778
A p p e n d i x G
Statistical Tables
TABLE G.1
Cumulative Areas Under the Standard Normal Distribution
z 0 1 2 3 4 5 6 7 8 9
Ϫ3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
Ϫ2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
Ϫ2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
Ϫ2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
Ϫ2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
Ϫ2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
Ϫ2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
Ϫ2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
Ϫ2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
Ϫ2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
Ϫ2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
Ϫ1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
Ϫ1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
Ϫ1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
Ϫ1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
Ϫ1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
Ϫ1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
Ϫ1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
Ϫ1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
Ϫ1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
Ϫ1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
Ϫ0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
Ϫ0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
Ϫ0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
continued
Appendix G Statistical Tables
779
TABLE G.1 (concluded)
z 0 1 2 3 4 5 6 7 8 9
Ϫ0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
Ϫ0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
Ϫ0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
Ϫ0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
Ϫ0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
Ϫ0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
Ϫ0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
Examples: If Z ~ Normal(0,1) then P(Z Յ Ϫ1.32) ϭ .0934 and P(Z Յ 1.84) ϭ .9671.
Source: This table was generated using the Stata®
function normd.
Appendix G Statistical Tables
780
TABLE G.2
Critical Values of the t Distribution
Significance Level
1-Tailed: .10 .05 .025 .01 .005
2-Tailed: .20 .10 .050 .02 .010
1 3.078 6.314 12.706 31.821 63.657
2 1.886 2.920 4.303 6.965 9.925
3 1.638 2.353 3.182 4.541 5.841
4 1.533 2.132 2.776 3.747 4.604
5 1.476 2.015 2.571 3.365 4.032
6 1.440 1.943 2.447 3.143 3.707
7 1.415 1.895 2.365 2.998 3.499
8 1.397 1.860 2.306 2.896 3.355
9 1.383 1.833 2.262 2.821 3.250
10 1.372 1.812 2.228 2.764 3.169
11 1.363 1.796 2.201 2.718 3.106
12 1.356 1.782 2.179 2.681 3.055
13 1.350 1.771 2.160 2.650 3.012
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
16 1.337 1.746 2.120 2.583 2.921
17 1.333 1.740 2.110 2.567 2.898
18 1.330 1.734 2.101 2.552 2.878
19 1.328 1.729 2.093 2.539 2.861
20 1.325 1.725 2.086 2.528 2.845
21 1.323 1.721 2.080 2.518 2.831
22 1.321 1.717 2.074 2.508 2.819
23 1.319 1.714 2.069 2.500 2.807
24 1.318 1.711 2.064 2.492 2.797
25 1.316 1.708 2.060 2.485 2.787
26 1.315 1.706 2.056 2.479 2.779
27 1.314 1.703 2.052 2.473 2.771
28 1.313 1.701 2.048 2.467 2.763
29 1.311 1.699 2.045 2.462 2.756
30 1.310 1.697 2.042 2.457 2.750
40 1.303 1.684 2.021 2.423 2.704
60 1.296 1.671 2.000 2.390 2.660
90 1.291 1.662 1.987 2.368 2.632
120 1.289 1.658 1.980 2.358 2.617
ϱ 1.282 1.645 1.960 2.326 2.576
Examples: The 1% critical value for a one-tailed test with 25 df is 2.485. The 5% critical for a two-tailed test
with large (Ͼ 120) df is 1.96.
Source: This table was generated using the Stata®
function invt.
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Appendix G Statistical Tables
781
TABLE G.3a
10% Critical Values of the F Distribution
Numerator Degrees of Freedom
1 2 3 4 5 6 7 8 9 10
10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32
11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25
12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19
13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14
14 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.10
15 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06
16 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03
17 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00
18 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98
19 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96
20 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94
21 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92
22 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.90
23 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89
24 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91 1.88
25 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87
26 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88 1.86
27 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87 1.85
28 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87 1.84
29 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86 1.83
30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82
40 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76
60 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74 1.71
90 2.76 2.36 2.15 2.01 1.91 1.84 1.78 1.74 1.70 1.67
120 2.75 2.35 2.13 1.99 1.90 1.82 1.77 1.72 1.68 1.65
ϱ 2.71 2.30 2.08 1.94 1.85 1.77 1.72 1.67 1.63 1.60
Example: The 10% critical value for numerator df ϭ 2 and denominator df ϭ 40 is 2.44.
Source: This table was generated using the Stata®
function invfprob.
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Appendix G Statistical Tables
782
TABLE G.3b
5% Critical Values of the F Distribution
Numerator Degrees of Freedom
1 2 3 4 5 6 7 8 9 10
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25
25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22
27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19
29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99
90 3.95 3.10 2.71 2.47 2.32 2.20 2.11 2.04 1.99 1.94
120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91
ϱ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83
Example: The 5% critical value for numerator df ϭ 4 and large denominator df (ϱ) is 2.37.
Source: This table was generated using the Stata®
function invfprob.
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Appendix G Statistical Tables
783
TABLE G.3c
1% Critical Values of the F Distribution
Numerator Degrees of Freedom
1 2 3 4 5 6 7 8 9 10
10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69
17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51
19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26
23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17
25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09
27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03
29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63
90 6.93 4.85 4.01 3.54 3.23 3.01 2.84 2.72 2.61 2.52
120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47
ϱ 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32
Example: The 1% critical value for numerator df ϭ 3 and denominator df ϭ 60 is 4.13.
Source: This table was generated using the Stata®
function invfprob.
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