28  Appendix 4

Table 28.1: t Table: critical values of the t distribution for a given degrees of freedom (df) and cumulative probability.
cum. prob.
0.50
0.75
0.80
0.85
0.90
0.95
0.975
0.99
0.995
one-tail
0.50
0.25
0.20
0.15
0.10
0.05
0.025
0.01
0.005
two-tails 1.00 0.50 0.40 0.30 0.20 0.10 0.05 0.02 0.01
df
1 0.000 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66
2 0.000 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925
3 0.000 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841
4 0.000 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604
5 0.000 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032
6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707
7 0.000 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499
8 0.000 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355
9 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250
10 0.000 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169
11 0.000 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106
12 0.000 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055
13 0.000 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012
14 0.000 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977
15 0.000 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947
16 0.000 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921
17 0.000 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898
18 0.000 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878
19 0.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861
20 0.000 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845
21 0.000 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831
22 0.000 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819
23 0.000 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807
24 0.000 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797
25 0.000 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787
26 0.000 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779
27 0.000 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771
28 0.000 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763
29 0.000 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756
30 0.000 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750
40 0.000 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704
60 0.000 0.679 0.848 1.045 1.296 1.671 2.000 2.390 2.660
80 0.000 0.678 0.846 1.043 1.292 1.664 1.990 2.374 2.639
100 0.000 0.677 0.845 1.042 1.290 1.660 1.984 2.364 2.626
1000 0.000 0.675 0.842 1.037 1.282 1.646 1.962 2.330 2.581
z 0.000 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576
Confidence Level 0% 50% 60% 70% 80% 90% 95% 98% 99%
Note

Row z in Table 28.1 gives the critical values of the standard normal distribution, which the t distribution approaches as degrees of freedom (df) increase. For df > 1000, the t distribution is practically indistinguishable from the standard normal.