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Appendices

Table A

Snedecor’s F-Distribution
P(F_cal > F_c) = 0.10
ν₂ Denominator	Numerator Degrees of Freedom (ν₁)
ν₂ Denominator	1	2	3	4	5	6	7	8	9	10
1	39.86	49.50	53.59	55.83	57.24	58.20	58.91	59.44	59.86	60.19
2	8.53	9.00	9.16	9.24	9.29	9.33	9.35	9.37	9.38	9.39
3	5.54	5.46	5.39	5.34	5.31	5.28	5.27	5.25	5.24	5.23
4	4.54	4.32	4.19	4.11	4.05	4.01	3.98	3.95	3.94	3.92
5	4.06	3.78	3.62	3.52	3.45	3.40	3.37	3.34	3.32	3.30
6	3.78	3.46	3.29	3.18	3.11	3.05	3.01	2.98	2.96	2.94
7	3.59	3.26	3.07	2.96	2.88	2.83	2.78	2.75	2.72	2.70
8	3.46	3.11	2.92	2.81	2.73	2.67	2.62	2.59	2.56	2.54
9	3.36	3.01	2.81	2.69	2.61	2.55	2.51	2.47	2.44	2.42
10	3.29	2.92	2.73	2.61	2.52	2.46	2.41	2.38	2.35	2.32
11	3.23	2.86	2.66	2.54	2.45	2.39	2.34	2.30	2.27	2.25
12	3.18	2.81	2.61	2.48	2.39	2.33	2.28	2.24	2.21	2.19
13	3.14	2.76	2.56	2.43	2.35	2.28	2.23	2.20	2.16	2.14
14	3.10	2.73	2.52	2.39	2.31	2.24	2.19	2.15	2.12	2.10
15	3.07	2.70	2.49	2.36	2.27	2.21	2.16	2.12	2.09	2.06
16	3.05	2.67	2.46	2.33	2.24	2.18	2.13	2.09	2.06	2.03
17	3.03	2.64	2.44	2.31	2.22	2.15	2.10	2.06	2.03	2.00
18	3.01	2.62	2.42	2.29	2.20	2.13	2.08	2.04	2.00	1.98
19	2.99	2.61	2.40	2.27	2.18	2.11	2.06	2.02	1.98	1.96
20	2.97	2.59	2.38	2.25	2.16	2.09	2.04	2.00	1.96	1.94
21	2.96	2.57	2.36	2.23	2.14	2.08	2.02	1.98	1.95	1.92
22	2.95	2.56	2.35	2.22	2.13	2.06	2.01	1.97	1.93	1.90
23	2.94	2.55	2.34	2.21	2.11	2.05	1.99	1.95	1.92	1.89
24	2.93	2.54	2.33	2.19	2.10	2.04	1.98	1.94	1.91	1.88
25	2.92	2.53	2.32	2.18	2.09	2.02	1.97	1.93	1.89	1.87
26	2.91	2.52	2.31	2.17	2.08	2.01	1.96	1.92	1.88	1.86
27	2.90	2.51	2.30	2.17	2.07	2.00	1.95	1.91	1.87	1.85
28	2.89	2.50	2.29	2.16	2.06	2.00	1.94	1.90	1.87	1.84
29	2.89	2.50	2.28	2.15	2.06	1.99	1.93	1.89	1.86	1.83
30	2.88	2.49	2.28	2.14	2.05	1.98	1.93	1.88	1.85	1.82
35	2.85	2.46	2.25	2.11	2.02	1.95	1.90	1.85	1.82	1.79
40	2.84	2.44	2.23	2.09	2.00	1.93	1.87	1.83	1.79	1.76
45	2.82	2.42	2.21	2.07	1.98	1.91	1.85	1.81	1.77	1.74
50	2.81	2.41	2.20	2.06	1.97	1.90	1.84	1.80	1.76	1.73
100	2.76	2.36	2.14	2.00	1.91	1.83	1.78	1.73	1.69	1.66

Table A

P(F_cal > F_c) = 0.05
ν₂ Denominator	Numerator Degrees of Freedom (ν₁)
ν₂ Denominator	1	2	3	4	5	6	7	8	9	10
1	161.45	199.50	215.71	224.58	230.16	233.99	236.77	238.88	240.54	241.88
2	18.51	19.00	19.16	19.25	19.30	19.33	19.35	19.37	19.38	19.40
3	10.13	9.55	9.28	9.12	9.01	8.94	8.89	8.85	8.81	8.79
4	7.71	6.94	6.59	6.39	6.26	6.16	6.09	6.04	6.00	5.96
5	6.61	5.79	5.41	5.19	5.05	4.95	4.88	4.82	4.77	4.74
6	5.99	5.14	4.76	4.53	4.39	4.28	4.21	4.15	4.10	4.06
7	5.59	4.74	4.35	4.12	3.97	3.87	3.79	3.73	3.68	3.64
8	5.32	4.46	4.07	3.84	3.69	3.58	3.50	3.44	3.39	3.35
9	5.12	4.26	3.86	3.63	3.48	3.37	3.29	3.23	3.18	3.14
10	4.96	4.10	3.71	3.48	3.33	3.22	3.14	3.07	3.02	2.98
11	4.84	3.98	3.59	3.36	3.20	3.09	3.01	2.95	2.90	2.85
12	4.75	3.89	3.49	3.26	3.11	3.00	2.91	2.85	2.80	2.75
13	4.67	3.81	3.41	3.18	3.03	2.92	2.83	2.77	2.71	2.67
14	4.60	3.74	3.34	3.11	2.96	2.85	2.76	2.70	2.65	2.60
15	4.54	3.68	3.29	3.06	2.90	2.79	2.71	2.64	2.59	2.54
16	4.49	3.63	3.24	3.01	2.85	2.74	2.66	2.59	2.54	2.49
17	4.45	3.59	3.20	2.96	2.81	2.70	2.61	2.55	2.49	2.45
18	4.41	3.55	3.16	2.93	2.77	2.66	2.58	2.51	2.46	2.60
19	4.38	3.52	3.13	2.90	2.74	2.63	2.54	2.48	2.42	2.38
20	4.35	3.49	3.10	2.87	2.71	2.60	2.51	2.45	2.39	2.35
21	4.32	3.47	3.07	2.84	2.68	2.57	2.49	2.42	2.37	2.32
22	4.30	3.44	3.05	2.82	2.66	2.55	2.46	2.40	2.34	2.30
23	4.28	3.42	3.03	2.80	2.64	2.53	2.44	2.37	2.32	2.27
24	4.26	3.40	3.01	2.78	2.62	2.51	2.42	2.36	2.30	2.25
25	4.24	3.39	2.99	2.76	2.00	2.49	2.40	2.34	2.28	2.24
26	4.23	3.37	2.98	2.74	2.59	2.47	2.39	2.32	2.27	2.22
27	4.21	3.35	2.96	2.73	2.57	2.46	2.37	2.31	2.25	2.20
28	4.20	3.34	2.95	2.71	2.56	2.45	2.36	2.29	2.24	2.19
29	4.18	3.33	2.93	2.70	2.55	2.43	2.35	2.28	2.22	2.18
30	4.17	3.32	2.92	2.69	2.53	2.42	2.33	2.27	2.21	2.16
35	4.12	3.27	2.87	2.64	2.49	2.37	2.29	2.22	2.16	2.11
40	4.08	3.23	2.84	2.61	2.45	2.34	2.25	2.18	2.12	2.08
45	4.06	3.20	2.81	2.58	2.42	2.31	2.22	2.15	2.10	2.05
50	4.03	3.18	2.79	2.56	2.40	2.29	2.20	2.13	2.07	2.03
100	3.94	3.09	2.70	2.46	2.31	2.19	2.10	2.03	1.97	1.93

Unlabelled Table

P(F_cal > F_c) = 0.025
ν₂ Denominator	Numerator Degrees of Freedom (ν₁)
ν₂ Denominator	1	2	3	4	5	6	7	8	9	10
1	647.8	799.5	864.2	899.6	921.8	937.1	948.2	956.7	963.3	963.3
2	38.51	39.00	39.17	39.25	39.30	39.33	39.36	39.37	39.39	39.40
3	17.44	16.04	15.44	15.10	14.88	14.73	14.62	14.54	14.47	14.42
4	12.22	10.65	9.98	9.60	9.36	9.20	9.07	8.98	8.90	3.84
5	10.01	8.43	7.76	7.39	7.15	6.98	6.85	6.76	6.68	6.62
6	8.81	7.26	6.60	6.23	5.99	5.82	5.70	5.60	5.52	5.46
7	8.07	6.54	5.89	5.52	5.29	5.12	4.99	4.90	4.82	4.76
8	7.57	6.06	5.42	5.05	4.82	4.65	4.53	4.43	4.36	4.30
9	7.21	5.71	5.08	4.72	4.48	4.32	4.20	4.10	4.03	3.96
10	6.94	5.46	4.83	4.47	4.24	4.07	3.95	3.85	3.78	3.72
11	6.72	5.26	4.63	4.28	4.04	3.88	3.76	3.66	3.59	3.53
12	6.55	5.10	4.47	4.12	3.89	3.73	3.61	3.51	3.44	3.37
13	6.41	4.97	4.35	4.00	3.77	3.60	3.48	3.39	3.31	3.25
14	6.30	4.86	4.24	3.89	3.66	3.50	3.38	3.29	3.21	3.15
15	6.20	4.77	4.15	3.80	3.58	3.41	3.29	3.20	3.12	3.06
16	6.12	4.69	4.08	3.73	3.50	3.34	3.22	3.12	3.05	2.99
17	6.04	4.62	4.01	3.66	3.44	3.28	3.16	3.06	2.98	2.92
18	5.98	4.56	3.95	3.61	3.38	3.22	3.10	3.01	2.93	2.87
19	5.92	4.51	3.90	3.56	3.33	3.17	3.05	2.96	2.88	2.82
20	5.87	4.46	3.86	3.51	3.29	3.13	3.01	2.91	2.84	2.77
21	5.83	4.42	3.82	3.48	3.25	3.09	2.97	2.87	2.80	2.73
22	5.79	4.38	3.78	3.44	3.22	3.05	2.93	2.84	2.76	2.70
23	5.75	4.35	3.75	3.41	3.18	3.02	2.90	2.81	2.73	2.67
24	5.72	4.32	3.72	3.38	3.15	2.99	2.87	2.78	2.70	2.64
25	5.69	4.29	3.69	3.35	3.13	2.97	2.85	2.75	2.68	2.61
26	5.66	4.27	3.67	3.33	3.10	2.94	2.82	2.73	2.65	2.59
27	5.63	4.24	3.65	3.31	3.08	2.92	2.80	2.71	2.63	2.57
28	5.61	4.22	3.63	3.29	3.06	2.90	2.78	2.69	2.61	2.55
29	5.59	4.20	3.61	3.27	3.04	2.88	2.76	2.67	2.59	2.53
30	5.57	4.18	3.59	3.25	3.03	2.87	2.75	2.65	2.57	2.51
40	5.42	4.05	3.46	3.13	2.90	2.74	2.62	2.53	2.45	2.39
60	5.29	3.93	3.34	3.01	2.79	2.63	2.51	2.41	2.33	2.27
120	5.15	3.80	3.23	2.89	2.67	2.52	2.39	2.30	2.22	2.16

Unlabelled Table

P(F_cal > F_c) = 0.01
ν₂ Denominator	Numerator Degrees of Freedom (ν₁)
ν₂ Denominator	1	2	3	4	5	6	7	8	9	10
1	4,052.2	4,999.3	5,403.5	5,624.3	5,764.0	5,859.0	5,928.3	5,981.0	6,022.4	6,055.9
2	98.50	99.00	99.16	99.25	99.30	99.33	99.36	99.38	99.39	99.40
3	34.12	30.82	29.46	28.71	28.24	27.91	27.67	27.49	27.34	27.23
4	21.20	18.00	16.69	15.98	15.52	15.21	14.98	14.80	14.66	14.55
5	16.26	13.27	12.06	11.39	10.97	10.67	10.46	10.29	10.16	10.05
6	13.75	10.92	9.78	9.15	8.75	8.47	8.26	8.10	7.98	7.87
7	12.25	9.55	8.45	7.85	7.46	7.19	6.99	6.84	6.72	6.62
8	11.26	8.65	7.59	7.01	6.63	6.37	6.18	6.03	5.91	5.81
9	10.56	8.02	6.99	6.42	6.06	5.80	5.61	5.47	5.35	5.26
10	10.04	7.56	6.55	5.99	5.64	5.39	5.20	5.06	4.94	4.85
11	9.65	7.21	6.22	5.67	5.32	5.07	4.89	4.74	4.63	4.54
12	9.33	6.93	5.95	5.41	5.06	4.82	4.64	4.50	4.39	4.30
13	9.07	6.70	5.74	5.21	4.86	4.62	4.44	4.30	4.19	4.10
14	8.86	6.51	5.56	5.04	4.69	4.46	4.28	4.14	4.03	3.94
15	8.68	6.36	5.42	4.89	4.56	4.32	4.14	4.00	3.89	3.80
16	8.53	6.23	5.29	4.77	4.44	4.20	4.03	3.89	3.78	3.69
17	8.40	6.11	5.19	4.67	4.34	4.10	3.93	3.79	3.68	3.59
18	8.29	6.01	5.09	4.58	4.25	4.01	3.84	3.71	3.60	3.51
19	8.18	5.93	5.01	4.50	4.17	3.94	3.77	3.63	3.52	3.43
20	8.10	5.85	4.94	4.43	4.10	3.87	3.70	3.56	3.46	3.37
21	8.02	5.78	4.87	4.37	4.04	3.81	3.64	3.51	3.40	3.31
22	7.95	5.72	4.82	4.31	3.99	3.76	3.59	3.45	3.35	3.26
23	7.88	5.66	4.76	4.26	3.94	3.71	3.54	3.41	3.30	3.21
24	7.82	5.61	4.72	4.22	3.90	3.67	3.50	3.36	3.26	3.17
25	7.77	5.57	4.68	4.18	3.85	3.63	3.46	3.32	3.22	3.13
26	7.72	5.53	4.64	4.14	3.82	3.59	3.42	3.29	3.18	3.09
27	7.68	5.49	4.60	4.11	3.78	3.56	3.39	3.26	3.15	3.06
28	7.64	5.45	4.57	4.07	3.75	3.53	3.36	3.23	3.12	3.03
29	7.60	5.42	4.54	4.04	3.73	3.50	3.33	3.20	3.09	3.00
30	7.56	5.39	4.51	4.02	3.70	3.47	3.30	3.17	3.07	2.98
35	7.42	5.27	4.40	3.91	3.59	3.37	3.20	3.07	2.96	2.88
40	7.31	5.18	4.31	3.83	3.51	3.29	3.12	2.99	2.89	2.80
45	7.23	5.11	4.25	3.77	3.45	3.23	3.07	2.94	2.83	2.74
50	7.17	5.06	4.20	3.72	3.41	3.19	3.02	2.89	2.78	2.70
100	6.90	4.82	3.98	3.51	3.21	2.99	2.82	2.69	2.59	2.50

Unlabelled Table

Critical values of the Snedecor’s F-distribution.

Table B

Student’s t-distribution
P(T_cal > t_c) = α
Degrees of Freedom ν	Associated Probability for a Right-Tailed Test
Degrees of Freedom ν	0.25	0.10	0.05	0.025	0.01	0.005	0.0025	0.001	0.0005
1	1.000	3.078	6.314	12.706	31.821	63.657	127.3	318.309	636.619
2	0.816	1.886	2.920	4.303	6.965	9.925	14.09	22.33	31.60
3	0.765	1.638	2.353	3.182	4.541	5.841	7.453	10.21	12.92
4	0.741	1.533	2.132	2.776	3.747	4.604	5.598	7.173	8.610
5	0.727	1.476	2.015	2.571	3.365	4.032	4.773	5.894	6.869
6	0.718	1.440	1.943	2.447	3.143	3.707	4.317	5.208	5.959
7	0.711	1.415	1.895	2.365	2.998	3.499	4.029	4.785	5.408
8	0.706	1.397	1.860	2.306	2.896	3.355	3.833	4.501	5.041
9	0.703	1.383	1.833	2.262	2.821	3.250	3.690	4.297	4.781
10	0.700	1.372	1.812	2.228	2.764	3.169	3.581	4.144	4.587
11	0.697	1.363	1.796	2.201	2.718	3.106	3.497	4.025	4.437
12	0.695	1.356	1.782	2.179	2.681	3.055	3.428	3.930	4.318
13	0.694	1.350	1.771	2.160	2.650	3.012	3.372	3.852	4.221
14	0.692	1.345	1.761	2.145	2.624	2.977	3.326	3.787	4.140
15	0.691	1.341	1.753	2.131	2.602	2.947	3.286	3.733	4.073
16	0.690	1.337	1.746	2.120	2.583	2.921	3.252	3.686	4.015
17	0.689	1.333	1.740	2.110	2.567	2.898	3.222	3.646	3.965
18	0.688	1.330	1.734	2.101	2.552	2.878	3.197	3.610	3.922
19	0.688	1.328	1.729	2.093	2.539	2.861	3.174	3.579	3.883
20	0.687	1.325	1.725	2.086	2.528	2.845	3.153	3.552	3.850
21	0.686	1.323	1.721	2.080	2.518	2.831	3.135	3.527	3.819
22	0.686	1.321	1.717	2.074	2.508	2.819	3.119	3.505	3.792
23	0.685	1.319	1.714	2.069	2.500	2.807	3.104	3.485	3.768
24	0.685	1.318	1.711	2.064	2.492	2.797	3.091	3.467	3.745
25	0.684	1.316	1.708	2.060	2.485	2.787	3.078	3.450	3.725
26	0.684	1.315	1.706	2.056	2.479	2.779	3.067	3.435	3.707
27	0.684	1.314	1.703	2.052	2.473	2.771	3.057	3.421	3.689
28	0.683	1.313	1.701	2.048	2.467	2.763	3.047	3.408	3.674
29	0.683	1.311	1.699	2.045	2.462	2.756	3.038	3.396	3.660
30	0.683	1.310	1.697	2.042	2.457	2.750	3.030	3.385	3.646
35	0.682	1.306	1.690	2.030	2.438	2.724	2.996	3.340	3.591
40	0.681	1.303	1.684	2.021	2.423	2.704	2.971	3.307	3.551
45	0.680	1.301	1.679	2.014	2.412	2.690	2.952	3.281	3.520
50	0.679	1.299	1.676	2.009	2.403	2.678	2.937	3.261	3.496
z	0.674	1.282	1.645	1.960	2.326	2.576	2.807	3.090	3.291

Table B

Critical values of the Student’s t-distribution.

Table C

Durbin-Watson Distribution (DW)
n	k (Number of Parameters – Includes Intercept)
	2		3		4		5		6		7		8		9		10
	d_L	d_U	d_L	d_U	d_L	d_U	d_L	d_U	d_L	d_U	d_L	d_U	d_L	d_U	d_L	d_U	d_L	d_U
6	0.610	1.400	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
7	0.700	1.356	0.467	1.896	–	–	–	–	–	–	–	–	–	–	–	–	–	–
8	0.763	1.332	0.559	1.777	0.367	2.287	–	–	–	–	–	–	–	–	–	–	–	–
9	0.824	1.320	0.629	1.699	0.455	2.128	0.296	2.588	–	–	–	–	–	–	–	–	–	–
10	0.879	1.320	0.697	1.641	0.525	2.016	0.376	2.414	0.243	2.822	–	–	–	–	–	–	–	–
11	0.927	1.324	0.758	1.604	0.595	1.928	0.444	2.283	0.315	2.645	0.203	3.004	–	–	–	–	–	–
12	0.971	1.331	0.812	1.579	0.658	1.864	0.512	2.177	0.380	2.506	0.268	2.832	0.171	3.149	–	–	–	–
13	1.010	0.861	0.861	1.562	0.715	1.816	0.574	2.094	0.444	2.390	0.328	2.692	0.230	2.985	0.147	3.266	–	–
14	1.045	1.350	0.905	1.551	0.767	1.779	0.632	2.030	0.505	2.296	0.389	2.572	0.286	2.848	0.200	3.111	0.127	3.360
15	1.077	1.361	0.946	1.543	0.814	1.750	0.685	1.977	0.562	2.220	0.447	2.471	0.343	2.727	0.251	2.979	0.175	3.216
16	1.106	1.371	0.982	1.539	0.857	1.728	0.734	1.935	0.615	2.157	0.502	2.388	0.398	2.624	0.304	2.860	0.222	3.090
17	1.133	1.381	1.015	1.536	0.897	1.710	0.779	1.900	0.664	2.104	0.554	2.318	0.451	2.537	0.356	2.757	0.272	2.975
18	1.158	1.391	1.046	1.535	0.933	1.696	0.820	1.872	0.710	2.060	0.603	2.258	0.502	2.461	0.407	2.668	0.321	2.873
19	1.180	1.401	1.074	1.536	0.967	1.685	0.859	1.848	0.752	2.023	0.649	2.206	0.549	2.396	0.456	2.589	0.369	2.783
20	1.201	1.411	1.100	1.537	0.998	1.676	0.894	1.828	0.792	1.991	0.691	2.162	0.595	2.339	0.502	2.521	0.416	2.704
21	1.221	1.420	1.125	1.538	1.026	1.669	0.927	1.812	0.829	1.964	0.731	2.124	0.637	2.290	0.546	2.461	0.461	2.633
22	1.239	1.429	1.147	1.541	1.053	1.664	0.958	1.797	0.863	1.940	0.769	2.090	0.677	1.246	0.588	2.407	0.504	2.571
23	1.257	1.437	1.168	1.543	1.078	1.660	0.986	1.785	0.895	1.920	0.804	2.061	0.715	2.208	0.628	2.360	0.545	2.514
24	1.273	1.446	1.188	1.546	1.101	1.656	1.013	1.775	0.925	1.902	0.837	2.035	0.750	2.174	0.666	2.318	0.584	2.464
25	1.288	1.454	1.206	1.550	1.123	1.654	1.038	1.767	0.953	1.886	0.868	2.013	0.784	2.144	0.702	2.280	0.621	2.419
26	1.302	1.461	1.224	1.553	1.143	1.652	1.062	1.759	0.979	1.873	0.897	1.992	0.816	2.117	0.735	2.246	0.657	2.379
27	1.316	1.469	1.240	1.556	1.162	1.651	1.084	1.753	1.004	1.861	0.925	1.974	0.845	2.093	0.767	2.216	0.691	2.342
28	1.328	1.476	1.255	1.560	1.1181	1.650	1.104	1.747	1.028	1.850	0.951	1.959	0.874	2.071	0.798	2.188	0.723	2.309
29	1.341	1.483	1.270	1.563	1.198	1.650	1.124	1.743	1.050	1.841	0.975	1.944	0.900	2.052	0.826	2.164	0.753	2.278
30	1.352	1.489	1.284	1.567	1.214	1.650	1.143	1.739	1.071	1.833	0.998	1.931	0.926	2.034	0.854	2.141	0.782	2.251
31	1.363	1.496	1.297	1.570	1.229	1.650	1.160	1.735	1.090	1.825	1.020	1.920	0.950	2.018	0.879	2.120	0.810	2.226
32	1.373	1.502	1.309	1.574	1.244	1.650	1.177	1.732	1.109	1.819	1.041	1.909	0.972	2.004	0.904	2.102	0.836	2.203
33	1.383	1.508	1.321	1.577	1.258	1.651	1.193	1.730	1.127	1.813	1.061	1.900	0.994	1.991	0.927	20.85	0.861	2.181
34	1.393	1.514	1.333	1.580	1.271	1.652	1.208	1.728	1.144	1.808	1.079	1.891	1.015	1.978	0.950	2.069	0.885	2.162
35	1.402	1.519	1.343	1.584	1.283	1.653	1.222	1.726	1.160	1.803	1.097	1.884	1.034	1.967	0.971	2.054	0.908	2.144
36	1.411	1.525	1.354	1.587	1.295	1.654	1.236	1.724	1.175	1.799	1.114	1.876	1.053	1.957	0.991	2.041	0.930	2.127
37	1.419	1.530	1.364	1.590	1.307	1.655	1.249	1.723	1.190	1.795	1.131	1.870	1.071	1.948	1.011	2.029	0.951	2.112
38	1.427	1.535	1.373	1.594	1.318	1.656	1.261	1.722	1.204	1.792	1.146	1.864	1.088	1.939	1.029	2.017	0.970	2.098
39	1.435	1.540	1.382	1.597	1.328	1.658	1.273	1.722	1.218	1.789	1.161	1.859	1.104	1.932	1.047	2.007	0.990	2.085
40	1.442	1.544	1.391	1.600	1.338	1.659	1.285	1.721	1.230	1.786	1.175	1.854	1.120	1.924	1.064	1.997	1.008	2.072
45	1.475	1.566	1.430	1.615	1.383	1.666	1.336	1.720	1.287	1.776	1.238	1.835	1.189	1.895	1.139	1.958	1.089	2.022
50	1.503	1.585	1.462	1.628	1.421	1.674	1.378	1.721	1.335	1.771	1.291	1.822	1.246	1.875	1.201	1.930	1.156	1.986
55	1.528	1.601	1.490	1.641	1.452	1.611	1.414	1.724	1.374	1.768	1.334	1.814	1.294	1.861	1.253	1.909	1.212	1.959
60	1.549	1.616	1.514	1.652	1.480	1.689	1.444	1.727	1.408	1.767	1.372	1.808	1.335	1.850	1.298	1.894	1.260	1.939
65	1.567	1.629	1.536	1.662	1.503	1.696	1.471	1.731	1.438	1.767	1.404	1.805	1.170	1.843	1.336	1.882	1.301	1.923
70	1.583	1.641	1.554	1.672	1.525	1.703	1.494	1.735	1.464	1.768	1.433	1.802	1.401	1.838	1.369	1.874	1.337	1.910
75	1.598	1.652	1.571	1.680	1.543	1.709	1.515	1.739	1.487	1.770	1.458	1.801	1.428	1.834	1.399	1.867	1.369	1.901
80	1.611	1.662	1.586	1.688	1.560	1.715	1.534	1.743	1.507	1.772	1.480	1.801	1.453	1.831	1.425	1.861	1.397	1.893
85	1.624	1.671	1.600	1.696	1.575	1.721	1.550	1.747	1.525	1.774	1.500	1.801	1.474	1.829	1.448	1.857	1.422	1.886
90	1.635	1.679	1.612	1.703	1.589	1.726	1.566	1.751	1.542	1.776	1.518	1.801	1.494	1.827	1.469	1.854	1.445	1.881
95	1.645	1.687	1.623	1.709	1.602	1.732	1.579	1.755	1.557	1.778	1.535	1.802	1.512	1.827	1.489	1.852	1.465	1.877
100	1.654	1.694	1.634	1.715	1.613	1.736	1.592	1.758	1.571	1.780	1.550	1.803	1.528	1.827	1.489	1.852	1.465	1.877
150	1.720	1.747	1.706	1.760	1.693	1.774	1.679	1.788	1.665	1.802	1.651	1.817	1.637	1.832	1.622	1.846	1.608	1.862
200	1.758	1.779	1.748	1.789	1.738	1.799	1.728	1.809	1.718	1.820	1.707	1.831	1.697	1.841	1.686	1.852	1.675	1.863

Table C

Table D

Chi-Square Distribution
P(χ_cal² with ν degrees of freedom > χ_c²) = α
Degrees of Freedom ν	0.99	0.975	0.95	0.9	0.1	0.05	0.025	0.01	0.005
1	0.000	0.001	0.004	0.016	2.706	3.841	5.024	6.635	7.879
2	0.020	0.051	0.103	0.211	4.605	5.991	7.378	9.210	10.597
3	0.115	0.216	0.352	0.584	6.251	7.815	9.348	11.345	12.838
4	0.297	0.484	0.711	1.064	7.779	9.488	11.143	13.277	14.860
5	0.554	0.831	1.145	1.610	9.236	11.070	12.832	15.086	16.750
6	0.872	1.237	1.635	2.204	10.645	12.592	14.449	16.812	18.548
7	1.239	1.690	2.167	2.833	12.017	14.067	16.013	18.475	20.278
8	1.647	2.180	2.733	3.490	13.362	15.507	17.535	20.090	21.955
9	2.088	2.700	3.325	4.168	14.684	16.919	19.023	21.666	23.589
10	2.558	3.247	3.940	4.865	15.987	18.307	20.483	23.209	25.188
11	3.053	3.816	4.575	5.578	17.275	19.675	21.920	24.725	26.757
12	3.571	4.404	5.226	6.304	18.549	21.026	23.337	26.217	28.300
13	4.107	5.009	5.892	7.041	19.812	22.362	24.736	27.688	29.819
14	4.660	5.629	6.571	7.790	21.064	23.685	26.119	29.141	31.319
15	5.229	6.262	7.261	8.547	22.307	24.996	27.488	30.578	32.801
16	5.812	6.908	7.962	9.312	23.542	26.296	28.845	32.000	34.267
17	6.408	7.564	8.672	10.085	24.769	27.587	30.191	33.409	35.718
18	7.015	8.231	9.390	10.865	25.989	28.869	31.526	34.805	37.156
19	7.633	8.907	10.117	11.651	27.204	30.144	32.852	36.191	38.582
20	8.260	9.591	10.851	12.443	28.412	31.410	34.170	37.566	39.997
21	8.897	10.283	11.591	13.240	29.615	32.671	35.479	38.932	41.401
22	9.542	10.982	12.338	14.041	30.813	33.924	36.781	40.289	42.796
23	10.196	11.689	13.091	14.848	32.007	35.172	38.076	41.638	44.181
24	10.856	12.401	13.848	15.659	33.196	36.415	39.364	42.980	45.558
25	11.524	13.120	14.611	16.473	34.382	37.652	40.646	44.314	46.928
26	12.198	13.844	15.379	17.292	35.563	38.885	41.923	45.642	48.290
27	12.878	14.573	16.151	18.114	36.741	40.113	43.195	46.963	49.645
28	13.565	15.308	16.928	18.939	37.916	41.337	44.461	48.278	50.994
29	14.256	16.047	17.708	19.768	39.087	42.557	45.722	49.588	52.335
30	14.953	16.791	18.493	20.599	40.256	43.773	46.979	50.892	53.672
31	15.655	17.539	19.281	21.434	41.422	44.985	48.232	52.191	55.002
32	16.362	18.291	20.072	22.271	42.585	46.194	49.480	53.486	56.328
33	17.073	19.047	20.867	23.110	43.745	47.400	50.725	54.775	57.648
34	17.789	19.806	21.664	23.952	44.903	48.602	51.966	56.061	58.964
35	18.509	20.569	22.465	24.797	46.059	49.802	53.203	57.342	60.275
36	19.233	21.336	23.269	25.643	47.212	50.998	54.437	58.619	61.581
37	19.960	22.106	24.075	26.492	48.363	52.192	55.668	59.893	62.883
38	20.691	22.878	24.884	27.343	49.513	53.384	56.895	61.162	64.181
39	21.426	23.654	25.695	28.196	50.660	54.572	58.120	62.428	65.475
40	22.164	24.433	26.509	29.051	51.805	55.758	59.342	63.691	66.766
41	22.906	25.215	27.326	29.907	52.949	56.942	60.561	64.950	68.053
42	23.650	25.999	28.144	30.765	54.090	58.124	61.777	66.206	69.336
43	24.398	26.785	28.965	31.625	55.230	59.304	62.990	67.459	70.616
44	25.148	27.575	29.787	32.487	56.369	60.481	64.201	68.710	71.892
45	25.901	28.366	30.612	33.350	57.505	61.656	65.410	69.957	73.166
46	26.657	29.160	31.439	34.215	58.641	62.830	66.616	71.201	74.437
47	27.416	29.956	32.268	35.081	59.774	64.001	67.821	72.443	75.704
48	28.177	30.754	33.098	35.949	60.907	65.171	69.023	73.683	76.969
49	28.941	31.555	33.930	36.818	62.038	66.339	70.222	74.919	78.231
50	29.707	32.357	34.764	37.689	63.167	67.505	71.420	76.154	79.490

Table D

Critical values (for a right-tailed unilateral test) of the chi-square distribution.

Table E

Standard Normal Distribution
P(z_cal > z_c) = α
z_c	Second Decimal of z_c
z_c	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.4960	0.4920	0.4880	0.4840	0.4801	0.4761	0.4721	0.4681	0.4641
0.1	0.4602	0.4562	0.4522	0.4483	0.4443	0.4404	0.4364	0.4325	0.4286	0.4247
0.2	0.4207	0.4168	0.4129	0.4090	0.4052	0.4013	0.3974	0.3936	0.3897	0.3859
0.3	0.3821	0.3783	0.3745	0.3707	0.3669	0.3632	0.3594	0.3557	0.3520	0.3483
0.4	0.3446	0.3409	0.3372	0.3336	0.3300	0.3264	0.3228	0.3192	0.3156	0.3121
0.5	0.3085	0.3050	0.3015	0.2981	0.2946	0.2912	0.2877	0.2842	0.2810	0.2776
0.6	0.2743	0.2709	0.2676	0.2643	0.2611	0.2578	0.2546	0.2514	0.2483	0.2451
0.7	0.2420	0.2389	0.2358	0.2327	0.2296	0.2266	0.2236	0.2206	0.2177	0.2148
0.8	0.2119	0.2090	0.2061	0.2033	0.2005	0.1977	0.1949	0.1922	0.1894	0.1867
0.9	0.1841	0.1814	0.1788	0.1762	0.1736	0.1711	0.1685	0.1660	0.1635	0.1611
1.0	0.1587	0.1562	0.1539	0.1515	0.1492	0.1469	0.1446	0.1423	0.1401	0.1379
1.1	0.1357	0.1335	0.1314	0.1292	0.1271	0.1251	0.1230	0.1210	0.1190	0.1170
1.2	0.1151	0.1131	0.1112	0.1093	0.1075	0.1056	0.1038	0.1020	0.1003	0.0985
1.3	0.0968	0.0951	0.0934	0.0918	0.0901	0.0885	0.0869	0.0853	0.0838	0.0823
1.4	0.0808	0.0793	0.0778	0.0764	0.0749	0.0735	0.0722	0.0708	0.0694	0.0681
1.5	0.0668	0.0655	0.0643	0.0630	0.0618	0.0606	0.0594	0.0582	0.0571	0.0559
1.6	0.0548	0.0537	0.0526	0.0516	0.0505	0.0495	0.0485	0.0475	0.0465	0.0455
1.7	0.0446	0.0436	0.0427	0.0418	0.0409	0.0401	0.0392	0.0384	0.0375	0.0367
1.8	0.0359	0.0352	0.0344	0.0336	0.0329	0.0322	0.0314	0.0307	0.0301	0.0294
1.9	0.0287	0.0281	0.0274	0.0268	0.0262	0.0256	0.0250	0.0244	0.0239	0.0233
2.0	0.0228	0.0222	0.0217	0.0212	0.0207	0.0202	0.0197	0.0192	0.0188	0.0183
2.1	0.0179	0.0174	0.0170	0.0166	0.0162	0.0158	0.0154	0.0150	0.0146	0.0143
2.2	0.0139	0.0136	0.0132	0.0129	0.0125	0.0122	0.0119	0.0116	0.0113	0.0110
2.3	0.0107	0.0104	0.0102	0.0099	0.0096	0.0094	0.0091	0.0089	0.0087	0.0084
2.4	0.0082	0.0080	0.0078	0.0075	0.0073	0.0071	0.0069	0.0068	0.0066	0.0064
2.5	0.0062	0.0060	0.0059	0.0057	0.0055	0.0054	0.0052	0.0051	0.0049	0.0048
2.6	0.0047	0.0045	0.0044	0.0043	0.0041	0.0040	0.0039	0.0038	0.0037	0.0036
2.7	0.0035	0.0034	0.0033	0.0032	0.0031	0.0030	0.0029	0.0028	0.0027	0.0026
2.8	0.0026	0.0025	0.0024	0.0023	0.0023	0.0022	0.0021	0.0021	0.0020	0.0019
2.9	0.0019	0.0018	0.0017	0.0017	0.0016	0.0016	0.0015	0.0015	0.0014	0.0014
3.0	0.0013	0.0013	0.0013	0.0012	0.0012	0.0011	0.0011	0.0011	0.0010	0.0010
3.1	0.0010	0.0009	0.0009	0.0009	0.008	0.0008	0.0008	0.0008	0.007	0.007
3.2	0.0007
3.3	0.0005
3.4	0.0003
3.5	0.00023
3.6	0.00016
3.7	0.00011
3.8	0.00007
3.9	0.00005
4.0	0.00003

Table E

Associated probability for a right-tailed test.

Table F₁

Binomial Distribution
$P [Y = k] = (\begin{array}{c} N \\ k \end{array}) p^{k} {(1 - p)}^{N - k}$ $P [Y = k] = (\begin{array}{c} N \\ k \end{array}) p^{k} {(1 - p)}^{N - k}$
		p
N	k	0.01	0.05	0.10	0.15	0.20	0.25	0.30	1/3	0.40	0.45	0.50
2	0	9801	9025	8100	7225	6400	5625	4900	4444	3600	3025	2500	2	2
	1	198	950	1800	2550	3200	3750	4200	4444	4800	4950	5000	1
	2	1	25	100	225	400	625	900	1111	1600	2025	2500	0
3	0	9703	8574	7290	6141	5120	4219	3430	2963	2160	1664	1250	3	3
	1	294	1354	2430	3251	3840	4219	4410	4444	4320	4084	3750	2
	2	3	71	270	574	960	1406	1890	2222	2880	3341	3750	1
	3	0	1	10	34	80	156	270	370	640	911	1250	0
4	0	9606	8145	6561	5220	4096	3164	2401	1975	1296	915	625	4	4
	1	388	1715	2916	3685	4096	4219	4116	3951	3456	2995	2500	3
	2	6	135	486	975	1536	2109	2646	2963	3456	3675	3750	2
	3	0	5	36	115	256	469	756	988	1536	2005	2500	1
	4	0	0	1	5	16	39	81	123	256	410	625	0
5	0	9510	7738	5905	4437	3277	2373	1681	1317	778	503	312	5	5
	1	480	2036	3280	3915	4096	3955	3602	3292	2592	2059	1562	4
	2	10	214	729	1382	2048	2637	3087	3292	3456	3369	3125	3
	3	0	11	81	244	512	879	1323	1646	2304	2757	3125	2
	4	0	0	4	22	64	146	283	412	768	1128	1562	1
	5	0	0	0	1	3	10	24	41	102	185	312	0
6	0	9415	7351	5314	3771	2621	1780	1176	878	467	277	156	6	6
	1	571	2321	3543	3993	3932	3560	3025	2634	1866	1359	938	5
	2	14	305	984	1762	2458	2966	3241	3292	3110	2780	2344	4
	3	0	21	146	415	819	1318	1852	2195	2765	3032	3125	3
	4	0	1	12	55	154	330	595	823	1382	1861	2344	2
	5	0	0	1	4	15	44	102	165	369	609	938	1
	6	0	0	0	0	1	2	7	14	41	83	156	0
7	0	9321	6983	4783	3206	2097	1335	824	585	280	152	78	7	7
	1	659	2573	3720	3960	3670	3115	2471	2048	1306	872	547	6
	2	20	406	1240	2097	2753	3115	3177	3073	2613	2140	1641	5
	3	0	36	230	617	1147	1730	2269	2561	2903	2918	2734	4
	4	0	2	26	109	287	577	972	1280	1935	2388	2734	3
	5	0	0	2	12	43	115	250	384	774	1172	1641	2
	6	0	0	0	1	4	13	36	64	172	320	547	1
	7	0	0	0	0	0	1	2	5	16	37	78	0
		0.99	0.95	0.90	0.85	0.80	0.75	0.70	2/3	0.60	0.55	0.50	k	N
	p
		p
N	k	0.01	0.05	0.10	0.15	0.20	0.25	0.30	1/3	0.40	0.45	0.50
8	0	9227	6634	4305	2725	1678	1001	576	390	168	84	39	8	8
	1	746	2793	3826	3847	3355	2670	1977	1561	896	548	312	7
	2	26	515	1488	2376	2936	3115	2965	2731	2090	1569	1094	6
	3	1	54	331	839	1468	2076	2541	2731	2787	2568	2188	5
	4	0	4	46	185	459	865	1361	1707	2322	2627	2734	4
	5	0	0	4	26	92	231	467	683	1239	1719	2188	3
	6	0	0	0	2	11	38	100	171	413	703	1094	2
	7	0	0	0	0	1	4	12	24	79	164	312	1
	8	0	0	0	0	0	0	1	2	7	17	39	0
9	0	9135	6302	3874	2316	1342	751	404	260	101	46	20	9	9
	1	830	2985	3874	3679	3020	2253	1556	1171	605	339	176	8
	2	34	629	1722	2597	3020	3003	2668	2341	1612	1110	703	7
	3	1	77	446	1069	1762	2336	2668	2731	2508	2119	1641	6
	4	0	6	74	283	661	1168	1715	2048	2508	2600	2461	5
	5	0	0	8	50	165	389	735	1024	1672	2128	2461	4
	6	0	0	1	6	28	87	210	341	743	1160	1641	3
	7	0	0	0	0	3	12	39	73	212	407	703	2
	8	0	0	0	0	0	1	4	9	35	83	176	1
	9	0	0	0	0	0	0	0	1	3	8	20	0
10	0	9044	5987	3487	1969	1074	563	282	173	60	25	10	10	10
	1	914	3151	3874	3474	2684	1877	1211	867	403	207	98	9
	2	42	746	1937	2759	3020	2816	2335	1951	1209	763	439	5
	3	1	105	574	1298	2013	2503	2668	2601	2150	1665	1172	7
	4	0	10	112	401	881	1460	2001	2276	2508	2384	2051	6
	5	0	1	15	85	264	584	1029	1366	2007	2340	2461	5
	6	0	0	1	12	55	162	368	569	1115	1596	2051	4
	7	0	0	0	1	8	31	90	163	425	746	1172	3
	8	0	0	0	0	1	4	14	30	106	229	439	2
	9	0	0	0	0	0	0	1	3	16	42	98	1
	10	0	0	0	0	0	0	0	0	1	3	10	0
15	0	8601	4633	2059	874	352	134	47	23	5	1	0	15	15
	1	1303	3658	3432	2312	1319	668	305	171	47	16	5	14
	2	92	1348	2669	2856	2309	1559	916	599	219	90	32	13
	3	4	307	1285	2184	2501	2252	1700	1299	634	318	139	12
	4	0	49	428	1156	1876	2252	2186	1948	1268	780	417	11
	5	0	6	105	449	1032	1651	2061	2143	1859	1404	916	10
	6	0	0	19	132	430	917	1472	1786	2066	1914	1527	9
	7	0	0	3	30	138	393	811	1148	1771	2013	1964	8
	8	0	0	0	5	35	131	348	574	1181	1647	1964	7
	9	0	0	0	1	7	34	116	223	612	1048	1527	6
	10	0	0	0	0	1	7	30	67	245	515	916	5
	11	0	0	0	0	0	1	6	15	74	191	417	4
	12	0	0	0	0	0	0	1	3	16	52	139	3
	13	0	0	0	0	0	0	0	0	3	10	32	2
	14	0	0	0	0	0	0	0	0	0	1	5	1
	15	0	0	0	0	0	0	0	0	0	0	0	0
		0.99	0.95	0.90	0.85	0.80	0.75	0.70	2/3	0.60	0.55	0.50	k	N
		p
		p
N	k	0.01	0.05	0.10	0.15	0.20	0.25	0.30	1/3	0.40	0.45	0.50
20	0	8179	3585	1216	388	115	32	8	3	0	0	0	20	20
	1	1652	3774	2702	1368	576	211	68	30	5	1	0	19
	2	159	1887	2852	2293	1369	669	278	143	31	8	2	18
	3	10	596	1901	2428	2054	1339	716	429	123	40	11	17
	4	0	133	898	1821	2182	1897	1304	911	350	139	46	16
	5	0	22	319	1028	1746	2023	1789	1457	746	365	148	15
	6	0	3	89	454	1091	1686	1916	1821	1244	746	370	14
	7	0	0	20	160	545	1124	1643	1821	1659	1221	739	13
	8	0	0	4	46	222	609	1144	1480	1797	1623	1201	12
	9	0	0	1	11	74	271	654	987	1597	1771	1602	11
	10	0	0	0	2	20	99	308	543	1171	1593	1762	10
	11	0	0	0	0	5	30	120	247	710	1185	1602	9
	12	0	0	0	0	1	8	39	92	355	727	1201	8
	13	0	0	0	0	0	2	10	28	146	366	739	7
	14	0	0	0	0	0	0	2	7	49	150	370	6
	15	0	0	0	0	0	0	0	1	13	49	148	5
	16	0	0	0	0	0	0	0	0	3	13	46	4
	17	0	0	0	0	0	0	0	0	0	2	11	3
	18	0	0	0	0	0	0	0	0	0	0	2	2
	19	0	0	0	0	0	0	0	0	0	0	0	1
	20	0	0	0	0	0	0	0	0	0	0	0	0
25	0	7778	2774	718	172	38	8	1	0	0	0	0	25	25
	1	1964	3650	1994	759	236	63	14	5	0	0	0	24
	2	238	2305	2659	1607	708	251	74	30	4	1	0	23
	3	18	930	2265	2174	1358	641	243	114	19	4	1	22
	4	1	269	1384	2110	1867	1175	572	313	71	18	4	21
	5	0	60	646	1564	1960	1645	1030	658	199	63	16	20
	6	0	10	239	920	1633	1828	1472	1096	442	172	53	19
	7	0	1	72	441	1108	1654	1712	1487	800	381	143	18
	8	0	0	18	175	623	1241	1651	1673	1200	701	322	17
	9	0	0	4	58	294	781	1336	1580	1511	1084	609	16
	10	0	0	1	16	118	417	916	1264	1612	1419	974	15
	11	0	0	0	4	40	189	536	862	1465	1583	1328	14
	12	0	0	0	1	12	74	268	503	1140	1511	1550	13
	13	0	0	0	0	3	25	115	251	760	1236	1550	12
	14	0	0	0	0	1	7	42	108	434	867	1328	11
	15	0	0	0	0	0	2	13	40	212	520	974	10
	16	0	0	0	0	0	0	4	12	88	266	609	9
	17	0	0	0	0	0	0	1	3	31	115	322	8
	18	0	0	0	0	0	0	0	1	9	42	143	7
	19	0	0	0	0	0	0	0	0	2	13	53	6
	20	0	0	0	0	0	0	0	0	0	3	16	5
	21	0	0	0	0	0	0	0	0	0	1	4	4
	22	0	0	0	0	0	0	0	0	0	0	1	3
	23	0	0	0	0	0	0	0	0	0	0	0	2
	24	0	0	0	0	0	0	0	0	0	0	0	1
	25	0	0	0	0	0	0	0	0	0	0	0	0
		0.99	0.95	0.90	0.85	0.80	0.75	0.70	2/3	0.60	0.55	0.50	k	N
		p
		p
N	k	0.01	0.05	0.10	0.15	0.20	0.25	0.30	1/3	0.40	0.45	0.50
30	0	7397	2146	424	76	12	2	0	0	0	0	0	30	30
	1	2242	3389	1413	404	93	18	3	1	0	0	0	29
	2	328	2586	2277	1034	337	86	18	6	0	0	0	28
	3	31	1270	2361	1703	785	269	72	26	3	0	0	27
	4	2	451	1771	2028	1325	604	208	89	12	2	0	26
	5	0	124	1023	1861	1723	1047	464	232	41	8	1	25
	6	0	27	474	1368	1795	1455	829	484	115	29	6	24
	7	0	5	180	828	1538	1662	1219	829	263	81	19	23
	8	0	1	58	420	1106	1593	1501	1192	505	191	55	22
	9	0	0	16	181	676	1298	1573	1457	823	382	133	21
	10	0	0	4	67	355	909	1416	1530	1152	656	280	20
	11	0	0	1	22	161	551	1103	1391	1396	976	509	19
	12	0	0	0	6	64	291	749	1101	1474	1265	805	18
	13	0	0	0	1	22	134	444	762	1360	1433	1115	17
	14	0	0	0	0	7	54	231	436	1101	1424	1354	16
	15	0	0	0	0	2	19	106	247	783	1242	1445	15
	16	0	0	0	0	0	6	42	116	489	953	1354	14
	17	0	0	0	0	0	2	15	48	269	642	1115	13
	18	0	0	0	0	0	0	5	17	129	379	805	12
	19	0	0	0	0	0	0	1	5	54	196	509	11
	20	0	0	0	0	0	0	0	1	20	88	280	10
	21	0	0	0	0	0	0	0	0	6	34	133	9
	22	0	0	0	0	0	0	0	0	1	12	55	8
	23	0	0	0	0	0	0	0	0	0	3	19	7
	24	0	0	0	0	0	0	0	0	0	1	6	6
	25	0	0	0	0	0	0	0	0	0	0	1	5
	26.	0	0	0	0	0	0	0	0	0	0	0	4
	27	0	0	0	0	0	0	0	0	0	0	0	3
	28	0	0	0	0	0	0	0	0	0	0	0	2
	29	0	0	0	0	0	0	0	0	0	0	0	1
	30	0	0	0	0	0	0	0	0	0	0	0	0
		0.99	0.95	0.90	0.85	0.80	0.75	0.70	2/3	0.60	0.55	0.50	k	N

Table F1

The decimal point was omitted. All entries should be read as .nnn.

For p ≤ .5, use the upper line for p and the left column for k.

For p > .5, use the bottom line for p and the right column for k.

Table F₂

Binomial Distribution
$P (Y \leq k) = \sum_{i = 0}^{k} (\begin{array}{c} N \\ i \end{array}) p^{i} {(1 - p)}^{N - i}$ $P (Y \leq k) = \sum_{i = 0}^{k} (\begin{array}{c} N \\ i \end{array}) p^{i} {(1 - p)}^{N - i}$
k
N	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
4	062	312	688	938	1.0
5	031	188	500	812	969	1.0
6	016	109	344	656	891	984	1.0
7	008	062	227	500	773	938	992	1.0
8	004	035	145	363	637	855	965	996	1.0
9	002	020	090	254	500	746	910	980	998	1.0
10	001	011	055	172	377	623	828	945	989	999	1.0
11		006	033	113	274	500	726	887	967	994	999 +	1.0
12		003	019	073	194	387	613	806	927	981	997	999 +	1.0
13		002	011	046	133	291	500	709	867	954	989	998	999 +	1.0
14		001	006	029	090	212	395	605	788	910	971	994	999 +	999 +	1.0
15			004	018	059	151	304	500	696	849	941	982	996	999 +	999 +	1.0
16			002	011	038	105	227	402	598	773	895	962	989	998	999 +	999 +	1.0
17			001	006	025	072	166	315	500	685	834	928	975	994	999	999 +	999 +	1.0
18			001	004	015	048	119	240	407	593	760	881	952	985	996	999	999 +	999 +
19				002	010	032	084	180	324	500	676	820	916	968	990	998	999 +	999 +
20				001	006	021	058	132	252	412	588	748	868	942	979	994	999	999 +
21				001	004	013	039	095	192	332	500	668	808	905	961	987	996	999
22					002	008	026	067	143	262	416	584	738	857	933	974	992	998
23					001	005	017	047	105	202	339	500	661	798	895	953	983	995
24					001	003	011	032	076	154	271	419	581	729	846	924	968	989
25						002	007	022	054	115	212	345	500	655	788	885	946	978
26						001	005	014	038	084	163	279	423	577	721	837	916	962
27						001	003	010	026	061	124	221	351	500	649	779	876	939
28							002	006	018	044	092	172	286	425	575	714	828	908
29							001	004	012	031	068	132	229	356	500	644	771	868
30							001	003	008	021	049	100	181	292	428	572	708	819
31								002	005	015	035	075	141	237	360	500	640	763
32								001	004	010	025	055	108	189	298	430	570	702
33								001	002	007	018	040	081	148	243	364	500	636
34									001	005	012	029	061	115	196	304	432	568
35									001	003	008	020	045	088	155	250	368	500

Table F2

Unilateral probabilities for the binomial test when p = q = 1/2.

Note: Decimal points and values less than 0.0005 were omitted.

Table G

Critical Values of D_c for the Kolmogorov-Smirnov Test Considering P(D_cal > D_c) = α
Sample Size (N)	Significance Level α
Sample Size (N)	0.20	0.15	0.10	0.05	0.01
1	0.900	0.925	0.950	0.975	0.995
2	0.684	0.726	0.776	0.842	0.929
3	0.565	0.597	0.642	0.708	0.828
4	0.494	0.525	0.564	0.624	0.733
5	0.446	0.474	0.510	0.565	0.669
6	0.410	0.436	0.470	0.521	0.618
7	0.381	0.405	0.438	0.486	0.577
8	0.358	0.381	0.411	0.457	0.543
9	0.339	0.360	0.388	0.432	0.514
10	0.322	0.342	0.368	0.410	0.490
11	0.307	0.326	0.352	0.391	0.468
12	0.295	0.313	0.338	0.375	0.450
13	0.284	0.302	0.325	0.361	0.433
14	0.274	0.292	0.314	0.349	0.418
15	0.266	0.283	0.304	0.338	0.404
16	0.258	0.274	0.295	0.328	0.392
17	0.250	0.266	0.286	0.318	0.381
18	0.244	0.259	0.278	0.309	0.371
19	0.237	0.252	0.272	0.301	0.363
20	0.231	0.246	0.264	0.294	0.356
25	0.21	0.22	0.24	0.27	0.32
30	0.19	0.20	0.22	0.24	0.29
35	0.18	0.19	0.21	0.23	0.27
Greater than 50	$\frac{1.07}{\sqrt{N}}$ $\frac{1.07}{\sqrt{N}}$	$\frac{1.14}{\sqrt{N}}$ $\frac{1.14}{\sqrt{N}}$	$\frac{1.22}{\sqrt{N}}$ $\frac{1.22}{\sqrt{N}}$	$\frac{1.36}{\sqrt{N}}$ $\frac{1.36}{\sqrt{N}}$	$\frac{1.63}{\sqrt{N}}$ $\frac{1.63}{\sqrt{N}}$

Table G

Table H₁

Critical Values of Shapiro-Wilk W_c Statistic Considering P(W_cal < W_c) = α
Sample Size N	Significance Level α
Sample Size N	0.01	0.02	0.05	0.10	0.50	0.90	0.95	0.98	0.99
3	0.753	0.758	0.767	0.789	0.959	0.998	0.999	1.000	1.000
4	0.687	0.707	0.748	0.792	0.935	0.987	0.992	0.996	0.997
5	0.686	0.715	0.762	0.806	0.927	0.979	0.986	0.991	0.993
6	0.713	0.743	0.788	0.826	0.927	0.974	0.981	0.936	0.989
7	0.730	0.760	0.803	0.838	0.928	0.972	0.979	0.985	0.988
8	0.749	0.778	0.818	0.851	0.932	0.972	0.978	0.984	0.987
9	0.764	0.791	0.829	0.859	0.935	0.972	0.978	0.984	0.986
10	0.781	0.806	0.842	0.869	0.938	0.972	0.978	0.983	0.986
11	0.792	0.817	0.850	0.876	0.940	0.973	0.979	0.984	0.986
12	0.805	0.828	0.859	0.883	0.943	0.973	0.979	0.984	0.986
13	0.814	0.837	0.866	0.889	0.945	0.974	0.979	0.984	0.986
14	0.825	0.846	0.874	0.895	0.947	0.975	0.980	0.984	0.986
15	0.835	0.855	0.881	0.901	0.950	0.976	0.980	0.984	0.987
16	0.844	0.863	0.887	0.906	0.952	0.975	0.981	0.985	0.987
17	0.851	0.869	0.892	0.910	0.954	0.977	0.981	0.985	0.987
18	0.858	0.874	0.897	0.914	0.956	0.978	0.982	0.986	0.988
19	0.863	0.879	0.901	0.917	0.957	0.978	0.982	0.986	0.988
20	0.868	0.884	0.905	0.920	0.959	0.979	0.983	0.986	0.988
21	0.873	0.888	0.908	0.823	0.960	0.980	0.983	0.987	0.989
22	0.878	0.892	0.911	0.926	0.961	0.980	0.984	0.987	0.989
23	0.881	0.895	0.914	0.928	0.962	0.981	0.984	0.987	0.989
24	0.884	0.898	0.916	0.930	0.963	0.981	0.984	0.987	0.989
25	0.888	0.901	0.918	0.931	0.964	0.981	0.985	0.988	0.989
26	0.891	0.904	0.920	0.933	0.965	0.982	0.985	0.988	0.989
27	0.894	0.906	0.923	0.935	0.965	0.982	0.985	0.988	0.990
28	0.896	0.908	0.924	0.936	0.966	0.982	0.985	0.988	0.990
29	0.898	0.910	0.926	0.937	0.966	0.982	0.985	0.988	0.990
30	0.900	0.912	0.927	0.939	0.967	0.983	0.985	0.988	0.900

Table H1

Table H₂

Coefficients a_i.n for the Shapiro-Wilk Normality Test
i / n		2	3	4	5	6	7	8	9	10
1		0.7071	0.7071	0.6872	0.6646	0.6431	0.6233	0.6052	0.5888	0.5739
2			0.0000	0.1677	0.2413	0.2806	0.3031	0.3164	0.3244	0.3291
3					0.0000	0.0875	0.1401	0.1743	0.1976	0.2141
4							0.0000	0.0561	0.0947	0.1224
5									0.0000	0.0399
i / n	11	12	13	14	15	16	17	18	19	20
1	0.5601	0.5475	0.5359	0.5251	0.5150	0.5056	0.4968	0.4886	0.4808	0.4734
2	0.3315	0.3325	0.3325	0.3318	0.3306	0.3290	0.3273	0.3253	0.3232	0.3211
3	0.2260	0.2347	0.2412	0.2460	0.2495	0.2521	0.2540	0.2553	0.2561	0.2565
4	0.1429	0.1586	0.1707	0.1802	0.1878	0.1939	0.1988	0.2027	0.2059	0.2085
5	0.0695	0.0922	0.1099	0.1240	0.1353	0.1447	0.1524	0.1587	0.1641	0.1686
6	0.0000	0.0303	0.0539	0.0727	0.0880	0.1005	0.1109	0.1197	0.1271	0.1334
7			0.0000	0.0240	0.0433	0.0593	0.0725	0.0837	0.0932	0.1013
8					0.0000	0.0196	0.0359	0.0496	0.0612	0.0711
9							0.0000	0.0163	0.0303	0.0422
10									0.0000	0.0140
i / n	21	22	23	24	25	26	27	28	29	30
1	0.4643	0.4590	0.4542	0.4493	0.4450	0.4407	0.4366	0.4328	0.4291	0.4254
2	0.3185	0.3156	0.3126	0.3098	0.3069	0.3043	0.3018	0.2992	0.2968	0.2944
3	0.2578	0.2571	0.2563	0.2554	0.2543	0.2533	0.2522	0.2510	0.2499	0.2487
4	0.2119	0.2131	0.2139	0.2145	0.2148	0.2151	0.2152	0.2151	0.2150	0.2148
5	0.1736	0.1764	0.1787	0.1807	0.1822	0.1836	0.1848	0.1857	0.1864	0.1870
6	0.1399	0.1443	0.1480	0.1512	0.1539	0.1563	0.1584	0.1601	0.1616	0.1630
7	0.1092	0.1150	0.1201	0.1245	0.1283	0.1316	0.1346	0.1372	0.1395	0.1415
8	0.0804	0.0878	0.0941	0.0997	0.1046	0.1089	0.1128	0.1162	0.1192	0.1219
9	0.0530	0.0618	0.0696	0.0764	0.0823	0.0876	0.0923	0.0965	0.1002	0.1036
10	0.0263	0.0368	0.0459	0.0539	0.0610	0.0672	0.0728	0.0778	0.0822	0.0862
11	0.0000	0.0122	0.0228	0.0321	0.0403	0.0476	0.0540	0.0598	0.0650	0.0697
12			0.0000	0.0107	0.0200	0.0284	0.0358	0.0424	0.0483	0.0537
13					0.0000	0.0094	0.0178	0.0253	0.0320	0.0381
14							0.0000	0.0084	0.0159	0.0227
15									0.0000	0.0076

Table H2

Table I

Wilcoxon Test
P(S_p > S_c ) = α
S_c	N
S_c	3	4	5	6	7	8	9	10	11	12	13	14	15
3	0.6250
4	0.3750
5	0.2500	0.5625
6	0.1250	0.4375
7		0.3125
8		0.1875	0.5000
9		0.1250	0.4063
10		0.0625	0.3125
11			0.2188	0.5000
12			0.1563	0.4219
13			0.0938	0.3438
14			0.0625	0.2813	0.5313
15			0.0313	0.2188	0.4688
16				0.1563	0.4063
17				0.1094	0.3438
18				0.0781	0.2891	0.5273
19				0.0469	0.2344	0.4727
20				0.0313	0.1875	0.4219
21				0.0156	0.1484	0.3711
22					0.1094	0.3203
23					0.0781	0.2734	0.5000
24					0.0547	0.2305	0.4551
25					0.0391	0.1914	0.4102
26					0.0234	0.1563	0.3672
27					0.0156	0.1250	0.3262
28					0.0078	0.0977	0.2852	0.5000
29						0.0742	0.2480	0.4609
30						0.0547	0.2129	0.4229
31						0.0391	0.1797	0.3848
32						0.0273	0.1504	0.3477
33						0.0195	0.1250	0.3125	0.5171
34						0.0117	0.1016	0.2783	0.4829
35						0.0078	0.0820	0.2461	0.4492
36						0.0039	0.0645	0.2158	0.4155
37							0.0488	0.1875	0.3823
38							0.0371	0.1611	0.3501
39							0.0273	0.1377	0.3188	0.5151
40							0.0195	0.1162	0.2886	0.4849
41							0.0137	0.0967	0.2598	0.4548
42							0.0098	0.0801	0.2324	0.4250
43							0.0059	0.0654	0.2065	0.3955
44							0.0039	0.0527	0.1826	0.3667
45							0.0020	0.0420	0.1602	0.3386
46								0.0322	0.1392	0.3110	0.5000
47								0.0244	0.1201	0.2847	0.4730
48								0.0186	0.1030	0.2593	0.4463
49								0.0137	0.0874	0.2349	0.4197
50								0.0098	0.0737	0.2119	0.3934
51								0.0068	0.0615	0.1902	0.3677
52								0.0049	0.0508	0.1697	0.3424
53								0.0029	0.0415	0.1506	0.3177	0.5000
54								0.0020	0.0337	0.1331	0.2939	0.4758
55								0.0010	0.0269	0.1167	0.2709	0.4516
56									0.0210	0.1018	0.2487	0.4276
57									0.0161	0.0881	0.2274	0.4039
58									0.0122	0.0757	0.2072	0.3804
59									0.0093	0.0647	0.1879	0.3574
60									0.0068	0.0549	0.1698	0.3349	0.5110
61									0.0049	0.0461	0.1527	0.3129	0.4890
62									0.0034	0.0386	0.1367	0.2915	0.4670
63									0.0024	0.0320	0.1219	0.2708	0.4452
64									0.0015	0.0261	0.1082	0.2508	0.4235
65									0.0010	0.0212	0.0955	0.2316	0.4020
66									0.0005	0.0171	0.0839	0.2131	0.3808
67										0.0134	0.0732	0.1955	0.3599
68										0.0105	0.0636	0.1788	0.3394
69										0.0081	0.0549	0.1629	0.3193
70										0.0061	0.0471	0.1479	0.2997
71										0.0046	0.0402	0.1338	0.2807
72										0.0034	0.0341	0.1206	0.2622
73										0.0024	0.0287	0.1083	0.2444
74										0.0017	0.0239	0.0969	0.2271
75										0.0012	0.0199	0.0863	0.2106
76										0.0007	0.0164	0.0765	0.1947
77										0.0005	0.0133	0.0676	0.1796
78										0.0002	0.0107	0.0594	0.1651
79											0.0085	0.0520	0.1514
80											0.0067	0.0453	0.1384
81											0.0052	0.0392	0.1262
82											0.0040	0.0338	0.1147
83											0.0031	0.0290	0.1039
84											0.0023	0.0247	0.0938
85											0.0017	0.0209	0.0844
86											0.0012	0.0176	0.0757
87											0.0009	0.0148	0.0677
88											0.0006	0.0123	0.0603
89											0.0004	0.0101	0.0535
90											0.0002	0.0083	0.0473
91											0.0001	0.0067	0.0416
92												0.0054	0.0365
93												0.0043	0.0319
94												0.0034	0.0277
95												0.0026	0.0240
96												0.0020	0.0206
97												0.0015	0.0177
98												0.0012	0.0151
99												0.0009	0.0128
100												0.0006	0.0108
101												0.0004	0.0090
102												0.0003	0.0075
103												0.0002	0.0062
104												0.0001	0.0051
105													0.0042
106													0.0034
107													0.0027
108													0.0021
109													0.0017
110													0.0013
111													0.0010
112													0.0008
113													0.0006
114													0.0004
115													0.0003
116													0.0002
117													0.0002
118													0.0001
119													0.0001
120													0.0000

Table I Table I

Right-tailed unilateral probabilities for the Wilcoxon test.

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