	1.318	1.711	2.064	2.492	2.797	3.745
25	0.684	0.856	1.058	1.316	1.708	2.060	2.485	2.787	3.725
26	0.684	0.856	1.057	1.315	1.706	2.056	2.479	2.779	3.707
27	0.684	0.855	1.056	1.314	1.703	2.052	2.473	2.771	3.690
28	0.683	0.855	1.056	1.313	1.701	2.048	2.467	2.763	3.674
29	0.683	0.854	1.055	1.311	1.699	2.045	2.462	2.756	3.659
30	0.683	0.854	1.055	1.310	1.697	2.042	2.457	2.750	3.646
40	0.681	0.851	1.050	1.303	1.684	2.021	2.423	2.704	3.551
60	0.679	0.848	1.045	1.296	1.671	2.000	2.390	2.660	3.460
120	0.677	0.845	1.041	1.289	1.658	1.980	2.358	2.617	3.373
∞	0.674	0.842	1.036	1.282	1.645	1.960	2.326	2.576	3.291

F表(5%,1%)

\(F(Φ_1,Φ_2:P)\)
P=0.05・・細字
P=0.01・・青太字

上側確率5%と1%を求める表

Φ2/Φ1	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120	∞
1	161 4052	200 5000	216 5403	225 5625	230 5764	234 5859	237 5928	239 5981	241 6022	242 6056	244 6106	246 6157	248 6209	249 6235	250 6261	251 6287	252 6313	253 6339	254 6366
2	18.5 98.5	19.0 99.0	19.2 99.2	19.2 99.2	19.3 99.3	19.3 99.3	19.4 99.4	19.4 99.4	19.4 99.4	19.4 99.4	19.4 99.4	19.4 99.4	19.4 99.4	19.5 99.5	19.5 99.5	19.5 99.5	19.5 99.5	19.5 99.5	19.5 99.5
3	10.1 34.1	9.55 30.8	9.28 29.5	9.12 28.7	9.01 28.2	8.94 29.5	8.89 28.7	8.85 28.2	8.81 27.9	8.79 27.7	8.74 27.5	8.7 27.3	8.66 26.7	8.64 26.6	8.62 26.5	8.59 26.4	8.57 26.3	8.55 26.2	8.53 26.1
4	7.71 21.2	6.94 18.0	6.59 16.7	6.39 16.0	6.26 15.5	6.16 15.2	6.09 15.0	6.04 14.8	6.00 14.7	5.96 14.5	5.91 14.4	5.86 14.2	5.8 14.0	5.77 13.9	5.75 13.8	5.72 13.7	5.69 13.7	5.66 13.6	5.63 13.5
5	6.61 16.3	5.79 5.41	5.41 12.1	5.19 11.4	5.05 11.0	4.95 10.7	4.88 10.5	4.82 10.3	4.77 10.2	4.74 10.1	4.68 9.89	4.62 9.72	4.56 9.55	4.53 9.47	4.5 9.38	4.46 9.29	4.43 9.2	4.4 9.11	4.36 9.02
6	5.99 13.7	5.14 10.9	4.76 9.78	4.53 9.15	4.39 8.75	4.28 8.47	4.21 8.26	4.15 8.10	4.10 7.98	4.06 7.87	4.00 7.72	3.94 7.56	3.87 7.40	3.84 7.31	3.81 7.23	3.77 7.14	3.74 7.06	3.70 6.97	3.67 6.88
7	5.59 13.7	4.74 9.55	4.35 8.45	4.12 7.85	3.97 7.46	3.87 7.19	3.79 6.99	3.73 6.84	3.68 6.72	3.64 6.62	3.57 6.47	3.51 6.31	3.44 6.16	3.41 6.07	3.38 5.99	3.34 5.91	3.30 5.82	3.27 5.74	3.23 5.65
8	5.32 11.3	4.46 8.65	4.07 7.59	3.84 7.01	3.69 6.63	3.58 6.37	3.50 6.18	3.44 6.03	3.39 5.91	3.35 5.81	3.28 5.67	3.22 5.52	3.15 5.36	3.12 5.28	3.08 5.20	3.04 5.12	3.01 5.03	2.97 4.95	2.93 4.86
9	5.12 10.6	4.26 8.02	3.86 6.99	3.63 6.42	3.48 6.06	3.37 5.80	3.29 5.61	3.23 5.43	3.18 5.35	3.14 5.26	3.07 5.11	3.01 4.96	2.94 4.81	2.90 4.73	2.86 4.65	2.83 4.57	2.79 4.48	2.75 4.40	2.71 4.31
10	4.96 10.0	4.10 7.56	3.71 6.55	3.48 5.99	3.33 5.64	3.22 5.39	3.14 5.20	3.07 5.06	3.02 4.94	2.98 4.85	2.91 4.71	2.85 4.56	2.77 4.41	2.74 4.33	2.70 4.25	2.66 4.17	2.62 4.08	2.58 4.00	2.54 3.91
11	4.84 9.65	3.98 7.21	3.59 6.22	3.36 5.67	3.20 5.32	3.09 5.07	3.01 4.89	2.95 4.74	2.90 4.63	2.85 4.54	2.79 4.40	2.72 4.25	2.65 4.10	2.61 4.02	2.57 3.94	2.53 3.86	2.49 3.78	2.45 3.69	2.40 3.60
12	4.75 9.33	3.89 6.93	3.49 5.95	3.26 5.41	3.11 5.06	3.00 4.82	2.91 4.64	2.85 4.50	2.80 4.39	2.75 4.30	2.69 4.16	2.62 4.01	2.54 3.86	2.51 3.78	2.47 3.70	2.43 3.62	2.38 3.54	2.34 3.45	2.30 3.36
13	4.67 9.07	3.81 6.70	3.41 5.74	3.18 5.21	3.03 4.86	2.92 4.62	2.83 4.44	2.77 4.3	2.71 4.19	2.67 4.10	2.60 3.96	2.53 3.85	2.46 3.66	2.42 3.59	2.38 3.51	2.34 3.43	2.30 3.34	2.25 3.25	2.21 3.17
14	4.60 8.86	3.74 6.51	3.34 5.56	3.11 5.04	2.96 4.69	2.85 4.46	2.76 4.28	2.70 4.14	2.65 3.94	2.60 3.94	2.53 3.80	2.46 3.66	2.39 3.51	2.35 3.43	2.31 3.35	2.27 3.27	2.22 3.18	2.18 3.09	2.13 3.00
15	4.54 8.68	3.68 6.36	3.29 5.42	3.06 4.86	2.90 4.56	2.79 4.32	2.71 4.14	2.64 4.00	2.59 3.89	2.54 3.80	2.48 3.67	2.40 3.52	2.33 3.37	2.29 3.29	2.25 3.21	2.20 3.13	2.16 3.05	2.11 2.96	2.07 2.87
16	4.49 8.53	3.63 6.23	3.24 5.29	3.01 4.77	2.85 4.44	2.74 4.20	2.66 4.03	2.59 3.89	2.54 3.78	2.49 3.69	2.42 3.69	2.35 3.41	2.28 3.26	2.24 3.18	2.19 3.10	2.15 3.02	2.11 2.93	2.06 2.84	2.01 2.75
17	4.45 8.40	3.59 6.11	3.20 5.18	2.96 4.67	2.81 4.34	2.70 4.10	2.61 3.93	2.55 3.79	2.49 3.68	2.45 3.45	2.38 3.46	2.31 3.31	2.23 3.15	2.19 3.08	2.15 3.00	2.10 2.92	2.06 2.83	2.01 2.75	1.96 2.65
18	4.41 8.29	3.55 6.01	3.16 5.09	2.93 4.58	2.77 4.25	2.66 4.01	2.58 3.84	2.51 3.71	2.46 3.60	2.41 3.51	2.34 3.60	2.27 3.23	2.19 3.08	2.15 3.00	2.11 2.92	2.06 2.84	2.02 2.75	1.97 2.66	1.92 2.57
19	4.38 8.18	3.52 5.93	3.13 5.01	2.90 4.50	2.74 4.17	2.63 3.94	2.54 3.77	2.48 3.63	2.42 3.52	2.38 3.43	2.31 3.30	2.23 3.15	2.16 3.00	2.11 2.93	2.07 2.84	2.03 2.76	1.98 2.67	1.93 2.58	1.88 2.49
20	4.35 8.10	3.49 5.85	3.10 4.94	2.87 4.43	2.71 4.10	2.60 3.87	2.51 3.70	2.45 3.56	2.39 3.46	2.35 3.37	2.28 3.23	2.20 3.09	2.12 2.94	2.08 2.86	2.04 2.78	1.99 2.69	1.95 2.61	1.90 2.52	1.84 2.42
21	4.32 8.02	3.47 5.78	3.07 4.87	2.84 4.37	2.68 4.04	2.57 3.81	2.49 3.64	2.42 3.52	2.37 3.40	2.32 3.31	2.25 3.17	2.18 3.03	2.10 2.88	2.05 2.80	2.01 2.72	1.96 2.64	1.92 2.55	1.87 2.46	1.81 2.36
22	4.30 7.95	3.44 5.72	3.05 4.82	2.82 4.31	2.66 3.99	2.55 3.76	2.46 3.59	2.40 3.45	2.34 3.35	2.30 3.26	2.23 3.12	2.15 2.98	2.07 2.83	2.03 2.75	1.98 2.67	1.94 2.58	1.89 2.50	1.84 2.40	1.78 2.31
23	4.28 7.88	3.42 5.66	3.03 4.76	2.80 4.260	2.64 3.94	2.53 3.71	2.44 3.54	2.37 3.41	2.32 3.30	2.27 3.21	2.20 3.20	2.13 2.93	2.05 2.78	2.01 2.70	1.96 2.62	1.91 2.54	1.86 2.45	1.81 2.35	1.76 2.26
24	4.26 7.82	3.40 5.61	3.01 4.72	2.78 4.22	2.62 3.90	2.51 3.67	2.42 3.51	2.36 3.36	2.30 3.26	2.25 3.17	2.18 3.03	2.11 2.89	2.03 2.74	1.98 2.66	1.94 2.58	1.89 2.49	1.84 2.40	1.79 2.31	1.73 2.21
25	4.24 7.77	3.39 5.57	2.99 4.68	2.76 4.18	2.60 3.85	2.49 3.63	2.40 3.46	2.34 3.32	2.28 3.22	2.24 3.13	2.16 2.99	2.09 2.85	2.01 2.70	1.96 2.62	1.92 2.54	1.87 2.45	1.82 2.36	1.77 2.27	1.71 2.17
26	4.23 7.72	3.37 5.56	2.98 4.64	2.74 4.14	2.59 3.82	2.47 3.59	2.39 3.42	2.32 3.29	2.27 3.18	2.22 3.09	2.15 2.96	2.07 2.81	1.99 2.66	1.95 2.58	1.90 2.50	1.85 2.42	1.80 2.33	1.75 2.23	1.69 2.13
27	4.21 7.68	3.35 5.49	2.96 4.60	2.73 4.11	2.57 3.78	2.46 3.56	2.37 3.39	2.31 3.26	2.25 3.15	2.20 3.06	2.13 2.90	2.06 2.78	1.97 2.63	1.93 2.55	1.88 2.47	1.84 2.38	1.79 2.29	1.73 2.20	1.67 2.10
28	4.20 7.64	3.34 5.45	2.95 4.57	2.71 4.07	2.56 3.75	2.45 3.53	2.36 3.36	2.29 3.23	2.24 3.12	2.19 3.03	2.12 2.90	2.04 2.75	1.96 2.60	1.91 2.52	1.87 2.44	1.82 2.35	1.77 2.26	1.71 2.17	1.65 2.06
29	4.18 7.60	3.33 5.42	2.93 4.54	2.70 4.04	2.55 3.73	2.43 3.50	2.35 3.33	2.28 3.20	2.22 3.09	2.18 3.00	2.10 2.87	2.03 2.73	1.94 2.57	1.90 2.49	1.85 2.41	1.81 2.33	1.75 2.23	1.70 2.14	1.64 2.03
30	4.17 7.56	3.32 5.39	2.92 4.51	2.69 4.02	2.53 3.70	2.42 3.47	2.33 3.30	2.27 3.17	2.21 3.07	2.16 2.98	2.09 2.84	2.01 2.70	1.93 2.55	1.89 2.47	1.84 2.37	1.79 2.30	1.74 2.21	1.68 2.11	1.62 2.01
40	4.08 7.31	3.23 5.18	2.84 4.31	2.61 3.83	2.45 3.51	2.34 3.29	2.25 3.12	2.18 2.99	2.12 2.89	2.08 2.80	2.00 2.66	1.92 2.52	1.84 2.37	1.79 2.29	1.74 2.20	1.69 2.11	1.64 2.02	1.58 1.92	1.51 1.80
60	4.00 7.08	3.15 4.98	2.76 4.13	2.53 3.65	2.37 3.34	2.25 3.12	2.17 2.95	2.10 2.82	2.04 2.72	1.99 2.63	1.92 2.50	1.84 2.35	1.75 2.20	1.70 2.12	1.65 2.03	1.59 1.94	1.53 1.84	1.47 1.73	1.39 1.60
120	3.92 6.85	3.07 4.79	2.68 3.95	2.45 3.48	2.29 3.17	2.18 2.96	2.09 2.79	2.02 2.66	1.96 2.56	1.91 2.47	1.83 2.34	1.75 2.19	1.66 2.03	1.61 1.95	1.55 1.86	1.50 1.76	1.43 1.66	1.35 1.53	1.25 1.38
∞	3.84 6.63	3.00 4.61	3.00 3.78	2.37 3.32	2.21 3.02	2.10 2.80	2.01 2.64	1.94 2.51	1.88 2.41	1.83 2.32	1.75 2.18	1.67 2.04	1.57 1.88	1.52 1.79	1.46 1.70	1.39 1.59	1.32 1.47	1.22 1.32	1.0 1.0

F表(10%)

Φ2/Φ1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
60
120
∞