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
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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
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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
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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
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Tail probabilities P
df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005
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 5.99 6.74 7.78 9.49 11.14 11.67 13.28 14.86 16.42 18.47 20.00
5 6.63 7.29 8.12 9.24 11.07 12.83 13.39 15.09 16.75 18.39 20.51 22.11
6 7.84 8.56 9.45 10.64 12.59 14.45 15.03 16.81 18.55 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 19.68 21.67 23.59 25.46 27.88 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 17.28 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 15.98 16.98 18.20 19.81 22.36 24.74 25.47 27.69 29.82 31.88 34.53 36.48
14 17.12 18.15 19.41 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 32.67 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 58.16 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