Tables - Basic & Clinical Biostatistics, 4th Edition

Basic & Clinical Biostatistics, 4th Edition

Appendices

CHAPTER GUIDE TO STATISTICAL TESTS IN BASIC & CLINICAL BIOSTATISTICS

Figure. No caption available.

Appendix A: Tables

Table A-1. Random numbers.

927415	956121	168117	169280	326569	266541
926937	515107	014658	159944	821115	317592
867169	388342	832261	993050	639410	698969
867169	542747	032683	131188	926198	371071
512500	843384	085361	398488	774767	383837
062454	423050	670884	840940	845839	979662
806702	881309	772977	367506	729850	457758
837815	163631	622143	938278	231305	219737
926839	453853	767825	284716	916182	467113
854813	731620	978100	589512	147694	389180
851595	452454	262448	688990	461777	647487
449353	556695	806050	123754	722070	935916
169116	586865	756231	469281	258737	989450
139470	358095	528858	660128	342072	681203
433775	761861	107191	515960	759056	150336
221922	232624	398839	495004	881970	792001
740207	078048	854928	875559	246288	000144
525873	755998	866034	444933	785944	018016
734185	499711	254256	616625	243045	251938
773112	463857	781983	078184	380752	492215
638951	982155	747821	773030	594005	526828
868888	769341	477611	628714	250645	853454
611034	167642	701316	589251	330456	681722
379290	955292	664549	656401	320855	215201
411257	411484	068629	050150	106933	900095
407167	435509	578642	268724	366564	511815
895893	438644	330273	590506	820439	976891
986683	830515	284065	813310	554920	111395
335421	814351	508062	663801	365001	924418
927660	793888	507773	975109	625175	552278
957559	236000	471608	888683	146821	034687
694904	499959	950969	085327	352611	335924
863016	494926	871064	665892	076333	990558
876958	865769	882966	236535	541645	819783
619813	221175	370697	566925	705564	472934
476626	646911	337167	865652	195448	116729
578292	863854	145858	206557	430943	591126
286553	981699	232269	819656	867825	890737
819064	712344	033613	457019	478176	342104
383035	043025	201591	127424	771948	762990
879392	378486	198814	928028	493486	373709
924020	273258	851781	003514	685749	713570
502523	157212	472643	439301	718562	196269
815316	651530	080430	912635	820240	533626
914984	444954	053723	079387	530020	703312
312248	619263	715357	923412	252522	913950
030964	407872	419563	426527	565215	243717
870561	984049	445361	315827	651925	464440
820157	006091	670091	478357	490641	082559
519649	761345	761354	794613	330132	319843

Table A-2. Areas under the standard normal curve.^a

z	Area Between -z & +z	Area in Two Tails (< -z & > +z)	Area in One Tail (< -z or > +z)
0.00	0.000	1.000	0.500
0.05	0.040	0.960	0.480
0.10	0.080	0.920	0.460
0.15	0.119	0.881	0.440
0.20	0.159	0.841	0.421
0.25	0.197	0.803	0.401
0.30	0.236	0.764	0.382
0.35	0.274	0.726	0.363
0.40	0.311	0.689	0.345
0.45	0.347	0.653	0.326
0.50	0.383	0.617	0.309
0.55	0.418	0.582	0.291
0.60	0.451	0.549	0.274
0.65	0.484	0.516	0.258
0.70	0.516	0.484	0.242
0.75	0.547	0.453	0.227
0.80	0.576	0.424	0.212
0.85	0.605	0.395	0.198
0.90	0.632	0.368	0.184
0.95	0.658	0.342	0.171
1.00^a	0.683	0.317	0.159
1.05	0.706	0.294	0.147
1.10	0.729	0.271	0.136
1.15	0.750	0.250	0.125
1.20	0.770	0.230	0.115
1.25	0.789	0.211	0.106
1.28^a	0.800	0.200	0.100
1.30	0.806	0.194	0.097
1.35	0.823	0.177	0.089
1.40	0.838	0.162	0.081
1.45	0.853	0.147	0.074
1.50	0.866	0.134	0.067
1.55	0.879	0.121	0.061
1.60	0.890	0.110	0.055
1.645^a	0.900	0.100	0.050
1.65	0.901	0.099	0.049
1.70	0.911	0.089	0.045
1.75	0.920	0.080	0.040
1.80	0.928	0.072	0.036
1.85	0.936	0.064	0.032
1.90	0.943	0.057	0.029
1.95	0.949	0.051	0.026
1.96^a	0.950	0.050	0.025
2.00	0.954	0.046	0.023
2.05	0.960	0.040	0.020
2.10	0.964	0.036	0.018
2.15	0.968	0.032	0.016
2.20	0.972	0.028	0.014
2.25	0.976	0.024	0.012
2.30	0.979	0.021	0.011
2.326^a	0.980	0.020	0.010
2.35	0.981	0.019	0.009
2.40	0.984	0.016	0.008
2.45	0.986	0.014	0.007
2.50	0.988	0.012	0.006
2.55	0.989	0.011	0.005
2.575^a	0.990	0.010	0.005
2.60	0.991	0.009	0.005
2.65	0.992	0.008	0.004
2.70	0.993	0.007	0.003
2.75	0.994	0.006	0.003
2.80	0.995	0.005	0.003
2.85	0.996	0.004	0.002
2.90	0.996	0.004	0.002
2.95	0.997	0.003	0.002
3.00	0.997	0.003	0.001
^aCommonly used values are underlined. Source: Adapted and reproduced, with permission, from Table 1 in Pearson ES, Hartley HO (editors):Biometrika Tables for Statisticians, 3rd ed, Vol 1. Cambridge University Press, 1966. Used with the kind permission of the Biometrika trustees.

Table A-3. Percentage points or critical values for the t distribution corresponding to commonly used areas under the curve.

Degrees of Freedom	Area in 1 Tail
	0.05	0.025	0.01	0.005	0.0005
	Area in 2 Tails
	0.10	0.05	0.02	0.01	0.001
1	6.314	12.706	31.821	63.657	636.62
2	2.920	4.303	6.965	9.925	31.598
3	2.353	3.182	4.541	5.841	12.924
4	2.132	2.776	3.747	4.604	8.610
5	2.015	2.571	3.365	4.032	6.869
6	1.943	2.447	3.143	3.707	5.959
7	1.895	2.365	2.998	3.499	5.408
8	1.860	2.306	2.896	3.355	5.041
9	1.833	2.262	2.821	3.250	4.781
10	1.812	2.228	2.764	3.169	4.587
11	1.796	2.201	2.718	3.106	4.437
12	1.782	2.179	2.681	3.055	4.318
13	1.771	2.160	2.650	3.012	4.221
14	1.761	2.145	2.624	2.977	4.140
15	1.753	2.131	2.602	2.947	4.073
16	1.746	2.120	2.583	2.921	4.015
17	1.740	2.110	2.567	2.898	3.965
18	1.734	2.101	2.552	2.878	3.922
19	1.729	2.093	2.539	2.861	3.883
20	1.725	2.086	2.528	2.845	3.850
21	1.721	2.080	2.518	2.831	3.819
22	1.717	2.074	2.508	2.819	3.792
23	1.714	2.069	2.500	2.807	3.767
24	1.711	2.064	2.492	2.797	3.745
25	1.708	2.060	2.485	2.787	3.725
26	1.706	2.056	2.479	2.779	3.707
27	1.703	2.052	2.473	2.771	3.690
28	1.701	2.048	2.467	2.763	3.674
29	1.699	2.045	2.462	2.756	3.659
30	1.697	2.042	2.457	2.750	3.646
40	1.684	2.021	2.423	2.704	3.551
60	1.671	2.000	2.390	2.660	3.460
120	1.658	1.980	2.358	2.617	3.373
∞	1.645	1.960	2.326	2.576	3.291
Source: Adapted and reproduced, with permission, from Table 12 in Pearson ES, Hartley HO (editors):Biometrika Tables for Statisticians, 3rd ed, Vol 1. Cambridge University Press, 1966. Used with the kind permission of the Biometrika Trustees.

Table A-4. Percentage points or critical values for the F distribution corresponding to areas of 0.05 and 0.01 under the upper tail of the distribution.

Degrees of Freedom, Denominator	Area	Degrees of Freedom, Numerator
Degrees of Freedom, Denominator	Area	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120	∞
1	0.05	161.4	199.5	215.7	224.6	230.2	234.2	236.8	238.9	240.5	241.9	243.9	245.9	248.0	249.1	250.1	251.1	252.2	253.3	254.3
1	0.01	4052	4999.5	5403	5625	5764	5859	5928	5981	6022	6056	6106	6157	6209	6235	6261	6287	6313	6339	6366
2	0.05	18.51	19.00	19.16	19.25	19.30	19.33	19.35	19.37	19.38	19.40	19.41	19.43	19.45	19.45	19.46	19.47	19.48	19.49	19.50
2	0.01	98.50	99.00	99.17	99.25	99.30	99.33	99.36	99.37	99.39	99.40	99.42	99.43	99.45	99.46	99.47	99.47	99.48	99.49	99.50
3	0.05	10.13	9.55	9.28	9.12	9.01	8.94	8.89	8.85	8.81	8.79	8.74	8.70	8.66	8.64	8.62	8.59	8.57	8.55	8.53
3	0.01	34.12	30.82	29.46	28.71	28.24	27.91	27.67	27.49	27.35	27.23	27.05	26.87	26.69	26.60	26.50	26.41	26.32	26.22	26.13
4	0.05	7.71	6.94	6.59	6.39	6.26	6.16	6.09	6.04	6.00	5.96	5.91	5.86	5.80	5.77	5.75	5.72	5.69	5.66	5.63
4	0.01	21.20	18.00	16.69	15.98	15.52	15.21	14.98	14.80	14.66	14.55	14.37	14.20	14.02	13.93	13.84	13.75	13.65	13.56	13.46
5	0.05	6.61	5.79	5.41	5.19	5.05	4.95	4.88	4.82	4.77	4.74	4.68	4.62	4.56	4.53	4.50	4.46	4.43	4.40	4.36
5	0.01	16.26	13.27	12.06	11.39	10.97	10.67	10.46	10.29	10.16	10.05	9.89	9.72	9.55	9.47	9.38	9.29	9.20	9.11	9.02
6	0.05	5.99	5.14	4.76	4.53	4.39	4.28	4.21	4.15	4.10	4.06	4.00	3.94	3.87	3.84	3.81	3.77	3.74	3.70	3.67
6	0.01	13.75	10.92	9.78	9.15	8.75	8.47	8.26	8.10	7.98	7.87	7.72	7.56	7.40	7.31	7.23	7.14	7.06	6.97	6.88
7	0.05	5.59	4.74	4.35	4.12	3.97	3.87	3.79	3.73	3.68	3.64	3.57	3.51	3.44	3.41	3.38	3.34	3.30	3.27	3.23
7	0.01	12.25	9.55	8.45	7.85	7.46	7.19	6.99	6.84	6.72	6.62	6.47	6.31	6.16	6.07	5.99	5.91	5.82	5.74	5.65
8	0.05	5.32	4.46	4.07	3.84	3.69	3.58	3.50	3.44	3.39	3.35	3.28	3.22	3.15	3.12	3.08	3.04	3.01	2.97	2.93
8	0.01	11.26	8.65	7.59	7.01	6.63	6.37	6.18	6.03	5.91	5.81	5.67	5.52	5.36	5.28	5.20	5.12	5.03	4.95	4.86
9	0.05	5.12	4.26	3.86	3.63	3.48	3.37	3.29	3.23	3.18	3.14	3.07	3.01	2.94	2.90	2.86	2.83	2.79	2.75	2.71
9	0.01	10.56	8.02	6.99	6.42	6.06	5.80	5.61	5.47	5.35	5.26	5.11	4.96	4.81	4.73	4.65	4.57	4.48	4.40	4.31
10	0.05	4.96	4.10	3.71	3.48	3.33	3.22	3.14	3.07	3.02	2.98	2.91	2.85	2.77	2.74	2.70	2.66	2.62	2.58	2.54
10	0.01	10.04	7.56	6.55	5.99	5.64	5.39	5.20	5.06	4.94	4.85	4.71	4.56	4.41	4.33	4.25	4.17	4.08	4.00	3.91
12	0.05	4.75	3.89	3.49	3.26	3.11	3.00	2.91	2.85	2.80	2.75	2.69	2.62	2.54	2.51	2.47	2.43	2.38	2.34	2.30
12	0.01	9.33	6.93	5.95	5.41	5.06	4.82	4.64	4.50	4.39	4.30	4.16	4.01	3.86	3.78	3.70	3.62	3.54	3.45	3.36
15	0.05	4.54	3.68	3.29	3.06	2.90	2.79	2.71	2.64	2.59	2.54	2.48	2.40	2.33	2.29	2.25	2.20	2.16	2.11	2.07
15	0.01	8.68	6.36	5.42	4.89	4.56	4.32	4.14	4.00	3.89	3.80	3.67	3.52	3.37	3.29	3.21	3.13	3.05	2.96	2.87
20	0.05	4.35	3.49	3.10	2.87	2.71	2.60	2.51	2.45	2.39	2.35	2.28	2.20	2.12	2.08	2.04	1.99	1.95	1.90	1.84
20	0.01	8.10	5.85	4.94	4.43	4.10	3.87	3.70	3.56	3.46	3.37	3.23	3.09	2.94	2.86	2.78	2.69	2.61	2.52	2.42
24	0.05	4.26	3.40	3.01	2.78	2.62	2.51	2.42	2.36	2.30	2.25	2.18	2.11	2.03	1.98	1.94	1.89	1.84	1.79	1.73
24	0.01	7.82	5.61	4.72	4.22	3.90	3.67	3.50	3.36	3.26	3.17	3.03	2.89	2.74	2.66	2.58	2.49	2.40	2.31	2.21
30	0.05	4.17	3.32	2.92	2.69	2.53	2.42	2.33	2.27	2.21	2.16	2.09	2.01	1.93	1.89	1.84	1.79	1.74	1.68	1.62
30	0.01	7.56	5.39	4.51	4.02	3.70	3.47	3.30	3.17	3.07	2.98	2.84	2.70	2.55	2.47	2.39	2.30	2.21	2.11	2.01
40	0.05	4.08	3.23	2.84	2.61	2.45	2.34	2.25	2.18	2.12	2.08	2.00	1.92	1.84	1.79	1.74	1.69	1.64	1.58	1.51
40	0.01	7.31	5.18	4.31	3.83	3.51	3.29	3.12	2.99	2.89	2.80	2.66	2.52	2.37	2.29	2.20	2.11	2.02	1.92	1.80
60	0.05	4.00	3.15	2.76	2.53	2.37	2.25	2.17	2.10	2.04	1.99	1.92	1.84	1.75	1.70	1.65	1.59	1.53	1.47	1.39
60	0.01	7.08	4.98	4.13	3.65	3.34	3.12	2.95	2.82	2.72	2.63	2.50	2.35	2.20	2.12	2.03	1.94	1.84	1.73	1.60
120	0.05	3.92	3.07	2.68	2.45	2.29	2.17	2.09	2.02	1.96	1.91	1.83	1.75	1.66	1.61	1.55	1.50	1.43	1.35	1.25
120	0.01	6.85	4.79	3.95	3.48	3.17	2.96	2.79	2.66	2.56	2.47	2.34	2.19	2.03	1.95	1.86	1.76	1.66	1.53	1.38
∞	0.05	3.84	3.00	2.60	2.37	2.21	2.10	2.01	1.94	1.88	1.83	1.75	1.67	1.57	1.52	1.46	1.39	1.32	1.22	1.00
∞	0.01	6.63	4.61	3.78	3.32	3.02	2.80	2.64	2.51	2.41	2.32	2.18	2.04	1.88	1.79	1.70	1.59	1.47	1.32	1.00
Source: Adapted and reproduced, with permission, from Table 18 in Pearson ES, Hartley HO (editors): Biometrika Tables for Statisticians, 3rd ed, Vol 1. Cambridge University Press, 1966. Used with the kind permission of the Biometrika Trustees.

Table A-5. Percentage points or critical values for the χ² distribution corresponding to commonly used areas under the curve.

Degrees of Freedom	Area in Upper Tail
Degrees of Freedom	0.10	0.05	0.01	0.001
1	2.706	3.841	6.635	10.828
2	4.605	5.991	9.210	13.816
3	6.251	7.815	11.345	16.266
4	7.779	9.488	13.277	18.467
5	9.236	11.071	15.086	20.515
6	10.645	12.592	16.812	22.458
7	12.017	14.067	18.475	24.322
8	13.362	15.507	20.090	26.125
9	14.684	16.919	21.666	27.877
10	15.987	18.307	23.209	29.588
11	17.275	19.675	24.725	31.264
12	18.549	21.026	26.217	32.909
13	19.812	22.362	27.688	34.528
14	21.064	23.685	29.141	36.123
15	22.307	24.996	30.578	37.697
16	23.542	26.296	32.000	39.252
17	24.769	27.587	33.409	40.790
18	25.989	28.869	34.805	42.312
19	27.204	30.144	36.191	43.820
20	28.412	31.410	37.566	45.315
21	29.615	32.671	38.932	46.797
22	30.813	33.924	40.289	48.268
23	32.007	35.173	41.638	49.728
24	33.196	36.415	42.980	51.179
25	34.382	37.653	44.314	52.620
26	35.563	38.885	45.642	54.052
27	36.741	40.113	46.963	55.476
28	37.916	41.337	48.278	56.892
29	39.088	42.557	49.588	58.302
30	40.256	43.773	50.892	59.703
40	51.805	55.759	63.691	73.402
50	63.167	67.505	76.154	86.661
60	74.397	79.082	88.379	99.607
70	85.527	90.531	100.425	112.317
80	96.578	101.879	112.329	124.839
90	107.565	113.145	124.116	137.208
100	118.498	124.342	135.807	149.449
Source: Adapted and reproduced, with permission, from Table 8 in Pearson ES, Hartley HO (editors):Biometrika Tables for Statisticians, 3rd ed, Vol 1. Cambridge University Press, 1966. Used with the kind permission of the Biometrika Trustees.

Table A-6. z Transformation^a of the correlation coefficient.

r	z	r	z
0.00	0.000	0.50	0.549
0.01	0.010	0.51	0.563
0.02	0.020	0.52	0.576
0.03	0.030	0.53	0.590
0.04	0.040	0.54	0.604
0.05	0.050	0.55	0.618
0.06	0.060	0.56	0.633
0.07	0.070	0.57	0.648
0.08	0.080	0.58	0.663
0.09	0.090	0.59	0.678
0.10	0.100	0.60	0.693
0.11	0.110	0.61	0.709
0.12	0.121	0.62	0.725
0.13	0.131	0.63	0.741
0.14	0.141	0.64	0.758
0.15	0.151	0.65	0.775
0.16	0.161	0.66	0.793
0.17	0.172	0.67	0.811
0.18	0.182	0.68	0.829
0.19	0.192	0.69	0.848
0.20	0.203	0.70	0.867
0.21	0.213	0.71	0.887
0.22	0.224	0.72	0.908
0.23	0.234	0.73	0.929
0.24	0.245	0.74	0.951
0.25	0.255	0.75	0.973
0.26	0.266	0.76	0.996
0.27	0.277	0.77	1.020
0.28	0.288	0.78	1.045
0.29	0.299	0.79	1.071
0.30	0.310	0.80	1.099
0.31	0.321	0.81	1.127
0.32	0.332	0.82	1.157
0.33	0.343	0.83	1.188
0.34	0.354	0.84	1.221
0.35	0.365	0.85	1.256
0.36	0.377	0.86	1.293
0.37	0.388	0.87	1.333
0.38	0.400	0.88	1.376
0.39	0.412	0.89	1.422
0.40	0.424	0.90	1.472
0.41	0.436	0.91	1.528
0.42	0.448	0.92	1.589
0.43	0.460	0.93	1.658
0.44	0.472	0.94	1.738
0.45	0.485	0.95	1.832
0.46	0.497	0.96	1.946
0.47	0.510	0.97	2.092
0.48	0.523	0.98	2.298
0.49	0.536	0.99	2.647
^az = 1/2 {ln[(1 + r)/(1 - r)]}. Source: Adapted and reproduced, with permission, from Table 14 in Pearson ES, Hartley HO (editors):Biometrika Tables for Statisticians, 3rd ed, Vol 1. Cambridge University Press, 1966. Used with the kind permission of the Biometrika Trustees.

Figure A-1. 95% Confidence intervals for population proportion. (Adapted and reproduced, with permission, from Pearson ES, Hartley HO (editors): Biometrika Tables for Statisticians, 3rd ed., Vol. 1. Cambridge University Press, 1966.)

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