Critical Value Tables
Percentages Under Normal Curve
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2518 0.2549
0.7 0.2580 0.2612 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389
1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
Percentages Under Normal Curve (continued)
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890
2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916
2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936
2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964
2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974
2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
2.9 0.4891 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986
3.0 0.4986 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990
3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993
3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995
3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997
3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 0.4998
3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998
3.6 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.7 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.8 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.5000 0.5000 0.5000
3.9 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
Pearson r (p. < .05 Level)
Level of Significance for Two-Tailed Test
df .10 .05 .02 .01 .002 .001
1 0.988 0.997 1.000 1.000 1.000 1.000
2 0.900 0.950 0.980 0.990 0.998 0.999
3 0.805 0.878 0.934 0.959 0.986 0.991
4 0.729 0.811 0.882 0.917 0.963 0.974
5 0.669 0.754 0.833 0.875 0.935 0.951
6 0.621 0.707 0.789 0.834 0.905 0.925
7 0.582 0.666 0.750 0.798 0.875 0.898
8 0.549 0.632 0.715 0.765 0.847 0.872
9 0.521 0.602 0.685 0.735 0.820 0.847
10 0.497 0.576 0.658 0.708 0.795 0.823
11 0.476 0.553 0.634 0.684 0.772 0.801
12 0.458 0.532 0.612 0.661 0.750 0.780
13 0.441 0.514 0.592 0.641 0.730 0.760
14 0.426 0.497 0.574 0.623 0.711 0.742
15 0.412 0.482 0.558 0.606 0.694 0.725
16 0.400 0.468 0.543 0.590 0.678 0.708
17 0.389 0.456 0.529 0.575 0.662 0.693
18 0.378 0.444 0.516 0.561 0.648 0.679
19 0.369 0.433 0.503 0.549 0.635 0.665
20 0.360 0.423 0.492 0.537 0.622 0.652
Pearson r (continued)
df .10 .05 .02 .01 .002 .001
21 0.352 0.413 0.482 0.526 0.610 0.640
22 0.344 0.404 0.472 0.515 0.599 0.629
23 0.337 0.396 0.462 0.505 0.588 0.618
24 0.330 0.388 0.453 0.496 0.578 0.607
25 0.323 0.381 0.445 0.487 0.568 0.597
26 0.317 0.374 0.437 0.479 0.559 0.588
27 0.311 0.367 0.430 0.471 0.550 0.579
28 0.306 0.361 0.423 0.463 0.541 0.570
30 0.296 0.349 0.409 0.449 0.526 0.554
40 0.257 0.304 0.358 0.393 0.463 0.490
50 0.231 0.273 0.322 0.354 0.419 0.443
60 0.211 0.250 0.295 0.325 0.385 0.408
80 0.183 0.217 0.257 0.283 0.336 0.357
100 0.164 0.195 0.230 0.254 0.303 0.321
200 0.116 0.138 0.164 0.181 0.216 0.230
500 0.073 0.088 0.104 0.115 0.138 0.146
Critical Values for t (p. < .05 Level)
Level of Significance for Two-Tailed Test
df .10 .05 .02 .01 .002 .001
1 6.314 12.706 31.820 63.657 318.309 636.619
2 2.920 4.303 6.965 9.925 22.327 31.599
3 2.353 3.182 4.541 5.841 10.215 12.924
4 2.132 2.776 3.747 4.604 7.173 8.610
5 2.015 2.571 3.365 4.032 5.893 6.869
6 1.943 2.447 3.143 3.707 5.208 5.959
7 1.895 2.365 2.998 3.499 4.785 5.408
8 1.860 2.306 2.896 3.355 4.501 5.041
9 1.833 2.262 2.821 3.250 4.297 4.781
10 1.812 2.228 2.764 3.169 4.144 4.587
11 1.796 2.201 2.718 3.106 4.025 4.437
12 1.782 2.179 2.681 3.055 3.930 4.318
13 1.771 2.160 2.650 3.012 3.852 4.221
14 1.761 2.145 2.624 2.977 3.787 4.140
15 1.753 2.131 2.602 2.947 3.733 4.073
16 1.746 2.120 2.583 2.921 3.686 4.015
17 1.740 2.110 2.567 2.898 3.646 3.965
18 1.734 2.101 2.552 2.878 3.610 3.922
19 1.729 2.093 2.539 2.861 3.579 3.883
20 1.725 2.086 2.528 2.845 3.552 3.850
Critical values of t (continued)
df .10 .05 .02 .01 .002 .001
21 1.721 2.080 2.518 2.831 3.527 3.819
22 1.717 2.074 2.508 2.819 3.505 3.792
23 1.714 2.069 2.500 2.807 3.485 3.768
24 1.711 2.064 2.492 2.797 3.467 3.745
25 1.708 2.060 2.485 2.787 3.450 3.725
26 1.706 2.056 2.479 2.779 3.435 3.707
27 1.703 2.052 2.473 2.771 3.421 3.690
28 1.701 2.048 2.467 2.763 3.408 3.674
29 1.699 2.045 2.462 2.756 3.396 3.659
30 1.697 2.042 2.457 2.750 3.385 3.646
50 1.676 2.009 2.403 2.678 3.261 3.496
100 1.660 1.984 2.364 2.626 3.174 3.390
150 & over 1.645 1.960 2.326 2.576 3.090 3.291
Chi-Square (p. < .05 Level)
Level of Significance for Two-Tailed Test
df .10 .05 .02 .01 .002 .001
1 2.706 3.841 5.412 6.635 9.550 10.828
2 4.605 5.991 7.824 9.210 12.430 13.816
3 6.251 7.815 9.837 11.345 14.796 16.267
4 7.779 9.488 11.668 13.277 16.924 18.468
5 9.236 11.071 13.388 15.086 18.908 20.516
6 10.645 12.592 15.033 16.812 20.792 22.459
7 12.017 14.067 16.622 18.475 22.601 24.323
8 13.362 15.507 18.168 20.090 24.353 26.124
9 14.684 16.919 19.679 21.666 26.056 27.877
10 15.987 18.307 21.161 23.209 27.722 29.588
11 17.275 19.675 22.618 24.725 29.354 31.264
12 18.549 21.026 24.054 26.217 30.957 32.909
13 19.812 22.362 25.472 27.688 32.535 34.528
14 21.064 23.685 26.873 29.141 34.091 36.123
15 22.307 24.996 28.259 30.578 35.628 37.697
16 23.542 26.296 29.633 32.000 37.146 39.252
17 24.769 27.587 30.995 33.409 38.648 40.790
Chi Square (Continued)
Level of Significance for Two-Tailed Test
df .10 .05 .02 .01 .002 .001
18 25.989 28.869 32.346 34.805 40.136 42.312
19 27.204 30.144 33.687 36.191 41.610 43.820
20 28.412 31.410 35.020 37.566 43.072 45.315
21 29.615 32.671 36.343 38.932 44.522 46.797
22 30.813 33.924 37.659 40.289 45.962 48.268
23 32.007 35.172 38.968 41.638 47.391 49.728
24 33.196 36.415 40.270 42.980 48.812 51.179
25 34.382 37.652 41.566 44.314 50.223 52.620
26 35.563 38.885 42.856 45.642 51.627 54.052
27 36.741 40.113 44.140 46.963 53.023 55.476
28 37.916 41.337 45.419 48.278 54.411 56.892
29 39.087 42.557 46.693 49.588 55.792 58.301
30 40.256 43.773 47.962 50.892 57.167 59.703
50 63.167 67.505 72.613 76.154 83.657 86.661
100 118.498 124.342 131.142 135.807 145.577 149.449
500 540.930 553.127 567.070 576.493 595.882 603.446