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  7. Z, T and χ2 Tables

Z, t, and χ2 Tables

Z Table: Negative Values

[printable version]

Body of table gives area under Z curve to the left of z.

Example: P[Z < -2.92] = .0018 

  z      .00    .01    .02    .03    .04    .05    .06    .07    .08    .09
-3.80  .0001  .0001  .0001  .0001  .0001  .0001  .0001  .0001  .0001  .0001
-3.70  .0001  .0001  .0001  .0001  .0001  .0001  .0001  .0001  .0001  .0001
-3.60  .0002  .0002  .0001  .0001  .0001  .0001  .0001  .0001  .0001  .0001
-3.50  .0002  .0002  .0002  .0002  .0002  .0002  .0002  .0002  .0002  .0002
-3.40  .0003  .0003  .0003  .0003  .0003  .0003  .0003  .0003  .0003  .0002
-3.30  .0005  .0005  .0005  .0004  .0004  .0004  .0004  .0004  .0004  .0003
-3.20  .0007  .0007  .0006  .0006  .0006  .0006  .0006  .0005  .0005  .0005
-3.10  .0010  .0009  .0009  .0009  .0008  .0008  .0008  .0008  .0007  .0007
-3.00  .0013  .0013  .0013  .0012  .0012  .0011  .0011  .0011  .0010  .0010
-2.90  .0019  .0018  .0018  .0017  .0016  .0016  .0015  .0015  .0014  .0014
-2.80  .0026  .0025  .0024  .0023  .0023  .0022  .0021  .0021  .0020  .0019
-2.70  .0035  .0034  .0033  .0032  .0031  .0030  .0029  .0028  .0027  .0026
-2.60  .0047  .0045  .0044  .0043  .0041  .0040  .0039  .0038  .0037  .0036
-2.50  .0062  .0060  .0059  .0057  .0055  .0054  .0052  .0051  .0049  .0048
-2.40  .0082  .0080  .0078  .0075  .0073  .0071  .0069  .0068  .0066  .0064
-2.30  .0107  .0104  .0102  .0099  .0096  .0094  .0091  .0089  .0087  .0084
-2.20  .0139  .0136  .0132  .0129  .0125  .0122  .0119  .0116  .0113  .0110
-2.10  .0179  .0174  .0170  .0166  .0162  .0158  .0154  .0150  .0146  .0143
-2.00  .0228  .0222  .0217  .0212  .0207  .0202  .0197  .0192  .0188  .0183
-1.90  .0287  .0281  .0274  .0268  .0262  .0256  .0250  .0244  .0239  .0233
-1.80  .0359  .0351  .0344  .0336  .0329  .0322  .0314  .0307  .0301  .0294
-1.70  .0446  .0436  .0427  .0418  .0409  .0401  .0392  .0384  .0375  .0367
-1.60  .0548  .0537  .0526  .0516  .0505  .0495  .0485  .0475  .0465  .0455
-1.50  .0668  .0655  .0643  .0630  .0618  .0606  .0594  .0582  .0571  .0559
-1.40  .0808  .0793  .0778  .0764  .0749  .0735  .0721  .0708  .0694  .0681
-1.30  .0968  .0951  .0934  .0918  .0901  .0885  .0869  .0853  .0838  .0823
-1.20  .1151  .1131  .1112  .1093  .1075  .1056  .1038  .1020  .1003  .0985
-1.10  .1357  .1335  .1314  .1292  .1271  .1251  .1230  .1210  .1190  .1170
-1.00  .1587  .1562  .1539  .1515  .1492  .1469  .1446  .1423  .1401  .1379
-0.90  .1841  .1814  .1788  .1762  .1736  .1711  .1685  .1660  .1635  .1611
-0.80  .2119  .2090  .2061  .2033  .2005  .1977  .1949  .1922  .1894  .1867
-0.70  .2420  .2389  .2358  .2327  .2296  .2266  .2236  .2206  .2177  .2148
-0.60  .2743  .2709  .2676  .2643  .2611  .2578  .2546  .2514  .2483  .2451
-0.50  .3085  .3050  .3015  .2981  .2946  .2912  .2877  .2843  .2810  .2776
-0.40  .3446  .3409  .3372  .3336  .3300  .3264  .3228  .3192  .3156  .3121
-0.30  .3821  .3783  .3745  .3707  .3669  .3632  .3594  .3557  .3520  .3483
-0.20  .4207  .4168  .4129  .4090  .4052  .4013  .3974  .3936  .3897  .3859
-0.10  .4602  .4562  .4522  .4483  .4443  .4404  .4364  .4325  .4286  .4247
-0.00  .5000  .4960  .4920  .4880  .4840  .4801  .4761  .4721  .4681  .4641

Z Table: Positive Values

[printable version]

Body of table gives area under Z curve to the left of z.

Example: P[Z < 2.92] = .9982 

  z      .00    .01    .02    .03    .04    .05    .06    .07    .08    .09
 0.00  .5000  .5040  .5080  .5120  .5160  .5199  .5239  .5279  .5319  .5359
 0.10  .5398  .5438  .5478  .5517  .5557  .5596  .5636  .5675  .5714  .5753
 0.20  .5793  .5832  .5871  .5910  .5948  .5987  .6026  .6064  .6103  .6141
 0.30  .6179  .6217  .6255  .6293  .6331  .6368  .6406  .6443  .6480  .6517
 0.40  .6554  .6591  .6628  .6664  .6700  .6736  .6772  .6808  .6844  .6879
 0.50  .6915  .6950  .6985  .7019  .7054  .7088  .7123  .7157  .7190  .7224
 0.60  .7257  .7291  .7324  .7357  .7389  .7422  .7454  .7486  .7517  .7549
 0.70  .7580  .7611  .7642  .7673  .7704  .7734  .7764  .7794  .7823  .7852
 0.80  .7881  .7910  .7939  .7967  .7995  .8023  .8051  .8078  .8106  .8133
 0.90  .8159  .8186  .8212  .8238  .8264  .8289  .8315  .8340  .8365  .8389
 1.00  .8413  .8438  .8461  .8485  .8508  .8531  .8554  .8577  .8599  .8621
 1.10  .8643  .8665  .8686  .8708  .8729  .8749  .8770  .8790  .8810  .8830
 1.20  .8849  .8869  .8888  .8907  .8925  .8944  .8962  .8980  .8997  .9015
 1.30  .9032  .9049  .9066  .9082  .9099  .9115  .9131  .9147  .9162  .9177
 1.40  .9192  .9207  .9222  .9236  .9251  .9265  .9279  .9292  .9306  .9319
 1.50  .9332  .9345  .9357  .9370  .9382  .9394  .9406  .9418  .9429  .9441
 1.60  .9452  .9463  .9474  .9484  .9495  .9505  .9515  .9525  .9535  .9545
 1.70  .9554  .9564  .9573  .9582  .9591  .9599  .9608  .9616  .9625  .9633
 1.80  .9641  .9649  .9656  .9664  .9671  .9678  .9686  .9693  .9699  .9706
 1.90  .9713  .9719  .9726  .9732  .9738  .9744  .9750  .9756  .9761  .9767
 2.00  .9772  .9778  .9783  .9788  .9793  .9798  .9803  .9808  .9812  .9817
 2.10  .9821  .9826  .9830  .9834  .9838  .9842  .9846  .9850  .9854  .9857
 2.20  .9861  .9864  .9868  .9871  .9875  .9878  .9881  .9884  .9887  .9890
 2.30  .9893  .9896  .9898  .9901  .9904  .9906  .9909  .9911  .9913  .9916
 2.40  .9918  .9920  .9922  .9925  .9927  .9929  .9931  .9932  .9934  .9936
 2.50  .9938  .9940  .9941  .9943  .9945  .9946  .9948  .9949  .9951  .9952
 2.60  .9953  .9955  .9956  .9957  .9959  .9960  .9961  .9962  .9963  .9964
 2.70  .9965  .9966  .9967  .9968  .9969  .9970  .9971  .9972  .9973  .9974
 2.80  .9974  .9975  .9976  .9977  .9977  .9978  .9979  .9979  .9980  .9981
 2.90  .9981  .9982  .9982  .9983  .9984  .9984  .9985  .9985  .9986  .9986
 3.00  .9987  .9987  .9987  .9988  .9988  .9989  .9989  .9989  .9990  .9990
 3.10  .9990  .9991  .9991  .9991  .9992  .9992  .9992  .9992  .9993  .9993
 3.20  .9993  .9993  .9994  .9994  .9994  .9994  .9994  .9995  .9995  .9995
 3.30  .9995  .9995  .9995  .9996  .9996  .9996  .9996  .9996  .9996  .9997
 3.40  .9997  .9997  .9997  .9997  .9997  .9997  .9997  .9997  .9997  .9998
 3.50  .9998  .9998  .9998  .9998  .9998  .9998  .9998  .9998  .9998  .9998
 3.60  .9998  .9998  .9999  .9999  .9999  .9999  .9999  .9999  .9999  .9999
 3.70  .9999  .9999  .9999  .9999  .9999  .9999  .9999  .9999  .9999  .9999
 3.80  .9999  .9999  .9999  .9999  .9999  .9999  .9999  .9999  .9999  .9999

t Table

 [printable version]
df
degrees of freedom for t curve
P
area under the t curve with df degrees of freedom to the right of t(df)
Example:
P[t(2) > 2.92] = 0.05
P[-2.92 < t(2) < 2.92] = 0.9 
						P
	0.25	0.2	0.15	0.1	0.05	0.025	0.02	0.01	0.005	0.0025	0.001	0.0005
df
1	1.000	1.376	1.963	3.078	6.314	12.706	15.895	31.821	63.657	127.321	318.309	636.619
2	0.817	1.061	1.386	1.886	2.920	4.303	4.849	6.965	9.925	14.089	22.327	31.599
3	0.765	0.979	1.250	1.638	2.353	3.182	3.482	4.541	5.841	7.453	10.215	12.924
4	0.741	0.941	1.190	1.533	2.132	2.776	2.999	3.747	4.604	5.598	7.173	8.610
5	0.727	0.920	1.156	1.476	2.015	2.571	2.757	3.365	4.032	4.773	5.893	6.869
6	0.718	0.906	1.134	1.440	1.943	2.447	2.612	3.143	3.707	4.317	5.208	5.959
7	0.711	0.896	1.119	1.415	1.895	2.365	2.517	2.998	3.499	4.029	4.785	5.408
8	0.706	0.889	1.108	1.397	1.860	2.306	2.449	2.896	3.355	3.833	4.501	5.041
9	0.703	0.883	1.100	1.383	1.833	2.262	2.398	2.821	3.250	3.690	4.297	4.781
10	0.700	0.879	1.093	1.372	1.812	2.228	2.359	2.764	3.169	3.581	4.144	4.587
11	0.697	0.876	1.088	1.363	1.796	2.201	2.328	2.718	3.106	3.497	4.025	4.437
12	0.696	0.873	1.083	1.356	1.782	2.179	2.303	2.681	3.055	3.428	3.930	4.318
13	0.694	0.870	1.079	1.350	1.771	2.160	2.282	2.650	3.012	3.372	3.852	4.221
14	0.692	0.868	1.076	1.345	1.761	2.145	2.264	2.624	2.977	3.326	3.787	4.140
15	0.691	0.866	1.074	1.341	1.753	2.131	2.249	2.602	2.947	3.286	3.733	4.073
16	0.690	0.865	1.071	1.337	1.746	2.120	2.235	2.583	2.921	3.252	3.686	4.015
17	0.689	0.863	1.069	1.333	1.740	2.110	2.224	2.567	2.898	3.222	3.646	3.965
18	0.688	0.862	1.067	1.330	1.734	2.101	2.214	2.552	2.878	3.197	3.610	3.922
19	0.688	0.861	1.066	1.328	1.729	2.093	2.205	2.539	2.861	3.174	3.579	3.883
20	0.687	0.860	1.064	1.325	1.725	2.086	2.197	2.528	2.845	3.153	3.552	3.850
21	0.686	0.859	1.063	1.323	1.721	2.080	2.189	2.518	2.831	3.135	3.527	3.819
22	0.686	0.858	1.061	1.321	1.717	2.074	2.183	2.508	2.819	3.119	3.505	3.792
23	0.685	0.858	1.060	1.319	1.714	2.069	2.177	2.500	2.807	3.104	3.485	3.768
24	0.685	0.857	1.059	1.318	1.711	2.064	2.172	2.492	2.797	3.091	3.467	3.745
25	0.684	0.856	1.058	1.316	1.708	2.060	2.167	2.485	2.787	3.078	3.450	3.725
26	0.684	0.856	1.058	1.315	1.706	2.056	2.162	2.479	2.779	3.067	3.435	3.707
27	0.684	0.855	1.057	1.314	1.703	2.052	2.158	2.473	2.771	3.057	3.421	3.690
28	0.683	0.855	1.056	1.313	1.701	2.048	2.154	2.467	2.763	3.047	3.408	3.674
29	0.683	0.854	1.055	1.311	1.699	2.045	2.150	2.462	2.756	3.038	3.396	3.659
30	0.683	0.854	1.055	1.310	1.697	2.042	2.147	2.457	2.750	3.030	3.385	3.646
40	0.681	0.851	1.050	1.303	1.684	2.021	2.123	2.423	2.704	2.971	3.307	3.551
50	0.679	0.849	1.047	1.299	1.676	2.009	2.109	2.403	2.678	2.937	3.261	3.496
60	0.679	0.848	1.045	1.296	1.671	2.000	2.099	2.390	2.660	2.915	3.232	3.460
80	0.678	0.846	1.043	1.292	1.664	1.990	2.088	2.374	2.639	2.887	3.195	3.416
100	0.677	0.845	1.042	1.290	1.660	1.984	2.081	2.364	2.626	2.871	3.174	3.390
1000	0.675	0.842	1.037	1.282	1.646	1.962	2.056	2.330	2.581	2.813	3.098	3.300
z*	0.674	0.841	1.036	1.282	1.645	1.960	2.054	2.326	2.576	2.807	3.090	3.291

	50%	60%	70%	80%	90%	95%	96%	98%	99%	99.5%	99.8%	99.9%
					Confidence level C

χ2 Table
df
degrees of freedom for χ2 curve
P
area under the χ2 curve with df degrees of freedom to the right 
                 		                 Tail probabilities P
	0.25	 0.20	 0.15	 0.10	 0.05	 0.025	 0.02 	 0.01	0.005  0.0025	0.001	0.0005 
  df
  1 	 1.32 	 1.64	 2.07	 2.71	 3.84	 5.02	 5.41	 6.63 	 7.88	 9.14	10.83	12.12
  2 	 2.77	 3.22	 3.79	 4.61	 5.99	 7.38	 7.82	 9.21 	10.60	11.98	13.82	15.20
  3 	 4.11    4.64    5.32	 6.25	 7.81	 9.35	 9.84	11.34 	12.84	14.32	16.27	17.73
  4 	 5.39	 5.59	 6.74	 7.78	 9.49	11.14	11.67	13.23 	14.86	16.42	18.47	20.00
  5 	 6.63	 7.29	 8.12	 9.24	11.07	12.83	13.33	15.09 	16.75	18.39	20.51	22.11
  6 	 7.84	 8.56	 9.45	10.64	12.53	14.45	15.03	16.81 	13.55	20.25	22.46	24.10
  7 	 9.04	 9.80	10.75	12.02	14.07	16.01	16.62 	18.48	20.28	22.04	24.32	26.02
  8 	10.22	11.03	12.03	13.36	15.51	17.53	18.17 	20.09	21.95	23.77	26.12	27.87
  9 	11.39	12.24	13.29	14.68	16.92	19.02	19.63 	21.67	23.59	25.46	27.83	29.67
 10 	12.55	13.44	14.53	15.99	18.31	20.48	21.16 	23.21	25.19	27.11	29.59	31.42
 11 	13.70	14.63	15.77	17.29	19.68	21.92	22.62	24.72	26.76	28.73	31.26	33.14
 12 	14.85	15.81	16.99	18.55	21.03	23.34	24.05	26.22	28.30	30.32	32.91	34.82
 13 	15.93	15.58	18.90	19.81	22.36	24.74	25.47	27.69	29.82	31.88	34.53	36.48
 14 	17.12	18.15	19.4	21.06	23.68	26.12	26.87	29.14	31.32	33.43	36.12	38.11
 15 	18.25	19.31	20.60	22.31	25.00	27.49	28.26	30.58	32.80	34.95	37.70	39.72
 16 	19.37	20.47	21.79	23.54	26.30	28.85	29.63	32.00	34.27	36.46	39.25	41.31
 17 	20.49	21.61	22.98	24.77	27.59	30.19	31.00	33.41	35.72	37.95	40.79	42.88
 18 	21.60	22.76	24.16	25.99	28.87	31.53	32.35	34.81	37.16	39.42	42.31	44.43
 19 	22.72	23.90	25.33	27.20	30.14	32.85	33.69	36.19	38.58	40.88	43.82	45.97
 20 	23.83	25.04	26.50	28.41	31.41	34.17	35.02	37.57	40.00	42.34	45.31	47.50
 21 	24.93	26.17	27.66	29.62	39.67	35.48	36.34	38.93	41.40	43.78	46.80	49.01
 22 	26.04	27.30	28.82	30.81	33.92	36.78	37.66	40.29	42.80	45.20	48.27	50.51
 23 	27.14	28.43	29.98	32.01	35.17	38.08	38.97	41.64	44.18	46.62	49.73	52.00
 24 	28.24	29.55	31.13	33.20	36.42	39.36	40.27	42.98	45.56	48.03	51.18	53.48
 25 	29.34	30.68	32.28	34.38	37.65	40.65	41.57	44.31	46.93	49.44	52.62	54.95
 26 	30.43	31.79	33.43	35.56	38.89	41.92	42.86	45.64	48.29	50.83	54.05	56.41
 27 	31.53	32.91	34.57	36.74	40.11	43.19	44.14	46.96	49.64	52.22	55.48	57.86
 28 	32.62	34.03	35.71	37.92	41.34	44.46	45.42	48.28	50.99	53.59	56.89	59.30
 29 	33.71	35.14	36.85	39.09	42.56	45.72	46.69	49.59	52.34	54.97	58.30	60.73
 30 	34.80	36.25	37.99	40.26	43.77	46.98	47.96	50.89	53.67	56.33	59.70	62.16
 40 	45.62	47.27	49.24	51.81	55.76	59.34	60.44	63.69	66.77	69.70	73.40	76.09
 50 	56.33	53.16	60.35	63.17	67.50	71.42	72.61	76.15	79.49	82.66	86.66	89.56
 60 	66.98	68.97	71.34	74.40	79.08	83.30	84.58	88.38	91.95	95.34	99.61	102.7
 80 	88.13	90.41	93.11	96.58	101.9	106.6	108.1	112.3	116.3	120.1	124.8	128.3
100 	109.1	111.7	114.7	118.5	124.3	129.6	131.1	135.8	140.2	144.3	149.4	153.2

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