Finding Probability Using Tree Diagrams and Outcome Tables 4.5.
Probability Tables
19
Standard Normal Distribution Table Provides Area to Right of Given Z Value Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 3.6 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 3.7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
description
Standard Normal Distribution
Transcript of Probability Tables
Standard Normal Distribution
Table Provides Area to Right of Given Z Value
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007
3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005
3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003
3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002
3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
3.6 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
3.7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2
t Distribution
Table provides value of t Shaded* columns may not be on tables distributed for exam use
Area to Right shown at top of table
df 0.250 0.200 0.150 0.100 0.050 0.025 0.020 0.010 0.005 0.001
1 1.0000 1.3764 1.9626 3.0777 6.3137 12.7062 15.8945 31.8210 63.6559 318.2888
2 0.8165 1.0607 1.3862 1.8856 2.9200 4.3027 4.8487 6.9645 9.9250 22.3285
3 0.7649 0.9785 1.2498 1.6377 2.3534 3.1824 3.4819 4.5407 5.8408 10.2143
4 0.7407 0.9410 1.1896 1.5332 2.1318 2.7765 2.9985 3.7469 4.6041 7.1729
5 0.7267 0.9195 1.1558 1.4759 2.0150 2.5706 2.7565 3.3649 4.0321 5.8935
6 0.7176 0.9057 1.1342 1.4398 1.9432 2.4469 2.6122 3.1427 3.7074 5.2075
7 0.7111 0.8960 1.1192 1.4149 1.8946 2.3646 2.5168 2.9979 3.4995 4.7853
8 0.7064 0.8889 1.1081 1.3968 1.8595 2.3060 2.4490 2.8965 3.3554 4.5008
9 0.7027 0.8834 1.0997 1.3830 1.8331 2.2622 2.3984 2.8214 3.2498 4.2969
10 0.6998 0.8791 1.0931 1.3722 1.8125 2.2281 2.3593 2.7638 3.1693 4.1437
11 0.6974 0.8755 1.0877 1.3634 1.7959 2.2010 2.3281 2.7181 3.1058 4.0248
12 0.6955 0.8726 1.0832 1.3562 1.7823 2.1788 2.3027 2.6810 3.0545 3.9296
13 0.6938 0.8702 1.0795 1.3502 1.7709 2.1604 2.2816 2.6503 3.0123 3.8520
14 0.6924 0.8681 1.0763 1.3450 1.7613 2.1448 2.2638 2.6245 2.9768 3.7874
15 0.6912 0.8662 1.0735 1.3406 1.7531 2.1315 2.2485 2.6025 2.9467 3.7329
16 0.6901 0.8647 1.0711 1.3368 1.7459 2.1199 2.2354 2.5835 2.9208 3.6861
17 0.6892 0.8633 1.0690 1.3334 1.7396 2.1098 2.2238 2.5669 2.8982 3.6458
18 0.6884 0.8620 1.0672 1.3304 1.7341 2.1009 2.2137 2.5524 2.8784 3.6105
19 0.6876 0.8610 1.0655 1.3277 1.7291 2.0930 2.2047 2.5395 2.8609 3.5793
20 0.6870 0.8600 1.0640 1.3253 1.7247 2.0860 2.1967 2.5280 2.8453 3.5518
21 0.6864 0.8591 1.0627 1.3232 1.7207 2.0796 2.1894 2.5176 2.8314 3.5271
22 0.6858 0.8583 1.0614 1.3212 1.7171 2.0739 2.1829 2.5083 2.8188 3.5050
23 0.6853 0.8575 1.0603 1.3195 1.7139 2.0687 2.1770 2.4999 2.8073 3.4850
24 0.6848 0.8569 1.0593 1.3178 1.7109 2.0639 2.1715 2.4922 2.7970 3.4668
25 0.6844 0.8562 1.0584 1.3163 1.7081 2.0595 2.1666 2.4851 2.7874 3.4502
26 0.6840 0.8557 1.0575 1.3150 1.7056 2.0555 2.1620 2.4786 2.7787 3.4350
27 0.6837 0.8551 1.0567 1.3137 1.7033 2.0518 2.1578 2.4727 2.7707 3.4210
28 0.6834 0.8546 1.0560 1.3125 1.7011 2.0484 2.1539 2.4671 2.7633 3.4082
29 0.6830 0.8542 1.0553 1.3114 1.6991 2.0452 2.1503 2.4620 2.7564 3.3963
30 0.6828 0.8538 1.0547 1.3104 1.6973 2.0423 2.1470 2.4573 2.7500 3.3852
31 0.6825 0.8534 1.0541 1.3095 1.6955 2.0395 2.1438 2.4528 2.7440 3.3749
32 0.6822 0.8530 1.0535 1.3086 1.6939 2.0369 2.1409 2.4487 2.7385 3.3653
33 0.6820 0.8526 1.0530 1.3077 1.6924 2.0345 2.1382 2.4448 2.7333 3.3563
34 0.6818 0.8523 1.0525 1.3070 1.6909 2.0322 2.1356 2.4411 2.7284 3.3480
35 0.6816 0.8520 1.0520 1.3062 1.6896 2.0301 2.1332 2.4377 2.7238 3.3400
36 0.6814 0.8517 1.0516 1.3055 1.6883 2.0281 2.1309 2.4345 2.7195 3.3326
37 0.6812 0.8514 1.0512 1.3049 1.6871 2.0262 2.1287 2.4314 2.7154 3.3256
38 0.6810 0.8512 1.0508 1.3042 1.6860 2.0244 2.1267 2.4286 2.7116 3.3190
39 0.6808 0.8509 1.0504 1.3036 1.6849 2.0227 2.1247 2.4258 2.7079 3.3127
40 0.6807 0.8507 1.0500 1.3031 1.6839 2.0211 2.1229 2.4233 2.7045 3.3069
50 0.6794 0.8489 1.0473 1.2987 1.6759 2.0086 2.1087 2.4033 2.6778 3.2614
60 0.6786 0.8477 1.0455 1.2958 1.6706 2.0003 2.0994 2.3901 2.6603 3.2317
70 0.6780 0.8468 1.0442 1.2938 1.6669 1.9944 2.0927 2.3808 2.6479 3.2108
80 0.6776 0.8461 1.0432 1.2922 1.6641 1.9901 2.0878 2.3739 2.6387 3.1952
90 0.6772 0.8456 1.0424 1.2910 1.6620 1.9867 2.0839 2.3685 2.6316 3.1832
100 0.6770 0.8452 1.0418 1.2901 1.6602 1.9840 2.0809 2.3642 2.6259 3.1738
110 0.6767 0.8449 1.0413 1.2893 1.6588 1.9818 2.0784 2.3607 2.6213 3.1660
120 0.6765 0.8446 1.0409 1.2886 1.6576 1.9799 2.0763 2.3578 2.6174 3.1595
∞ 0.6745 0.8416 1.0364 1.2816 1.6449 1.9600 2.0537 2.3263 2.5758 3.0902
3
Chi Square Distribution
Table provides value of Chi Square
Area to Right shown at top of table
df 0.995 0.990 0.980 0.975 0.950 0.900 0.100 0.050 0.025 0.020 0.010 0.005
1 0.000 0.000 0.001 0.001 0.004 0.016 2.706 3.841 5.024 5.412 6.635 7.879
2 0.010 0.020 0.040 0.051 0.103 0.211 4.605 5.991 7.378 7.824 9.210 10.597
3 0.072 0.115 0.185 0.216 0.352 0.584 6.251 7.815 9.348 9.837 11.345 12.838
4 0.207 0.297 0.429 0.484 0.711 1.064 7.779 9.488 11.143 11.668 13.277 14.860
5 0.412 0.554 0.752 0.831 1.145 1.610 9.236 11.070 12.832 13.388 15.086 16.750
6 0.676 0.872 1.134 1.237 1.635 2.204 10.645 12.592 14.449 15.033 16.812 18.548
7 0.989 1.239 1.564 1.690 2.167 2.833 12.017 14.067 16.013 16.622 18.475 20.278
8 1.344 1.647 2.032 2.180 2.733 3.490 13.362 15.507 17.535 18.168 20.090 21.955
9 1.735 2.088 2.532 2.700 3.325 4.168 14.684 16.919 19.023 19.679 21.666 23.589
10 2.156 2.558 3.059 3.247 3.940 4.865 15.987 18.307 20.483 21.161 23.209 25.188
11 2.603 3.053 3.609 3.816 4.575 5.578 17.275 19.675 21.920 22.618 24.725 26.757
12 3.074 3.571 4.178 4.404 5.226 6.304 18.549 21.026 23.337 24.054 26.217 28.300
13 3.565 4.107 4.765 5.009 5.892 7.041 19.812 22.362 24.736 25.471 27.688 29.819
14 4.075 4.660 5.368 5.629 6.571 7.790 21.064 23.685 26.119 26.873 29.141 31.319
15 4.601 5.229 5.985 6.262 7.261 8.547 22.307 24.996 27.488 28.259 30.578 32.801
16 5.142 5.812 6.614 6.908 7.962 9.312 23.542 26.296 28.845 29.633 32.000 34.267
17 5.697 6.408 7.255 7.564 8.672 10.085 24.769 27.587 30.191 30.995 33.409 35.718
18 6.265 7.015 7.906 8.231 9.390 10.865 25.989 28.869 31.526 32.346 34.805 37.156
19 6.844 7.633 8.567 8.907 10.117 11.651 27.204 30.144 32.852 33.687 36.191 38.582
20 7.434 8.260 9.237 9.591 10.851 12.443 28.412 31.410 34.170 35.020 37.566 39.997
21 8.034 8.897 9.915 10.283 11.591 13.240 29.615 32.671 35.479 36.343 38.932 41.401
22 8.643 9.542 10.600 10.982 12.338 14.041 30.813 33.924 36.781 37.659 40.289 42.796
23 9.260 10.196 11.293 11.689 13.091 14.848 32.007 35.172 38.076 38.968 41.638 44.181
24 9.886 10.856 11.992 12.401 13.848 15.659 33.196 36.415 39.364 40.270 42.980 45.558
25 10.520 11.524 12.697 13.120 14.611 16.473 34.382 37.652 40.646 41.566 44.314 46.928
26 11.160 12.198 13.409 13.844 15.379 17.292 35.563 38.885 41.923 42.856 45.642 48.290
27 11.808 12.878 14.125 14.573 16.151 18.114 36.741 40.113 43.195 44.140 46.963 49.645
28 12.461 13.565 14.847 15.308 16.928 18.939 37.916 41.337 44.461 45.419 48.278 50.994
29 13.121 14.256 15.574 16.047 17.708 19.768 39.087 42.557 45.722 46.693 49.588 52.335
30 13.787 14.953 16.306 16.791 18.493 20.599 40.256 43.773 46.979 47.962 50.892 53.672
31 14.458 15.655 17.042 17.539 19.281 21.434 41.422 44.985 48.232 49.226 52.191 55.002
32 15.134 16.362 17.783 18.291 20.072 22.271 42.585 46.194 49.480 50.487 53.486 56.328
33 15.815 17.073 18.527 19.047 20.867 23.110 43.745 47.400 50.725 51.743 54.775 57.648
34 16.501 17.789 19.275 19.806 21.664 23.952 44.903 48.602 51.966 52.995 56.061 58.964
35 17.192 18.509 20.027 20.569 22.465 24.797 46.059 49.802 53.203 54.244 57.342 60.275
36 17.887 19.233 20.783 21.336 23.269 25.643 47.212 50.998 54.437 55.489 58.619 61.581
37 18.586 19.960 21.542 22.106 24.075 26.492 48.363 52.192 55.668 56.730 59.893 62.883
38 19.289 20.691 22.304 22.878 24.884 27.343 49.513 53.384 56.895 57.969 61.162 64.181
39 19.996 21.426 23.069 23.654 25.695 28.196 50.660 54.572 58.120 59.204 62.428 65.475
40 20.707 22.164 23.838 24.433 26.509 29.051 51.805 55.758 59.342 60.436 63.691 66.766
50 27.991 29.707 31.664 32.357 34.764 37.689 63.167 67.505 71.420 72.613 76.154 79.490
60 35.534 37.485 39.699 40.482 43.188 46.459 74.397 79.082 83.298 84.580 88.379 91.952
70 43.275 45.442 47.893 48.758 51.739 55.329 85.527 90.531 95.023 96.387 100.425 104.215
80 51.172 53.540 56.213 57.153 60.391 64.278 96.578 101.879 106.629 108.069 112.329 116.321
90 59.196 61.754 64.635 65.647 69.126 73.291 107.565 113.145 118.136 119.648 124.116 128.299
100 67.328 70.065 73.142 74.222 77.929 82.358 118.498 124.342 129.561 131.142 135.807 140.170
4
Chi Square Distribution, continued
Table provides value of Chi Square
Area to Right shown at top of table
df 0.995 0.990 0.980 0.975 0.950 0.900 0.100 0.050 0.025 0.020 0.010 0.005
110 75.550 78.458 81.723 82.867 86.792 91.471 129.385 135.480 140.916 142.562 147.414 151.948
120 83.852 86.923 90.367 91.573 95.705 100.624 140.233 146.567 152.211 153.918 158.950 163.648
130 92.223 95.451 99.066 100.331 104.662 109.811 151.045 157.610 163.453 165.219 170.423 175.278
140 100.655 104.034 107.815 109.137 113.659 119.029 161.827 168.613 174.648 176.471 181.841 186.847
150 109.142 112.668 116.608 117.985 122.692 128.275 172.581 179.581 185.800 187.678 193.207 198.360
160 117.679 121.346 125.440 126.870 131.756 137.546 183.311 190.516 196.915 198.846 204.530 209.824
170 126.261 130.064 134.308 135.790 140.849 146.839 194.017 201.423 207.995 209.978 215.812 221.242
180 134.884 138.821 143.210 144.741 149.969 156.153 204.704 212.304 219.044 221.077 227.056 232.620
190 143.545 147.610 152.141 153.721 159.112 165.485 215.371 223.160 230.064 232.146 238.266 243.959
200 152.241 156.432 161.100 162.728 168.279 174.835 226.021 233.994 241.058 243.187 249.445 255.264
210 160.969 165.282 170.085 171.759 177.465 184.201 236.655 244.808 252.027 254.202 260.595 266.537
220 169.727 174.160 179.094 180.813 186.671 193.582 247.274 255.602 262.973 265.193 271.717 277.779
230 178.512 183.063 188.125 189.889 195.895 202.978 257.879 266.378 273.898 276.162 282.814 288.994
240 187.324 191.990 197.177 198.984 205.135 212.386 268.471 277.138 284.802 287.110 293.888 300.183
250 196.160 200.939 206.249 208.098 214.392 221.806 279.050 287.882 295.689 298.039 304.939 311.346
260 205.020 209.908 215.339 217.229 223.663 231.238 289.619 298.611 306.557 308.949 315.970 322.487
270 213.901 218.897 224.446 226.377 232.947 240.680 300.176 309.326 317.409 319.841 326.981 333.606
280 222.803 227.905 233.570 235.541 242.245 250.133 310.723 320.028 328.245 330.718 337.974 344.704
290 231.724 236.930 242.710 244.720 251.556 259.596 321.260 330.717 339.067 341.579 348.948 355.783
300 240.663 245.973 251.864 253.912 260.878 269.068 331.788 341.395 349.874 352.425 359.906 366.844
310 249.621 255.030 261.032 263.118 270.212 278.548 342.308 352.062 360.668 363.257 370.849 377.887
320 258.594 264.103 270.213 272.337 279.556 288.037 352.819 362.717 371.450 374.075 381.776 388.914
330 267.584 273.190 279.407 281.568 288.910 297.534 363.322 373.363 382.219 384.881 392.689 399.924
340 276.588 282.292 288.613 290.810 298.274 307.039 373.818 383.999 392.977 395.675 403.587 410.920
350 285.608 291.406 297.831 300.064 307.648 316.550 384.306 394.626 403.723 406.457 414.474 421.901
360 294.641 300.532 307.060 309.328 317.030 326.069 394.787 405.244 414.459 417.229 425.347 432.867
370 303.688 309.671 316.300 318.602 326.421 335.594 405.262 415.853 425.185 427.989 436.208 443.820
380 312.747 318.822 325.549 327.886 335.820 345.126 415.730 426.454 435.901 438.739 447.058 454.761
390 321.819 327.983 334.809 337.179 345.227 354.664 426.193 437.047 446.608 449.480 457.897 465.690
400 330.903 337.155 344.078 346.482 354.641 364.207 436.649 447.632 457.306 460.211 468.724 476.607
410 339.998 346.338 353.356 355.793 364.063 373.757 447.100 458.211 467.994 470.933 479.542 487.511
420 349.104 355.530 362.643 365.112 373.491 383.312 457.545 468.782 478.675 481.646 490.350 498.406
430 358.220 364.732 371.938 374.440 382.927 392.872 467.985 479.347 489.348 492.351 501.148 509.290
440 367.346 373.943 381.242 383.775 392.369 402.437 478.419 489.904 500.012 503.047 511.937 520.162
450 376.483 383.163 390.553 393.118 401.817 412.007 488.849 500.456 510.670 513.736 522.717 531.026
460 385.629 392.392 399.872 402.468 411.272 421.582 499.274 511.002 521.320 524.417 533.488 541.880
470 394.784 401.629 409.199 411.825 420.732 431.161 509.695 521.541 531.963 535.091 544.251 552.725
480 403.949 410.874 418.532 421.189 430.198 440.745 520.111 532.075 542.599 545.757 555.007 563.561
490 413.122 420.127 427.872 430.559 439.670 450.334 530.523 542.604 553.228 556.417 565.753 574.387
500 422.303 429.387 437.219 439.936 449.147 459.926 540.930 553.127 563.851 567.070 576.493 585.206
510 431.493 438.656 446.573 449.319 458.629 469.523 551.334 563.645 574.468 577.716 587.225 596.017
520 440.691 447.930 455.933 458.708 468.116 479.123 561.733 574.157 585.079 588.356 597.950 606.820
530 449.895 457.212 465.299 468.103 477.608 488.727 572.129 584.665 595.684 598.990 608.668 617.614
540 459.108 466.501 474.671 477.504 487.105 498.335 582.521 595.168 606.284 609.618 619.379 628.402
550 468.327 475.796 484.049 486.910 496.607 507.947 592.909 605.667 616.878 620.241 630.084 639.183
560 477.555 485.098 493.432 496.321 506.113 517.562 603.294 616.161 627.466 630.857 640.782 649.956
5
F Distribution
Table Part One provides value of F (Right tail area = Alpha 0.10)
Numerator degrees of freedom
Denominator df 1 2 3 4 5 6 7 8 9 10
1 39.8636 49.5002 53.5933 55.8330 57.2400 58.2045 58.9062 59.4391 59.8575 60.1949
2 8.5263 9.0000 9.1618 9.2434 9.2926 9.3255 9.3491 9.3668 9.3805 9.3916
3 5.5383 5.4624 5.3908 5.3427 5.3091 5.2847 5.2662 5.2517 5.2400 5.2304
4 4.5448 4.3246 4.1909 4.1072 4.0506 4.0097 3.9790 3.9549 3.9357 3.9199
5 4.0604 3.7797 3.6195 3.5202 3.4530 3.4045 3.3679 3.3393 3.3163 3.2974
6 3.7760 3.4633 3.2888 3.1808 3.1075 3.0546 3.0145 2.9830 2.9577 2.9369
7 3.5894 3.2574 3.0741 2.9605 2.8833 2.8274 2.7849 2.7516 2.7247 2.7025
8 3.4579 3.1131 2.9238 2.8064 2.7264 2.6683 2.6241 2.5893 2.5612 2.5380
9 3.3603 3.0064 2.8129 2.6927 2.6106 2.5509 2.5053 2.4694 2.4403 2.4163
10 3.2850 2.9245 2.7277 2.6053 2.5216 2.4606 2.4140 2.3771 2.3473 2.3226
11 3.2252 2.8595 2.6602 2.5362 2.4512 2.3891 2.3416 2.3040 2.2735 2.2482
12 3.1766 2.8068 2.6055 2.4801 2.3940 2.3310 2.2828 2.2446 2.2135 2.1878
13 3.1362 2.7632 2.5603 2.4337 2.3467 2.2830 2.2341 2.1953 2.1638 2.1376
14 3.1022 2.7265 2.5222 2.3947 2.3069 2.2426 2.1931 2.1539 2.1220 2.0954
15 3.0732 2.6952 2.4898 2.3614 2.2730 2.2081 2.1582 2.1185 2.0862 2.0593
16 3.0481 2.6682 2.4618 2.3327 2.2438 2.1783 2.1280 2.0880 2.0553 2.0281
17 3.0262 2.6446 2.4374 2.3077 2.2183 2.1524 2.1017 2.0613 2.0284 2.0009
18 3.0070 2.6239 2.4160 2.2858 2.1958 2.1296 2.0785 2.0379 2.0047 1.9770
19 2.9899 2.6056 2.3970 2.2663 2.1760 2.1094 2.0580 2.0171 1.9836 1.9557
20 2.9747 2.5893 2.3801 2.2489 2.1582 2.0913 2.0397 1.9985 1.9649 1.9367
21 2.9610 2.5746 2.3649 2.2333 2.1423 2.0751 2.0233 1.9819 1.9480 1.9197
22 2.9486 2.5613 2.3512 2.2193 2.1279 2.0605 2.0084 1.9668 1.9327 1.9043
23 2.9374 2.5493 2.3387 2.2065 2.1149 2.0472 1.9949 1.9531 1.9189 1.8903
24 2.9271 2.5383 2.3274 2.1949 2.1030 2.0351 1.9826 1.9407 1.9063 1.8775
25 2.9177 2.5283 2.3170 2.1842 2.0922 2.0241 1.9714 1.9292 1.8947 1.8658
26 2.9091 2.5191 2.3075 2.1745 2.0822 2.0139 1.9610 1.9188 1.8841 1.8550
27 2.9012 2.5106 2.2987 2.1655 2.0730 2.0045 1.9515 1.9091 1.8743 1.8451
28 2.8938 2.5028 2.2906 2.1571 2.0645 1.9959 1.9427 1.9001 1.8652 1.8359
29 2.8870 2.4955 2.2831 2.1494 2.0566 1.9878 1.9345 1.8918 1.8568 1.8274
30 2.8807 2.4887 2.2761 2.1422 2.0492 1.9803 1.9269 1.8841 1.8490 1.8195
40 2.8353 2.4404 2.2261 2.0909 1.9968 1.9269 1.8725 1.8289 1.7929 1.7627
50 2.8087 2.4120 2.1967 2.0608 1.9660 1.8954 1.8405 1.7963 1.7598 1.7291
60 2.7911 2.3933 2.1774 2.0410 1.9457 1.8747 1.8194 1.7748 1.7380 1.7070
70 2.7786 2.3800 2.1637 2.0269 1.9313 1.8600 1.8044 1.7596 1.7225 1.6913
80 2.7693 2.3702 2.1535 2.0165 1.9206 1.8491 1.7933 1.7483 1.7110 1.6796
90 2.7621 2.3625 2.1457 2.0084 1.9123 1.8406 1.7846 1.7395 1.7021 1.6705
100 2.7564 2.3564 2.1394 2.0019 1.9057 1.8339 1.7778 1.7324 1.6949 1.6632
110 2.7517 2.3515 2.1343 1.9967 1.9004 1.8284 1.7721 1.7267 1.6891 1.6573
120 2.7478 2.3473 2.1300 1.9923 1.8959 1.8238 1.7675 1.7220 1.6842 1.6524
150 2.7393 2.3383 2.1207 1.9827 1.8861 1.8138 1.7572 1.7115 1.6736 1.6416
200 2.7308 2.3293 2.1114 1.9732 1.8763 1.8038 1.7470 1.7011 1.6630 1.6308
∞ 2.7055 2.3026 2.0838 1.9449 1.8473 1.7741 1.7167 1.6702 1.6315 1.5987
6
F Distribution
Table Part Two provides value of F (Right tail area = Alpha 0.10)
Numerator degrees of freedom
Den- df 11 12 13 14 15 16 17 18 19 20
1 60.4728 60.7051 60.9025 61.0726 61.2204 61.3500 61.4646 61.5664 61.6578 61.7401
2 9.4006 9.4082 9.4145 9.4200 9.4247 9.4288 9.4325 9.4358 9.4387 9.4413
3 5.2224 5.2156 5.2098 5.2047 5.2003 5.1964 5.1929 5.1898 5.1870 5.1845
4 3.9067 3.8955 3.8859 3.8776 3.8704 3.8639 3.8582 3.8531 3.8485 3.8443
5 3.2816 3.2682 3.2567 3.2468 3.2380 3.2303 3.2234 3.2172 3.2117 3.2067
6 2.9195 2.9047 2.8920 2.8809 2.8712 2.8626 2.8550 2.8481 2.8419 2.8363
7 2.6839 2.6681 2.6545 2.6426 2.6322 2.6230 2.6148 2.6074 2.6008 2.5947
8 2.5186 2.5020 2.4876 2.4752 2.4642 2.4545 2.4458 2.4380 2.4310 2.4246
9 2.3961 2.3789 2.3640 2.3510 2.3396 2.3295 2.3205 2.3123 2.3050 2.2983
10 2.3018 2.2841 2.2687 2.2553 2.2435 2.2330 2.2237 2.2153 2.2077 2.2007
11 2.2269 2.2087 2.1930 2.1792 2.1671 2.1563 2.1467 2.1380 2.1302 2.1230
12 2.1660 2.1474 2.1313 2.1173 2.1049 2.0938 2.0839 2.0750 2.0670 2.0597
13 2.1155 2.0966 2.0802 2.0658 2.0532 2.0419 2.0318 2.0227 2.0145 2.0070
14 2.0730 2.0537 2.0370 2.0224 2.0095 1.9981 1.9878 1.9785 1.9701 1.9625
15 2.0366 2.0171 2.0001 1.9853 1.9722 1.9605 1.9501 1.9407 1.9321 1.9243
16 2.0051 1.9854 1.9682 1.9532 1.9399 1.9281 1.9175 1.9079 1.8992 1.8913
17 1.9777 1.9577 1.9404 1.9252 1.9117 1.8997 1.8889 1.8792 1.8704 1.8624
18 1.9535 1.9333 1.9158 1.9004 1.8868 1.8747 1.8638 1.8539 1.8450 1.8368
19 1.9321 1.9117 1.8940 1.8785 1.8647 1.8524 1.8414 1.8314 1.8224 1.8142
20 1.9129 1.8924 1.8745 1.8588 1.8449 1.8325 1.8214 1.8113 1.8022 1.7938
21 1.8956 1.8750 1.8570 1.8412 1.8271 1.8146 1.8034 1.7932 1.7840 1.7756
22 1.8801 1.8593 1.8411 1.8252 1.8111 1.7984 1.7871 1.7768 1.7675 1.7590
23 1.8659 1.8450 1.8267 1.8107 1.7964 1.7837 1.7723 1.7619 1.7525 1.7439
24 1.8530 1.8319 1.8136 1.7974 1.7831 1.7703 1.7587 1.7483 1.7388 1.7302
25 1.8412 1.8200 1.8015 1.7853 1.7708 1.7579 1.7463 1.7358 1.7263 1.7175
26 1.8303 1.8090 1.7904 1.7741 1.7596 1.7466 1.7349 1.7243 1.7147 1.7059
27 1.8203 1.7989 1.7802 1.7638 1.7492 1.7361 1.7243 1.7137 1.7040 1.6951
28 1.8110 1.7895 1.7708 1.7542 1.7395 1.7264 1.7146 1.7039 1.6941 1.6852
29 1.8024 1.7808 1.7620 1.7454 1.7306 1.7174 1.7055 1.6947 1.6849 1.6759
30 1.7944 1.7727 1.7538 1.7371 1.7223 1.7090 1.6970 1.6862 1.6763 1.6673
40 1.7369 1.7146 1.6950 1.6778 1.6624 1.6486 1.6362 1.6249 1.6146 1.6052
50 1.7029 1.6802 1.6602 1.6426 1.6269 1.6128 1.6000 1.5884 1.5778 1.5681
60 1.6805 1.6574 1.6372 1.6193 1.6034 1.5890 1.5760 1.5642 1.5534 1.5435
70 1.6645 1.6413 1.6209 1.6028 1.5866 1.5721 1.5589 1.5470 1.5360 1.5259
80 1.6526 1.6292 1.6086 1.5904 1.5741 1.5594 1.5461 1.5340 1.5230 1.5128
90 1.6434 1.6199 1.5992 1.5808 1.5644 1.5496 1.5362 1.5240 1.5128 1.5025
100 1.6360 1.6124 1.5916 1.5731 1.5566 1.5418 1.5283 1.5160 1.5047 1.4943
110 1.6300 1.6063 1.5854 1.5669 1.5503 1.5353 1.5218 1.5094 1.4981 1.4877
120 1.6250 1.6012 1.5803 1.5617 1.5450 1.5300 1.5164 1.5039 1.4926 1.4821
150 1.6140 1.5901 1.5690 1.5502 1.5334 1.5182 1.5045 1.4919 1.4804 1.4698
200 1.6031 1.5789 1.5577 1.5388 1.5218 1.5065 1.4926 1.4799 1.4683 1.4575
∞ 1.5705 1.5458 1.5240 1.5046 1.4871 1.4714 1.4570 1.4439 1.4318 1.4206
7
F Distribution
Table Part One provides value of F (Right tail area = Alpha 0.05)
Numerator degrees of freedom
Den- df 1 2 3 4 5 6 7 8 9 10
1 161.4462 199.4995 215.7067 224.5833 230.1604 233.9875 236.7669 238.8842 240.5432 241.8819
2 18.5128 19.0000 19.1642 19.2467 19.2963 19.3295 19.3531 19.3709 19.3847 19.3959
3 10.1280 9.5521 9.2766 9.1172 9.0134 8.9407 8.8867 8.8452 8.8123 8.7855
4 7.7086 6.9443 6.5914 6.3882 6.2561 6.1631 6.0942 6.0410 5.9988 5.9644
5 6.6079 5.7861 5.4094 5.1922 5.0503 4.9503 4.8759 4.8183 4.7725 4.7351
6 5.9874 5.1432 4.7571 4.5337 4.3874 4.2839 4.2067 4.1468 4.0990 4.0600
7 5.5915 4.7374 4.3468 4.1203 3.9715 3.8660 3.7871 3.7257 3.6767 3.6365
8 5.3176 4.4590 4.0662 3.8379 3.6875 3.5806 3.5005 3.4381 3.3881 3.3472
9 5.1174 4.2565 3.8625 3.6331 3.4817 3.3738 3.2927 3.2296 3.1789 3.1373
10 4.9646 4.1028 3.7083 3.4780 3.3258 3.2172 3.1355 3.0717 3.0204 2.9782
11 4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.8962 2.8536
12 4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486 2.7964 2.7534
13 4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144 2.6710
14 4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458 2.6022
15 4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876 2.5437
16 4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935
17 4.4513 3.5915 3.1968 2.9647 2.8100 2.6987 2.6143 2.5480 2.4943 2.4499
18 4.4139 3.5546 3.1599 2.9277 2.7729 2.6613 2.5767 2.5102 2.4563 2.4117
19 4.3808 3.5219 3.1274 2.8951 2.7401 2.6283 2.5435 2.4768 2.4227 2.3779
20 4.3513 3.4928 3.0984 2.8661 2.7109 2.5990 2.5140 2.4471 2.3928 2.3479
21 4.3248 3.4668 3.0725 2.8401 2.6848 2.5727 2.4876 2.4205 2.3661 2.3210
22 4.3009 3.4434 3.0491 2.8167 2.6613 2.5491 2.4638 2.3965 2.3419 2.2967
23 4.2793 3.4221 3.0280 2.7955 2.6400 2.5277 2.4422 2.3748 2.3201 2.2747
24 4.2597 3.4028 3.0088 2.7763 2.6207 2.5082 2.4226 2.3551 2.3002 2.2547
25 4.2417 3.3852 2.9912 2.7587 2.6030 2.4904 2.4047 2.3371 2.2821 2.2365
26 4.2252 3.3690 2.9752 2.7426 2.5868 2.4741 2.3883 2.3205 2.2655 2.2197
27 4.2100 3.3541 2.9603 2.7278 2.5719 2.4591 2.3732 2.3053 2.2501 2.2043
28 4.1960 3.3404 2.9467 2.7141 2.5581 2.4453 2.3593 2.2913 2.2360 2.1900
29 4.1830 3.3277 2.9340 2.7014 2.5454 2.4324 2.3463 2.2782 2.2229 2.1768
30 4.1709 3.3158 2.9223 2.6896 2.5336 2.4205 2.3343 2.2662 2.2107 2.1646
40 4.0847 3.2317 2.8387 2.6060 2.4495 2.3359 2.2490 2.1802 2.1240 2.0773
50 4.0343 3.1826 2.7900 2.5572 2.4004 2.2864 2.1992 2.1299 2.0733 2.0261
60 4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665 2.0970 2.0401 1.9926
70 3.9778 3.1277 2.7355 2.5027 2.3456 2.2312 2.1435 2.0737 2.0166 1.9689
80 3.9604 3.1108 2.7188 2.4859 2.3287 2.2142 2.1263 2.0564 1.9991 1.9512
90 3.9469 3.0977 2.7058 2.4729 2.3157 2.2011 2.1131 2.0430 1.9856 1.9376
100 3.9362 3.0873 2.6955 2.4626 2.3053 2.1906 2.1025 2.0323 1.9748 1.9267
110 3.9274 3.0788 2.6871 2.4542 2.2969 2.1821 2.0939 2.0236 1.9661 1.9178
120 3.9201 3.0718 2.6802 2.4472 2.2899 2.1750 2.0868 2.0164 1.9588 1.9105
150 3.9042 3.0564 2.6649 2.4320 2.2745 2.1595 2.0711 2.0006 1.9428 1.8943
200 3.8884 3.0411 2.6498 2.4168 2.2592 2.1441 2.0556 1.9849 1.9269 1.8783
∞ 3.8414 2.9957 2.6049 2.3719 2.2141 2.0986 2.0096 1.9384 1.8799 1.8307
8
F Distribution
Table Part Two provides value of F (Right tail area = Alpha 0.05)
Numerator degrees of freedom
Den- df 11 12 13 14 15 16 17 18 19 20
1 242.9806 243.9047 244.6905 245.3635 245.9492 246.4658 246.9169 247.3244 247.6881 248.0156
2 19.4050 19.4125 19.4188 19.4243 19.4291 19.4332 19.4370 19.4402 19.4432 19.4457
3 8.7633 8.7447 8.7286 8.7149 8.7028 8.6923 8.6829 8.6745 8.6670 8.6602
4 5.9358 5.9117 5.8911 5.8733 5.8578 5.8441 5.8320 5.8211 5.8114 5.8025
5 4.7040 4.6777 4.6552 4.6358 4.6188 4.6038 4.5904 4.5785 4.5678 4.5581
6 4.0274 3.9999 3.9764 3.9559 3.9381 3.9223 3.9083 3.8957 3.8844 3.8742
7 3.6030 3.5747 3.5503 3.5292 3.5107 3.4944 3.4799 3.4669 3.4551 3.4445
8 3.3129 3.2839 3.2590 3.2374 3.2184 3.2016 3.1867 3.1733 3.1612 3.1503
9 3.1025 3.0729 3.0475 3.0255 3.0061 2.9890 2.9737 2.9600 2.9477 2.9365
10 2.9430 2.9130 2.8872 2.8647 2.8450 2.8276 2.8120 2.7980 2.7854 2.7740
11 2.8179 2.7876 2.7614 2.7386 2.7186 2.7009 2.6851 2.6709 2.6581 2.6464
12 2.7173 2.6866 2.6602 2.6371 2.6169 2.5989 2.5828 2.5684 2.5554 2.5436
13 2.6346 2.6037 2.5769 2.5536 2.5331 2.5149 2.4987 2.4841 2.4709 2.4589
14 2.5655 2.5342 2.5073 2.4837 2.4630 2.4446 2.4282 2.4134 2.4000 2.3879
15 2.5068 2.4753 2.4481 2.4244 2.4034 2.3849 2.3683 2.3533 2.3398 2.3275
16 2.4564 2.4247 2.3973 2.3733 2.3522 2.3335 2.3167 2.3016 2.2880 2.2756
17 2.4126 2.3807 2.3531 2.3290 2.3077 2.2888 2.2719 2.2567 2.2429 2.2304
18 2.3742 2.3421 2.3143 2.2900 2.2686 2.2496 2.2325 2.2172 2.2033 2.1906
19 2.3402 2.3080 2.2800 2.2556 2.2341 2.2149 2.1977 2.1823 2.1682 2.1555
20 2.3100 2.2776 2.2495 2.2250 2.2033 2.1840 2.1667 2.1511 2.1370 2.1242
21 2.2829 2.2504 2.2222 2.1975 2.1757 2.1563 2.1389 2.1232 2.1090 2.0960
22 2.2585 2.2258 2.1975 2.1727 2.1508 2.1313 2.1138 2.0980 2.0837 2.0707
23 2.2364 2.2036 2.1752 2.1502 2.1282 2.1086 2.0910 2.0751 2.0608 2.0476
24 2.2163 2.1834 2.1548 2.1298 2.1077 2.0880 2.0703 2.0543 2.0399 2.0267
25 2.1979 2.1649 2.1362 2.1111 2.0889 2.0691 2.0513 2.0353 2.0207 2.0075
26 2.1811 2.1479 2.1192 2.0939 2.0716 2.0518 2.0339 2.0178 2.0032 1.9898
27 2.1655 2.1323 2.1034 2.0781 2.0558 2.0358 2.0179 2.0017 1.9870 1.9736
28 2.1512 2.1179 2.0889 2.0635 2.0411 2.0210 2.0030 1.9868 1.9720 1.9586
29 2.1379 2.1045 2.0755 2.0500 2.0275 2.0073 1.9893 1.9730 1.9581 1.9446
30 2.1256 2.0921 2.0630 2.0374 2.0148 1.9946 1.9765 1.9601 1.9452 1.9317
40 2.0376 2.0035 1.9738 1.9476 1.9245 1.9038 1.8851 1.8682 1.8529 1.8389
50 1.9861 1.9515 1.9214 1.8949 1.8714 1.8503 1.8313 1.8141 1.7985 1.7841
60 1.9522 1.9174 1.8870 1.8602 1.8364 1.8151 1.7959 1.7784 1.7625 1.7480
70 1.9283 1.8932 1.8627 1.8357 1.8117 1.7902 1.7708 1.7531 1.7371 1.7223
80 1.9105 1.8753 1.8445 1.8174 1.7932 1.7716 1.7520 1.7342 1.7180 1.7032
90 1.8967 1.8613 1.8305 1.8032 1.7789 1.7571 1.7375 1.7196 1.7033 1.6883
100 1.8857 1.8503 1.8193 1.7919 1.7675 1.7456 1.7259 1.7079 1.6915 1.6764
110 1.8767 1.8412 1.8101 1.7827 1.7582 1.7363 1.7164 1.6984 1.6819 1.6667
120 1.8693 1.8337 1.8026 1.7750 1.7505 1.7285 1.7085 1.6904 1.6739 1.6587
150 1.8530 1.8172 1.7859 1.7582 1.7335 1.7113 1.6913 1.6730 1.6563 1.6410
200 1.8368 1.8008 1.7694 1.7415 1.7166 1.6943 1.6741 1.6556 1.6388 1.6233
∞ 1.7886 1.7522 1.7202 1.6918 1.6664 1.6435 1.6228 1.6039 1.5865 1.5705
9
F Distribution
Table Part One provides value of F (Right tail area = Alpha 0.025) Numerator degrees of freedom
Den
df 1 2 3 4 5 6 7 8 9 10
1 647.7931 799.4822 864.1509 899.5994 921.8347 937.1142 948.2028 956.6429 963.2786 968.6337
2 38.5062 39.0000 39.1656 39.2483 39.2984 39.3311 39.3557 39.3729 39.3866 39.3984
3 17.4434 16.0442 15.4391 15.1010 14.8848 14.7347 14.6244 14.5399 14.4730 14.4189
4 12.2179 10.6490 9.9792 9.6045 9.3645 9.1973 9.0741 8.9796 8.9046 8.8439
5 10.0069 8.4336 7.7636 7.3879 7.1464 6.9777 6.8530 6.7572 6.6810 6.6192
6 8.8131 7.2599 6.5988 6.2271 5.9875 5.8197 5.6955 5.5996 5.5234 5.4613
7 8.0727 6.5415 5.8898 5.5226 5.2852 5.1186 4.9949 4.8993 4.8232 4.7611
8 7.5709 6.0595 5.4160 5.0526 4.8173 4.6517 4.5285 4.4333 4.3572 4.2951
9 7.2093 5.7147 5.0781 4.7181 4.4844 4.3197 4.1970 4.1020 4.0260 3.9639
10 6.9367 5.4564 4.8256 4.4683 4.2361 4.0721 3.9498 3.8549 3.7790 3.7168
11 6.7241 5.2559 4.6300 4.2751 4.0440 3.8806 3.7586 3.6638 3.5879 3.5257
12 6.5538 5.0959 4.4742 4.1212 3.8911 3.7283 3.6065 3.5118 3.4358 3.3735
13 6.4143 4.9653 4.3472 3.9959 3.7667 3.6043 3.4827 3.3880 3.3120 3.2497
14 6.2979 4.8567 4.2417 3.8919 3.6634 3.5014 3.3799 3.2853 3.2093 3.1469
15 6.1995 4.7650 4.1528 3.8043 3.5764 3.4147 3.2934 3.1987 3.1227 3.0602
16 6.1151 4.6867 4.0768 3.7294 3.5021 3.3406 3.2194 3.1248 3.0488 2.9862
17 6.0420 4.6189 4.0112 3.6648 3.4379 3.2767 3.1556 3.0610 2.9849 2.9222
18 5.9781 4.5597 3.9539 3.6083 3.3820 3.2209 3.0999 3.0053 2.9291 2.8664
19 5.9216 4.5075 3.9034 3.5587 3.3327 3.1718 3.0509 2.9563 2.8801 2.8172
20 5.8715 4.4612 3.8587 3.5147 3.2891 3.1283 3.0074 2.9128 2.8365 2.7737
21 5.8266 4.4199 3.8188 3.4754 3.2501 3.0895 2.9686 2.8740 2.7977 2.7348
22 5.7863 4.3828 3.7829 3.4401 3.2151 3.0546 2.9338 2.8392 2.7628 2.6998
23 5.7498 4.3492 3.7505 3.4083 3.1835 3.0232 2.9023 2.8077 2.7313 2.6682
24 5.7166 4.3187 3.7211 3.3794 3.1548 2.9946 2.8738 2.7791 2.7027 2.6396
25 5.6864 4.2909 3.6943 3.3530 3.1287 2.9685 2.8478 2.7531 2.6766 2.6135
26 5.6586 4.2655 3.6697 3.3289 3.1048 2.9447 2.8240 2.7293 2.6528 2.5896
27 5.6331 4.2421 3.6472 3.3067 3.0828 2.9228 2.8021 2.7074 2.6309 2.5676
28 5.6096 4.2205 3.6264 3.2863 3.0626 2.9027 2.7820 2.6872 2.6106 2.5473
29 5.5878 4.2006 3.6072 3.2674 3.0438 2.8840 2.7633 2.6686 2.5919 2.5286
30 5.5675 4.1821 3.5893 3.2499 3.0265 2.8667 2.7460 2.6513 2.5746 2.5112
40 5.4239 4.0510 3.4633 3.1261 2.9037 2.7444 2.6238 2.5289 2.4519 2.3882
50 5.3403 3.9749 3.3902 3.0544 2.8326 2.6736 2.5530 2.4579 2.3808 2.3168
60 5.2856 3.9253 3.3425 3.0077 2.7863 2.6274 2.5068 2.4117 2.3344 2.2702
70 5.2470 3.8903 3.3090 2.9748 2.7537 2.5949 2.4743 2.3791 2.3017 2.2374
80 5.2183 3.8643 3.2841 2.9504 2.7295 2.5708 2.4502 2.3549 2.2775 2.2130
90 5.1962 3.8443 3.2649 2.9315 2.7109 2.5522 2.4316 2.3363 2.2588 2.1942
100 5.1786 3.8284 3.2496 2.9166 2.6961 2.5374 2.4168 2.3215 2.2439 2.1793
110 5.1642 3.8154 3.2372 2.9044 2.6840 2.5254 2.4048 2.3094 2.2318 2.1671
120 5.1523 3.8046 3.2269 2.8943 2.6740 2.5154 2.3948 2.2994 2.2217 2.1570
150 5.1263 3.7811 3.2043 2.8722 2.6521 2.4936 2.3730 2.2775 2.1998 2.1349
200 5.1004 3.7578 3.1820 2.8503 2.6304 2.4720 2.3513 2.2558 2.1780 2.1130
infinity 5.0239 3.6889 3.1162 2.7858 2.5665 2.4082 2.2875 2.1918 2.1137 2.0483
10
F Distribution
Table Part Two provides value of F (Right tail area = Alpha 0.025) Numerator degrees of freedom
Den
df 11 12 13 14 15 16 17 18 19 20
1 973.0284 976.7246 979.8387 982.5453 984.8736 986.9109 988.7153 990.3451 991.8003 993.0809
2 39.4066 39.4148 39.4211 39.4266 39.4311 39.4357 39.4393 39.4421 39.4457 39.4475
3 14.3741 14.3366 14.3045 14.2768 14.2527 14.2315 14.2127 14.1961 14.1808 14.1674
4 8.7936 8.7512 8.7150 8.6837 8.6566 8.6326 8.6113 8.5923 8.5753 8.5599
5 6.5678 6.5245 6.4876 6.4556 6.4277 6.4032 6.3814 6.3619 6.3444 6.3285
6 5.4098 5.3662 5.3290 5.2968 5.2686 5.2439 5.2218 5.2021 5.1844 5.1684
7 4.7095 4.6658 4.6285 4.5961 4.5678 4.5428 4.5206 4.5008 4.4829 4.4668
8 4.2434 4.1997 4.1622 4.1297 4.1012 4.0761 4.0538 4.0338 4.0158 3.9994
9 3.9121 3.8682 3.8306 3.7980 3.7693 3.7441 3.7216 3.7015 3.6833 3.6669
10 3.6649 3.6210 3.5832 3.5504 3.5217 3.4963 3.4736 3.4534 3.4351 3.4185
11 3.4737 3.4296 3.3917 3.3588 3.3299 3.3044 3.2816 3.2612 3.2428 3.2261
12 3.3215 3.2773 3.2393 3.2062 3.1772 3.1515 3.1286 3.1081 3.0896 3.0728
13 3.1975 3.1532 3.1150 3.0819 3.0527 3.0269 3.0039 2.9832 2.9646 2.9477
14 3.0946 3.0502 3.0119 2.9786 2.9493 2.9234 2.9003 2.8795 2.8607 2.8437
15 3.0078 2.9633 2.9249 2.8915 2.8621 2.8360 2.8128 2.7919 2.7730 2.7559
16 2.9337 2.8891 2.8506 2.8170 2.7875 2.7614 2.7380 2.7170 2.6980 2.6808
17 2.8696 2.8249 2.7863 2.7526 2.7230 2.6968 2.6733 2.6522 2.6331 2.6158
18 2.8137 2.7689 2.7302 2.6964 2.6667 2.6403 2.6168 2.5956 2.5764 2.5590
19 2.7645 2.7196 2.6808 2.6469 2.6171 2.5907 2.5670 2.5457 2.5264 2.5089
20 2.7209 2.6758 2.6369 2.6030 2.5731 2.5465 2.5228 2.5014 2.4821 2.4645
21 2.6819 2.6368 2.5978 2.5638 2.5338 2.5071 2.4833 2.4618 2.4424 2.4247
22 2.6469 2.6017 2.5626 2.5285 2.4984 2.4717 2.4478 2.4262 2.4067 2.3890
23 2.6152 2.5699 2.5308 2.4966 2.4665 2.4396 2.4156 2.3940 2.3745 2.3566
24 2.5865 2.5411 2.5019 2.4677 2.4374 2.4105 2.3865 2.3648 2.3452 2.3273
25 2.5603 2.5149 2.4756 2.4413 2.4110 2.3840 2.3599 2.3381 2.3184 2.3005
26 2.5363 2.4909 2.4515 2.4171 2.3867 2.3597 2.3355 2.3137 2.2939 2.2759
27 2.5143 2.4688 2.4293 2.3949 2.3644 2.3373 2.3131 2.2912 2.2713 2.2533
28 2.4940 2.4484 2.4089 2.3743 2.3438 2.3167 2.2924 2.2704 2.2505 2.2324
29 2.4752 2.4295 2.3900 2.3554 2.3248 2.2976 2.2732 2.2512 2.2313 2.2131
30 2.4578 2.4120 2.3724 2.3378 2.3072 2.2799 2.2554 2.2334 2.2134 2.1952
40 2.3343 2.2882 2.2481 2.2130 2.1819 2.1542 2.1293 2.1068 2.0864 2.0677
50 2.2627 2.2162 2.1758 2.1404 2.1090 2.0810 2.0558 2.0330 2.0122 1.9933
60 2.2159 2.1692 2.1286 2.0929 2.0613 2.0330 2.0076 1.9846 1.9636 1.9445
70 2.1829 2.1361 2.0953 2.0595 2.0277 1.9992 1.9736 1.9504 1.9293 1.9100
80 2.1584 2.1114 2.0706 2.0346 2.0026 1.9741 1.9483 1.9250 1.9037 1.8843
90 2.1395 2.0925 2.0515 2.0154 1.9833 1.9546 1.9288 1.9053 1.8840 1.8644
100 2.1245 2.0773 2.0363 2.0001 1.9679 1.9391 1.9132 1.8897 1.8682 1.8486
110 2.1123 2.0650 2.0239 1.9876 1.9554 1.9265 1.9005 1.8769 1.8554 1.8357
120 2.1021 2.0548 2.0136 1.9773 1.9450 1.9161 1.8900 1.8663 1.8447 1.8249
150 2.0799 2.0325 1.9911 1.9546 1.9222 1.8931 1.8669 1.8431 1.8213 1.8014
200 2.0578 2.0103 1.9688 1.9322 1.8996 1.8704 1.8440 1.8200 1.7981 1.7780
infinity 1.9927 1.9447 1.9028 1.8657 1.8326 1.8028 1.7760 1.7515 1.7291 1.7085
11
F Distribution
Table Part One provides value of F (Right tail area = Alpha 0.02)
Numerator degrees of freedom
Den- df 1 2 3 4 5 6 7 8 9 10
1 1012.5223 1249.4856 1350.5341 1405.8314 1440.6396 1464.4465 1481.7924 1495.0056 1505.3665 1513.6902
2 48.5052 48.9999 49.1655 49.2491 49.2983 49.3319 49.3555 49.3728 49.3874 49.3983
3 20.6178 18.8581 18.1099 17.6938 17.4286 17.2449 17.1103 17.0071 16.9257 16.8598
4 14.0396 12.1422 11.3434 10.8994 10.6157 10.4186 10.2735 10.1622 10.0742 10.0027
5 11.3228 9.4544 8.6702 8.2330 7.9530 7.7576 7.6137 7.5030 7.4151 7.3438
6 9.8764 8.0521 7.2870 6.8594 6.5847 6.3928 6.2508 6.1415 6.0546 5.9839
7 8.9877 7.2026 6.4539 6.0347 5.7647 5.5756 5.4355 5.3273 5.2413 5.1712
8 8.3895 6.6366 5.9014 5.4889 5.2227 5.0359 4.8972 4.7900 4.7046 4.6348
9 7.9605 6.2340 5.5097 5.1027 4.8395 4.6545 4.5169 4.4105 4.3255 4.2560
10 7.6384 5.9336 5.2182 4.8157 4.5550 4.3714 4.2347 4.1288 4.0442 3.9750
11 7.3879 5.7012 4.9932 4.5943 4.3357 4.1533 4.0174 3.9119 3.8275 3.7584
12 7.1877 5.5163 4.8145 4.4187 4.1617 3.9804 3.8450 3.7398 3.6557 3.5867
13 7.0241 5.3657 4.6692 4.2760 4.0205 3.8399 3.7051 3.6001 3.5161 3.4472
14 6.8879 5.2407 4.5488 4.1578 3.9036 3.7237 3.5892 3.4845 3.4006 3.3317
15 6.7729 5.1355 4.4474 4.0584 3.8052 3.6260 3.4918 3.3873 3.3035 3.2346
16 6.6744 5.0455 4.3609 3.9737 3.7214 3.5426 3.4087 3.3044 3.2206 3.1518
17 6.5892 4.9678 4.2863 3.9006 3.6491 3.4707 3.3371 3.2329 3.1492 3.0803
18 6.5147 4.9001 4.2213 3.8368 3.5861 3.4081 3.2747 3.1706 3.0869 3.0180
19 6.4490 4.8404 4.1641 3.7809 3.5307 3.3531 3.2199 3.1159 3.0322 2.9633
20 6.3907 4.7876 4.1134 3.7313 3.4817 3.3044 3.1713 3.0674 2.9837 2.9148
21 6.3386 4.7404 4.0682 3.6870 3.4379 3.2610 3.1280 3.0241 2.9405 2.8716
22 6.2917 4.6980 4.0276 3.6473 3.3987 3.2220 3.0892 2.9853 2.9017 2.8328
23 6.2494 4.6597 3.9910 3.6115 3.3633 3.1868 3.0541 2.9503 2.8667 2.7977
24 6.2108 4.6250 3.9578 3.5790 3.3312 3.1549 3.0223 2.9186 2.8350 2.7660
25 6.1758 4.5934 3.9275 3.5494 3.3020 3.1259 2.9934 2.8897 2.8060 2.7370
26 6.1436 4.5644 3.8998 3.5224 3.2752 3.0993 2.9669 2.8632 2.7796 2.7105
27 6.1141 4.5378 3.8744 3.4975 3.2507 3.0749 2.9426 2.8389 2.7553 2.6862
28 6.0868 4.5133 3.8510 3.4746 3.2281 3.0525 2.9202 2.8165 2.7329 2.6638
29 6.0616 4.4906 3.8293 3.4535 3.2072 3.0317 2.8995 2.7959 2.7122 2.6431
30 6.0381 4.4695 3.8092 3.4338 3.1878 3.0124 2.8803 2.7767 2.6930 2.6239
40 5.8722 4.3208 3.6674 3.2954 3.0511 2.8766 2.7448 2.6413 2.5576 2.4882
50 5.7757 4.2347 3.5854 3.2154 2.9721 2.7981 2.6666 2.5631 2.4793 2.4098
60 5.7126 4.1786 3.5320 3.1633 2.9207 2.7470 2.6156 2.5122 2.4283 2.3586
70 5.6683 4.1390 3.4944 3.1267 2.8845 2.7111 2.5798 2.4763 2.3924 2.3226
80 5.6352 4.1097 3.4666 3.0995 2.8578 2.6845 2.5533 2.4498 2.3658 2.2959
90 5.6098 4.0871 3.4451 3.0786 2.8371 2.6640 2.5328 2.4293 2.3453 2.2754
100 5.5895 4.0691 3.4281 3.0620 2.8207 2.6477 2.5165 2.4130 2.3290 2.2590
110 5.5730 4.0545 3.4142 3.0485 2.8074 2.6345 2.5033 2.3998 2.3157 2.2457
120 5.5593 4.0424 3.4027 3.0372 2.7963 2.6235 2.4923 2.3888 2.3047 2.2347
150 5.5294 4.0158 3.3775 3.0127 2.7721 2.5994 2.4684 2.3648 2.2806 2.2105
200 5.4997 3.9896 3.3526 2.9885 2.7482 2.5756 2.4446 2.3411 2.2568 2.1866
∞ 5.4119 3.9120 3.2791 2.9170 2.6777 2.5055 2.3746 2.2710 2.1866 2.1161
12
F Distribution
Table Part Two provides value of F (Right tail area = Alpha 0.02)
Numerator degrees of freedom
Den- df 11 12 13 14 15 16 17 18 19 20
1 1520.5587 1526.3213 1531.2107 1535.4017 1539.0106 1542.2702 1545.0642 1547.6253 1549.8372 1551.9327
2 49.4074 49.4147 49.4219 49.4274 49.4310 49.4365 49.4401 49.4429 49.4456 49.4483
3 16.8052 16.7593 16.7202 16.6865 16.6572 16.6315 16.6085 16.5883 16.5699 16.5533
4 9.9436 9.8938 9.8514 9.8148 9.7829 9.7548 9.7298 9.7076 9.6876 9.6695
5 7.2847 7.2348 7.1923 7.1555 7.1234 7.0952 7.0701 7.0477 7.0276 7.0094
6 5.9252 5.8757 5.8334 5.7968 5.7648 5.7366 5.7116 5.6892 5.6691 5.6509
7 5.1128 5.0636 5.0214 4.9850 4.9531 4.9249 4.9000 4.8776 4.8575 4.8393
8 4.5768 4.5277 4.4857 4.4493 4.4174 4.3893 4.3643 4.3420 4.3218 4.3036
9 4.1982 4.1493 4.1073 4.0709 4.0390 4.0109 3.9858 3.9634 3.9432 3.9249
10 3.9173 3.8684 3.8264 3.7900 3.7581 3.7299 3.7048 3.6823 3.6620 3.6437
11 3.7008 3.6519 3.6099 3.5735 3.5415 3.5132 3.4881 3.4655 3.4452 3.4267
12 3.5290 3.4802 3.4381 3.4017 3.3696 3.3413 3.3160 3.2934 3.2729 3.2544
13 3.3896 3.3407 3.2986 3.2620 3.2299 3.2015 3.1762 3.1534 3.1329 3.1143
14 3.2741 3.2252 3.1830 3.1464 3.1142 3.0857 3.0603 3.0374 3.0168 2.9981
15 3.1770 3.1280 3.0858 3.0490 3.0168 2.9882 2.9627 2.9398 2.9191 2.9003
16 3.0941 3.0450 3.0028 2.9660 2.9336 2.9050 2.8794 2.8564 2.8356 2.8167
17 3.0226 2.9735 2.9312 2.8943 2.8619 2.8331 2.8075 2.7844 2.7635 2.7446
18 2.9603 2.9112 2.8688 2.8318 2.7993 2.7705 2.7447 2.7216 2.7006 2.6816
19 2.9055 2.8563 2.8139 2.7769 2.7443 2.7154 2.6895 2.6663 2.6453 2.6262
20 2.8570 2.8077 2.7652 2.7281 2.6955 2.6665 2.6406 2.6173 2.5962 2.5770
21 2.8137 2.7644 2.7218 2.6847 2.6519 2.6229 2.5969 2.5735 2.5524 2.5331
22 2.7749 2.7255 2.6828 2.6456 2.6128 2.5837 2.5576 2.5342 2.5130 2.4937
23 2.7398 2.6904 2.6477 2.6104 2.5775 2.5483 2.5222 2.4987 2.4774 2.4580
24 2.7080 2.6585 2.6157 2.5784 2.5455 2.5162 2.4900 2.4665 2.4451 2.4257
25 2.6790 2.6295 2.5867 2.5493 2.5163 2.4870 2.4607 2.4371 2.4156 2.3962
26 2.6525 2.6029 2.5600 2.5226 2.4895 2.4602 2.4339 2.4101 2.3887 2.3691
27 2.6281 2.5785 2.5356 2.4981 2.4650 2.4355 2.4092 2.3854 2.3639 2.3443
28 2.6057 2.5560 2.5130 2.4755 2.4423 2.4128 2.3864 2.3626 2.3410 2.3214
29 2.5849 2.5352 2.4922 2.4546 2.4214 2.3918 2.3654 2.3415 2.3199 2.3002
30 2.5657 2.5159 2.4729 2.4352 2.4020 2.3724 2.3459 2.3219 2.3003 2.2805
40 2.4297 2.3797 2.3362 2.2982 2.2645 2.2345 2.2076 2.1832 2.1612 2.1410
50 2.3511 2.3007 2.2570 2.2187 2.1847 2.1545 2.1272 2.1026 2.0803 2.0598
60 2.2997 2.2492 2.2053 2.1668 2.1326 2.1021 2.0747 2.0499 2.0273 2.0067
70 2.2636 2.2130 2.1690 2.1302 2.0959 2.0653 2.0377 2.0127 1.9899 1.9691
80 2.2369 2.1861 2.1419 2.1031 2.0687 2.0379 2.0102 1.9850 1.9622 1.9412
90 2.2162 2.1654 2.1211 2.0822 2.0476 2.0167 1.9889 1.9637 1.9407 1.9197
100 2.1998 2.1489 2.1045 2.0655 2.0309 1.9999 1.9720 1.9467 1.9236 1.9025
110 2.1864 2.1355 2.0910 2.0520 2.0173 1.9862 1.9582 1.9328 1.9097 1.8885
120 2.1753 2.1243 2.0799 2.0407 2.0059 1.9748 1.9468 1.9213 1.8981 1.8769
150 2.1511 2.1000 2.0554 2.0161 1.9812 1.9499 1.9217 1.8961 1.8728 1.8514
200 2.1271 2.0758 2.0311 1.9917 1.9566 1.9252 1.8969 1.8711 1.8476 1.8261
∞ 2.0562 2.0045 1.9594 1.9195 1.8840 1.8521 1.8232 1.7970 1.7730 1.7510
13
F Distribution
Table Part One provides value of F (Right tail area = Alpha 0.01)
Numerator degrees of freedom
Den-df 1 2 3 4 5 6 7 8 9 10
1 4052.1845 4999.3396 5403.5336 5624.2570 5763.9554 5858.9503 5928.3338 5980.9536 6022.3974 6055.9250
2 98.5019 99.0003 99.1640 99.2513 99.3023 99.3314 99.3568 99.3750 99.3896 99.3969
3 34.1161 30.8164 29.4567 28.7100 28.2371 27.9106 27.6714 27.4895 27.3449 27.2285
4 21.1976 17.9998 16.6942 15.9771 15.5219 15.2068 14.9757 14.7988 14.6592 14.5460
5 16.2581 13.2741 12.0599 11.3919 10.9671 10.6722 10.4556 10.2893 10.1577 10.0511
6 13.7452 10.9249 9.7796 9.1484 8.7459 8.4660 8.2600 8.1017 7.9760 7.8742
7 12.2463 9.5465 8.4513 7.8467 7.4604 7.1914 6.9929 6.8401 6.7188 6.6201
8 11.2586 8.6491 7.5910 7.0061 6.6318 6.3707 6.1776 6.0288 5.9106 5.8143
9 10.5615 8.0215 6.9920 6.4221 6.0569 5.8018 5.6128 5.4671 5.3511 5.2565
10 10.0442 7.5595 6.5523 5.9944 5.6364 5.3858 5.2001 5.0567 4.9424 4.8491
11 9.6461 7.2057 6.2167 5.6683 5.3160 5.0692 4.8860 4.7445 4.6315 4.5393
12 9.3303 6.9266 5.9525 5.4119 5.0644 4.8205 4.6395 4.4994 4.3875 4.2961
13 9.0738 6.7009 5.7394 5.2053 4.8616 4.6203 4.4410 4.3021 4.1911 4.1003
14 8.8617 6.5149 5.5639 5.0354 4.6950 4.4558 4.2779 4.1400 4.0297 3.9394
15 8.6832 6.3588 5.4170 4.8932 4.5556 4.3183 4.1416 4.0044 3.8948 3.8049
16 8.5309 6.2263 5.2922 4.7726 4.4374 4.2016 4.0259 3.8896 3.7804 3.6909
17 8.3998 6.1121 5.1850 4.6689 4.3360 4.1015 3.9267 3.7909 3.6823 3.5931
18 8.2855 6.0129 5.0919 4.5790 4.2479 4.0146 3.8406 3.7054 3.5971 3.5081
19 8.1850 5.9259 5.0103 4.5002 4.1708 3.9386 3.7653 3.6305 3.5225 3.4338
20 8.0960 5.8490 4.9382 4.4307 4.1027 3.8714 3.6987 3.5644 3.4567 3.3682
21 8.0166 5.7804 4.8740 4.3688 4.0421 3.8117 3.6396 3.5056 3.3982 3.3098
22 7.9453 5.7190 4.8166 4.3134 3.9880 3.7583 3.5866 3.4530 3.3458 3.2576
23 7.8811 5.6637 4.7648 4.2635 3.9392 3.7102 3.5390 3.4057 3.2986 3.2106
24 7.8229 5.6136 4.7181 4.2185 3.8951 3.6667 3.4959 3.3629 3.2560 3.1681
25 7.7698 5.5680 4.6755 4.1774 3.8550 3.6272 3.4568 3.3239 3.2172 3.1294
26 7.7213 5.5263 4.6365 4.1400 3.8183 3.5911 3.4210 3.2884 3.1818 3.0941
27 7.6767 5.4881 4.6009 4.1056 3.7847 3.5580 3.3882 3.2558 3.1494 3.0618
28 7.6357 5.4529 4.5681 4.0740 3.7539 3.5276 3.3581 3.2259 3.1195 3.0320
29 7.5977 5.4205 4.5378 4.0449 3.7254 3.4995 3.3303 3.1982 3.0920 3.0045
30 7.5624 5.3903 4.5097 4.0179 3.6990 3.4735 3.3045 3.1726 3.0665 2.9791
40 7.3142 5.1785 4.3126 3.8283 3.5138 3.2910 3.1238 2.9930 2.8876 2.8005
50 7.1706 5.0566 4.1994 3.7195 3.4077 3.1864 3.0202 2.8900 2.7850 2.6981
60 7.0771 4.9774 4.1259 3.6491 3.3389 3.1187 2.9530 2.8233 2.7185 2.6318
70 7.0114 4.9218 4.0744 3.5997 3.2907 3.0712 2.9060 2.7765 2.6719 2.5852
80 6.9626 4.8807 4.0363 3.5631 3.2551 3.0361 2.8713 2.7420 2.6374 2.5508
90 6.9251 4.8491 4.0069 3.5350 3.2276 3.0091 2.8445 2.7154 2.6109 2.5243
100 6.8953 4.8239 3.9837 3.5127 3.2059 2.9877 2.8233 2.6943 2.5898 2.5033
110 6.8710 4.8034 3.9648 3.4946 3.1882 2.9703 2.8060 2.6771 2.5727 2.4862
120 6.8509 4.7865 3.9491 3.4795 3.1735 2.9559 2.7918 2.6629 2.5586 2.4721
150 6.8069 4.7495 3.9149 3.4468 3.1416 2.9244 2.7606 2.6319 2.5277 2.4412
200 6.7633 4.7128 3.8810 3.4143 3.1100 2.8933 2.7298 2.6012 2.4971 2.4106
∞ 6.6349 4.6052 3.7816 3.3192 3.0172 2.8020 2.6393 2.5113 2.4073 2.3209
14
F Distribution
Table Part Two provides value of F (Right tail area = Alpha 0.01)
Numerator degrees of freedom
Den-df 11 12 13 14 15 16 17 18 19 20
1 6083.3991 6106.6821 6125.7742 6143.0037 6156.9735 6170.0121 6181.1879 6191.4325 6200.7457 6208.6619
2 99.4078 99.4187 99.4223 99.4260 99.4332 99.4369 99.4405 99.4442 99.4478 99.4478
3 27.1320 27.0520 26.9829 26.9238 26.8719 26.8265 26.7864 26.7510 26.7191 26.6900
4 14.4523 14.3737 14.3064 14.2486 14.1981 14.1540 14.1144 14.0794 14.0481 14.0194
5 9.9626 9.8883 9.8248 9.7700 9.7223 9.6802 9.6429 9.6095 9.5797 9.5527
6 7.7896 7.7183 7.6575 7.6050 7.5590 7.5186 7.4826 7.4506 7.4219 7.3958
7 6.5381 6.4691 6.4100 6.3590 6.3144 6.2751 6.2400 6.2089 6.1808 6.1555
8 5.7343 5.6667 5.6089 5.5588 5.5152 5.4765 5.4423 5.4116 5.3841 5.3591
9 5.1779 5.1115 5.0545 5.0052 4.9621 4.9240 4.8902 4.8599 4.8327 4.8080
10 4.7716 4.7058 4.6496 4.6008 4.5582 4.5204 4.4869 4.4569 4.4299 4.4054
11 4.4624 4.3974 4.3416 4.2933 4.2509 4.2135 4.1802 4.1503 4.1234 4.0990
12 4.2198 4.1553 4.0998 4.0517 4.0096 3.9724 3.9392 3.9095 3.8827 3.8584
13 4.0245 3.9603 3.9052 3.8573 3.8154 3.7783 3.7452 3.7156 3.6889 3.6646
14 3.8640 3.8002 3.7452 3.6976 3.6557 3.6187 3.5857 3.5561 3.5294 3.5052
15 3.7299 3.6662 3.6115 3.5639 3.5222 3.4852 3.4523 3.4228 3.3961 3.3719
16 3.6162 3.5527 3.4981 3.4506 3.4090 3.3721 3.3392 3.3096 3.2829 3.2587
17 3.5185 3.4552 3.4007 3.3533 3.3117 3.2748 3.2419 3.2124 3.1857 3.1615
18 3.4338 3.3706 3.3162 3.2689 3.2273 3.1905 3.1575 3.1280 3.1013 3.0771
19 3.3596 3.2965 3.2422 3.1949 3.1533 3.1165 3.0836 3.0541 3.0274 3.0031
20 3.2941 3.2311 3.1769 3.1296 3.0880 3.0512 3.0183 2.9887 2.9620 2.9377
21 3.2359 3.1729 3.1187 3.0715 3.0300 2.9931 2.9602 2.9306 2.9038 2.8795
22 3.1837 3.1209 3.0667 3.0195 2.9779 2.9411 2.9082 2.8786 2.8518 2.8274
23 3.1368 3.0740 3.0199 2.9727 2.9311 2.8942 2.8613 2.8317 2.8049 2.7805
24 3.0944 3.0316 2.9775 2.9303 2.8887 2.8519 2.8189 2.7892 2.7624 2.7380
25 3.0558 2.9931 2.9389 2.8917 2.8502 2.8133 2.7803 2.7506 2.7238 2.6993
26 3.0205 2.9578 2.9038 2.8566 2.8150 2.7781 2.7451 2.7154 2.6885 2.6640
27 2.9882 2.9256 2.8715 2.8243 2.7827 2.7458 2.7127 2.6830 2.6561 2.6316
28 2.9585 2.8959 2.8418 2.7946 2.7530 2.7160 2.6830 2.6532 2.6263 2.6018
29 2.9311 2.8685 2.8144 2.7672 2.7256 2.6886 2.6555 2.6257 2.5987 2.5742
30 2.9057 2.8431 2.7890 2.7418 2.7002 2.6632 2.6301 2.6002 2.5732 2.5487
40 2.7273 2.6648 2.6107 2.5634 2.5216 2.4844 2.4511 2.4210 2.3937 2.3689
50 2.6250 2.5625 2.5083 2.4609 2.4190 2.3816 2.3481 2.3178 2.2903 2.2652
60 2.5587 2.4961 2.4419 2.3943 2.3523 2.3148 2.2811 2.2507 2.2230 2.1978
70 2.5122 2.4496 2.3953 2.3477 2.3055 2.2679 2.2341 2.2036 2.1758 2.1504
80 2.4777 2.4151 2.3608 2.3131 2.2709 2.2332 2.1993 2.1686 2.1408 2.1153
90 2.4513 2.3886 2.3342 2.2865 2.2442 2.2064 2.1725 2.1417 2.1138 2.0882
100 2.4302 2.3676 2.3132 2.2654 2.2230 2.1852 2.1511 2.1203 2.0923 2.0666
110 2.4132 2.3505 2.2960 2.2482 2.2058 2.1679 2.1338 2.1029 2.0748 2.0491
120 2.3990 2.3363 2.2818 2.2339 2.1915 2.1536 2.1194 2.0885 2.0603 2.0346
150 2.3681 2.3053 2.2508 2.2028 2.1603 2.1223 2.0880 2.0570 2.0287 2.0028
200 2.3375 2.2747 2.2201 2.1721 2.1294 2.0913 2.0569 2.0257 1.9973 1.9713
∞ 2.2477 2.1847 2.1299 2.0815 2.0385 2.0000 1.9652 1.9336 1.9048 1.8783
15
F Distribution
Table Part One provides value of F (Right tail area = Alpha 0.005)
Numerator degrees of freedom
Den df 1 2 3 4 5 6 7 8 9 10
1 16212.4634 19997.3583 21614.1343 22500.7534 23055.8217 23439.5266 23715.1980 23923.8143 24091.4524 24221.8375
2 198.5027 199.0120 199.1575 199.2448 199.3030 199.3321 199.3612 199.3758 199.3903 199.3903
3 55.5519 49.8003 47.4683 46.1951 45.3911 44.8381 44.4343 44.1250 43.8813 43.6848
4 31.3321 26.2844 24.2599 23.1539 22.4563 21.9752 21.6223 21.3522 21.1385 20.9666
5 22.7847 18.3136 16.5301 15.5560 14.9394 14.5133 14.2004 13.9607 13.7716 13.6179
6 18.6346 14.5442 12.9166 12.0276 11.4637 11.0731 10.7857 10.5656 10.3914 10.2500
7 16.2354 12.4037 10.8826 10.0504 9.5220 9.1554 8.8853 8.6779 8.5138 8.3803
8 14.6883 11.0426 9.5965 8.8053 8.3019 7.9519 7.6941 7.4958 7.3387 7.2107
9 13.6138 10.1068 8.7171 7.9558 7.4710 7.1338 6.8849 6.6932 6.5411 6.4172
10 12.8266 9.4269 8.0809 7.3428 6.8724 6.5447 6.3026 6.1159 5.9676 5.8467
11 12.2263 8.9121 7.6004 6.8808 6.4217 6.1016 5.8648 5.6821 5.5368 5.4183
12 11.7543 8.5097 7.2257 6.5211 6.0711 5.7571 5.5245 5.3451 5.2021 5.0854
13 11.3737 8.1864 6.9258 6.2334 5.7910 5.4819 5.2529 5.0761 4.9351 4.8200
14 11.0604 7.9217 6.6804 5.9983 5.5622 5.2573 5.0313 4.8566 4.7173 4.6034
15 10.7980 7.7007 6.4761 5.8029 5.3722 5.0708 4.8473 4.6743 4.5363 4.4236
16 10.5756 7.5138 6.3034 5.6378 5.2116 4.9134 4.6920 4.5206 4.3839 4.2719
17 10.3842 7.3537 6.1557 5.4968 5.0745 4.7789 4.5594 4.3893 4.2535 4.1424
18 10.2182 7.2148 6.0278 5.3747 4.9561 4.6628 4.4448 4.2760 4.1410 4.0304
19 10.0727 7.0934 5.9160 5.2680 4.8526 4.5613 4.3449 4.1770 4.0428 3.9329
20 9.9440 6.9865 5.8177 5.1743 4.7615 4.4721 4.2569 4.0900 3.9564 3.8470
21 9.8294 6.8915 5.7304 5.0911 4.6808 4.3931 4.1789 4.0128 3.8799 3.7709
22 9.7270 6.8064 5.6524 5.0168 4.6088 4.3225 4.1093 3.9440 3.8116 3.7030
23 9.6347 6.7300 5.5823 4.9500 4.5441 4.2591 4.0469 3.8822 3.7502 3.6420
24 9.5513 6.6609 5.5190 4.8898 4.4856 4.2019 3.9905 3.8264 3.6949 3.5870
25 9.4753 6.5982 5.4615 4.8351 4.4326 4.1500 3.9394 3.7758 3.6447 3.5370
26 9.4060 6.5410 5.4091 4.7852 4.3843 4.1027 3.8928 3.7297 3.5989 3.4916
27 9.3423 6.4886 5.3611 4.7396 4.3402 4.0594 3.8501 3.6875 3.5570 3.4499
28 9.2837 6.4404 5.3170 4.6977 4.2996 4.0197 3.8110 3.6488 3.5186 3.4117
29 9.2298 6.3958 5.2764 4.6591 4.2621 3.9831 3.7749 3.6131 3.4832 3.3765
30 9.1798 6.3546 5.2388 4.6234 4.2276 3.9493 3.7415 3.5801 3.4505 3.3440
40 8.8278 6.0664 4.9758 4.3738 3.9860 3.7129 3.5088 3.3498 3.2220 3.1167
50 8.6256 5.9016 4.8259 4.2317 3.8486 3.5785 3.3764 3.2189 3.0921 2.9875
60 8.4947 5.7950 4.7290 4.1399 3.7600 3.4918 3.2911 3.1345 3.0083 2.9042
70 8.4026 5.7204 4.6613 4.0758 3.6980 3.4313 3.2315 3.0755 2.9498 2.8460
80 8.3346 5.6652 4.6113 4.0285 3.6524 3.3867 3.1876 3.0320 2.9066 2.8031
90 8.2823 5.6228 4.5728 3.9922 3.6173 3.3524 3.1538 2.9987 2.8735 2.7701
100 8.2407 5.5892 4.5424 3.9634 3.5895 3.3252 3.1271 2.9722 2.8472 2.7439
110 8.2068 5.5619 4.5177 3.9400 3.5669 3.3032 3.1054 2.9507 2.8259 2.7227
120 8.1789 5.5393 4.4972 3.9207 3.5482 3.2849 3.0875 2.9329 2.8083 2.7052
150 8.1177 5.4899 4.4525 3.8785 3.5075 3.2452 3.0483 2.8942 2.7698 2.6670
200 8.0572 5.4412 4.4084 3.8368 3.4673 3.2059 3.0097 2.8560 2.7319 2.6292
∞ 7.8794 5.2983 4.2794 3.7151 3.3499 3.0913 2.8968 2.7444 2.6211 2.5188
16
F Distribution
Table Part Two provides value of F (Right tail area = Alpha 0.005)
Numerator degrees of freedom
Den- df 11 12 13 14 15 16 17 18 19 20
1 24333.5962 24426.7285 24504.9596 24572.0148 24631.6195 24683.7735 24728.4770 24765.7299 24802.9828 24836.5104
2 199.4194 199.4194 199.4194 199.4194 199.4340 199.4486 199.4486 199.4486 199.4486 199.4486
3 43.5248 43.3865 43.2701 43.1719 43.0846 43.0082 42.9391 42.8809 42.8263 42.7790
4 20.8238 20.7046 20.6028 20.5146 20.4382 20.3709 20.3108 20.2581 20.2108 20.1671
5 13.4914 13.3846 13.2932 13.2150 13.1463 13.0858 13.0326 12.9849 12.9421 12.9035
6 10.1327 10.0345 9.9503 9.8776 9.8139 9.7580 9.7086 9.6643 9.6247 9.5888
7 8.2696 8.1764 8.0968 8.0279 7.9676 7.9149 7.8678 7.8257 7.7880 7.7539
8 7.1045 7.0149 6.9383 6.8721 6.8144 6.7632 6.7180 6.6775 6.6411 6.6082
9 6.3142 6.2273 6.1530 6.0886 6.0325 5.9829 5.9388 5.8994 5.8640 5.8319
10 5.7462 5.6614 5.5886 5.5256 5.4706 5.4221 5.3790 5.3403 5.3055 5.2740
11 5.3196 5.2363 5.1649 5.1031 5.0488 5.0011 4.9586 4.9206 4.8863 4.8552
12 4.9884 4.9063 4.8358 4.7748 4.7213 4.6741 4.6322 4.5945 4.5607 4.5300
13 4.7240 4.6429 4.5733 4.5129 4.4599 4.4132 4.3716 4.3343 4.3008 4.2703
14 4.5085 4.4281 4.3591 4.2993 4.2468 4.2005 4.1591 4.1222 4.0887 4.0585
15 4.3294 4.2497 4.1813 4.1219 4.0698 4.0237 3.9827 3.9458 3.9126 3.8826
16 4.1785 4.0993 4.0313 3.9723 3.9205 3.8747 3.8338 3.7971 3.7642 3.7342
17 4.0495 3.9709 3.9033 3.8445 3.7929 3.7473 3.7066 3.6702 3.6372 3.6073
18 3.9382 3.8599 3.7926 3.7340 3.6827 3.6372 3.5967 3.5603 3.5275 3.4977
19 3.8410 3.7631 3.6961 3.6378 3.5866 3.5412 3.5008 3.4645 3.4318 3.4020
20 3.7555 3.6779 3.6111 3.5530 3.5020 3.4568 3.4164 3.3802 3.3475 3.3178
21 3.6798 3.6024 3.5358 3.4779 3.4270 3.3818 3.3416 3.3054 3.2728 3.2431
22 3.6122 3.5350 3.4686 3.4108 3.3600 3.3150 3.2747 3.2387 3.2060 3.1764
23 3.5515 3.4745 3.4083 3.3506 3.2999 3.2549 3.2148 3.1787 3.1461 3.1165
24 3.4967 3.4199 3.3538 3.2962 3.2456 3.2007 3.1606 3.1246 3.0920 3.0624
25 3.4470 3.3704 3.3044 3.2469 3.1964 3.1515 3.1114 3.0755 3.0429 3.0133
26 3.4017 3.3252 3.2593 3.2019 3.1515 3.1067 3.0666 3.0307 2.9981 2.9685
27 3.3602 3.2840 3.2181 3.1608 3.1104 3.0656 3.0256 2.9896 2.9571 2.9275
28 3.3222 3.2460 3.1803 3.1230 3.0727 3.0279 2.9880 2.9520 2.9194 2.8899
29 3.2871 3.2110 3.1454 3.0882 3.0379 2.9932 2.9532 2.9173 2.8847 2.8551
30 3.2547 3.1787 3.1132 3.0561 3.0057 2.9610 2.9211 2.8851 2.8526 2.8230
40 3.0284 2.9531 2.8880 2.8312 2.7811 2.7365 2.6966 2.6607 2.6281 2.5984
50 2.8997 2.8247 2.7599 2.7032 2.6531 2.6085 2.5686 2.5326 2.4999 2.4702
60 2.8166 2.7418 2.6772 2.6205 2.5705 2.5259 2.4859 2.4498 2.4171 2.3872
70 2.7587 2.6840 2.6193 2.5627 2.5127 2.4681 2.4281 2.3919 2.3591 2.3291
80 2.7159 2.6413 2.5767 2.5201 2.4700 2.4254 2.3853 2.3492 2.3163 2.2862
90 2.6830 2.6085 2.5439 2.4873 2.4373 2.3926 2.3525 2.3163 2.2833 2.2532
100 2.6570 2.5825 2.5179 2.4614 2.4113 2.3666 2.3265 2.2902 2.2572 2.2270
110 2.6358 2.5614 2.4969 2.4403 2.3902 2.3455 2.3053 2.2690 2.2359 2.2058
120 2.6183 2.5439 2.4794 2.4228 2.3727 2.3280 2.2878 2.2514 2.2183 2.1881
150 2.5802 2.5059 2.4413 2.3848 2.3346 2.2899 2.2496 2.2131 2.1800 2.1496
200 2.5425 2.4683 2.4038 2.3472 2.2970 2.2521 2.2118 2.1753 2.1420 2.1116
∞ 2.4324 2.3583 2.2938 2.2371 2.1868 2.1417 2.1011 2.0642 2.0306 1.9998
17
Critical Values for the Durbin-Watson Statistic (alpha=0.05)
K=1 K=2 K=3 K=4 K=5
n dL dU dL dU dL dU dL dU dL dU
15 1.08 1.36 0.95 1.54 0.82 1.75 0.69 1.97 0.56 2.21
16 1.10 1.37 0.98 1.54 0.86 1.73 0.74 1.93 0.62 2.15
17 1.13 1.38 1.02 1.54 0.90 1.71 0.78 1.90 0.67 2.10
18 1.16 1.39 1.05 1.53 0.93 1.69 0.82 1.87 0.71 2.06
19 1.18 1.40 1.08 1.53 0.97 1.68 0.86 1.85 0.75 2.02
20 1.20 1.41 1.10 1.54 1.00 1.68 0.90 1.83 0.79 1.99
21 1.22 1.42 1.13 1.54 1.03 1.67 0.93 1.81 0.83 1.96
22 1.24 1.43 1.15 1.54 1.05 1.66 0.96 1.80 0.86 1.94
23 1.26 1.44 1.17 1.54 1.08 1.66 0.99 1.79 0.90 1.92
24 1.27 1.45 1.19 1.55 1.10 1.66 1.01 1.78 0.93 1.90
25 1.29 1.45 1.21 1.55 1.12 1.66 1.04 1.77 0.95 1.89
26 1.30 1.46 1.22 1.55 1.14 1.65 1.06 1.76 0.98 1.88
27 1.32 1.47 1.24 1.56 1.16 1.65 1.08 1.76 1.01 1.86
28 1.33 1.48 1.26 1.56 1.18 1.65 1.10 1.75 1.03 1.85
29 1.34 1.48 1.27 1.56 1.20 1.65 1.12 1.74 1.05 1.84
30 1.35 1.49 1.28 1.57 1.21 1.65 1.14 1.74 1.07 1.83
31 1.36 1.50 1.30 1.57 1.23 1.65 1.16 1.74 1.09 1.83
32 1.37 1.50 1.31 1.57 1.24 1.65 1.18 1.73 1.11 1.82
33 1.38 1.51 1.32 1.58 1.26 1.65 1.19 1.73 1.13 1.81
34 1.39 1.51 1.33 1.58 1.27 1.65 1.21 1.73 1.15 1.81
35 1.40 1.52 1.34 1.58 1.28 1.65 1.22 1.73 1.16 1.80
36 1.41 1.52 1.35 1.59 1.29 1.65 1.24 1.73 1.18 1.80
37 1.42 1.53 1.36 1.59 1.31 1.66 1.25 1.72 1.19 1.80
38 1.43 1.54 1.37 1.59 1.32 1.66 1.26 1.72 1.21 1.79
39 1.43 1.54 1.38 1.60 1.33 1.66 1.27 1.72 1.22 1.79
40 1.44 1.54 1.39 1.60 1.34 1.66 1.29 1.72 1.23 1.79
45 1.48 1.57 1.43 1.62 1.38 1.67 1.34 1.72 1.29 1.78
50 1.50 1.59 1.46 1.63 1.42 1.67 1.38 1.72 1.34 1.77
55 1.53 1.60 1.49 1.64 1.45 1.68 1.41 1.72 1.38 1.77
60 1.55 1.62 1.51 1.65 1.48 1.69 1.44 1.73 1.41 1.77
65 1.57 1.63 1.54 1.66 1.50 1.70 1.47 1.73 1.44 1.77
70 1.58 1.64 1.55 1.67 1.52 1.70 1.49 1.74 1.46 1.77
75 1.60 1.65 1.57 1.68 1.54 1.71 1.51 1.74 1.49 1.77
80 1.61 1.66 1.59 1.69 1.56 1.72 1.53 1.74 1.51 1.77
85 1.62 1.67 1.60 1.70 1.57 1.72 1.55 1.75 1.52 1.77
90 1.63 1.68 1.61 1.70 1.59 1.73 1.57 1.75 1.54 1.78
95 1.64 1.69 1.62 1.71 1.60 1.73 1.58 1.75 1.56 1.78
100 1.65 1.69 1.63 1.72 1.61 1.74 1.59 1.76 1.57 1.78
18
Critical Values for the Durbin-Watson Statistic (alpha=0.025)
K=1 K=2 K=3 K=4 K=5
n dL dU dL dU dL dU dL dU dL dU
15 0.95 1.23 0.83 1.40 0.71 1.61 0.59 1.84 0.48 2.09
16 0.98 1.24 0.86 1.40 0.75 1.59 0.64 1.80 0.53 2.03
17 1.01 1.25 0.90 1.40 0.79 1.58 0.68 1.77 0.57 1.98
18 1.03 1.26 0.93 1.40 0.82 1.56 0.72 1.74 0.62 1.93
19 1.06 1.28 0.96 1.41 0.86 1.55 0.76 1.72 0.66 1.90
20 1.08 1.28 0.99 1.41 0.89 1.55 0.79 1.70 0.70 1.87
21 1.10 1.30 1.01 1.41 0.92 1.54 0.83 1.69 0.73 1.84
22 1.12 1.31 1.04 1.42 0.95 1.54 0.86 1.68 0.77 1.82
23 1.14 1.32 1.06 1.42 0.97 1.54 0.89 1.67 0.80 1.80
24 1.16 1.33 1.08 1.43 1.00 1.54 0.91 1.66 0.83 1.79
25 1.18 1.34 1.10 1.43 1.02 1.54 0.94 1.65 0.86 1.77
26 1.19 1.35 1.12 1.44 1.04 1.54 0.96 1.65 0.88 1.76
27 1.21 1.36 1.13 1.44 1.06 1.54 0.99 1.64 0.91 1.75
28 1.22 1.37 1.15 1.45 1.08 1.54 1.01 1.64 0.93 1.74
29 1.24 1.38 1.17 1.45 1.10 1.54 1.03 1.63 0.96 1.73
30 1.25 1.38 1.18 1.46 1.12 1.54 1.05 1.63 0.98 1.73
31 1.26 1.39 1.20 1.47 1.13 1.55 1.07 1.63 1.00 1.72
32 1.27 1.40 1.21 1.47 1.15 1.55 1.08 1.63 1.02 1.71
33 1.28 1.41 1.22 1.48 1.16 1.55 1.10 1.63 1.04 1.71
34 1.29 1.41 1.24 1.48 1.17 1.55 1.12 1.63 1.06 1.70
35 1.30 1.42 1.25 1.48 1.19 1.55 1.13 1.63 1.07 1.70
36 1.31 1.43 1.26 1.49 1.20 1.56 1.15 1.63 1.09 1.70
37 1.32 1.43 1.27 1.49 1.21 1.56 1.16 1.62 1.10 1.70
38 1.33 1.44 1.28 1.50 1.23 1.56 1.17 1.62 1.12 1.70
39 1.34 1.44 1.29 1.50 1.24 1.56 1.19 1.63 1.13 1.69
40 1.35 1.45 1.30 1.51 1.25 1.57 1.20 1.63 1.15 1.69
45 1.39 1.48 1.34 1.53 1.30 1.58 1.25 1.63 1.21 1.69
50 1.42 1.50 1.38 1.54 1.34 1.59 1.30 1.64 1.26 1.69
55 1.45 1.52 1.41 1.56 1.37 1.60 1.33 1.64 1.30 1.69
60 1.47 1.54 1.44 1.57 1.40 1.61 1.37 1.65 1.33 1.69
65 1.49 1.55 1.46 1.59 1.43 1.62 1.40 1.66 1.36 1.69
70 1.51 1.57 1.48 1.60 1.45 1.63 1.42 1.66 1.39 1.70
75 1.53 1.58 1.50 1.61 1.47 1.64 1.45 1.67 1.42 1.70
80 1.54 1.59 1.52 1.62 1.49 1.65 1.47 1.67 1.44 1.70
85 1.56 1.60 1.53 1.63 1.51 1.65 1.49 1.68 1.46 1.71
90 1.57 1.61 1.55 1.64 1.53 1.66 1.50 1.69 1.48 1.71
95 1.58 1.62 1.56 1.65 1.54 1.67 1.52 1.69 1.50 1.71
100 1.59 1.63 1.57 1.65 1.55 1.67 1.53 1.70 1.51 1.72
19
Critical Values for the Durbin-Watson Statistic (alpha=0.01)
K=1 K=2 K=3 K=4 K=5
n dL dU dL dU dL dU dL dU dL dU
15 0.81 1.07 0.70 1.25 0.59 1.46 0.49 1.70 0.39 1.96
16 0.84 1.09 0.74 1.25 0.63 1.44 0.53 1.66 0.44 1.90
17 0.87 1.10 0.77 1.25 0.67 1.43 0.57 1.63 0.48 1.85
18 0.90 1.12 0.80 1.26 0.71 1.42 0.61 1.60 0.52 1.80
19 0.93 1.13 0.83 1.26 0.74 1.41 0.65 1.58 0.56 1.77
20 0.95 1.15 0.86 1.27 0.77 1.41 0.68 1.57 0.60 1.74
21 0.97 1.16 0.89 1.27 0.80 1.41 0.72 1.55 0.63 1.71
22 1.00 1.17 0.91 1.28 0.83 1.40 0.75 1.54 0.66 1.69
23 1.02 1.19 0.94 1.29 0.86 1.40 0.77 1.53 0.70 1.67
24 1.04 1.20 0.96 1.30 0.88 1.41 0.80 1.53 0.72 1.66
25 1.05 1.21 0.98 1.30 0.90 1.41 0.83 1.52 0.75 1.65
26 1.07 1.22 1.00 1.31 0.93 1.41 0.85 1.52 0.78 1.64
27 1.09 1.23 1.02 1.32 0.95 1.41 0.88 1.51 0.81 1.63
28 1.10 1.24 1.04 1.32 0.97 1.41 0.90 1.51 0.83 1.62
29 1.12 1.25 1.05 1.33 0.99 1.42 0.92 1.51 0.85 1.61
30 1.13 1.26 1.07 1.34 1.01 1.42 0.94 1.51 0.88 1.61
31 1.15 1.27 1.08 1.34 1.02 1.42 0.96 1.51 0.90 1.60
32 1.16 1.28 1.10 1.35 1.04 1.43 0.98 1.51 0.92 1.60
33 1.17 1.29 1.11 1.36 1.05 1.43 1.00 1.51 0.94 1.59
34 1.18 1.30 1.13 1.36 1.07 1.43 1.01 1.51 0.95 1.59
35 1.19 1.31 1.14 1.37 1.08 1.44 1.03 1.51 0.97 1.59
36 1.21 1.32 1.15 1.38 1.10 1.44 1.04 1.51 0.99 1.59
37 1.22 1.32 1.16 1.38 1.11 1.45 1.06 1.51 1.00 1.59
38 1.23 1.33 1.18 1.39 1.12 1.45 1.07 1.52 1.02 1.58
39 1.24 1.34 1.19 1.39 1.14 1.45 1.09 1.52 1.03 1.58
40 1.25 1.34 1.20 1.40 1.15 1.46 1.10 1.52 1.05 1.58
45 1.29 1.38 1.24 1.42 1.20 1.48 1.16 1.53 1.11 1.58
50 1.32 1.40 1.28 1.45 1.24 1.49 1.20 1.54 1.16 1.59
55 1.36 1.43 1.32 1.47 1.28 1.51 1.25 1.55 1.21 1.59
60 1.38 1.45 1.35 1.48 1.32 1.52 1.28 1.56 1.25 1.60
65 1.41 1.47 1.38 1.50 1.35 1.53 1.31 1.57 1.28 1.61
70 1.43 1.49 1.40 1.52 1.37 1.55 1.34 1.58 1.31 1.61
75 1.45 1.50 1.42 1.53 1.39 1.56 1.37 1.59 1.34 1.62
80 1.47 1.52 1.44 1.54 1.42 1.57 1.39 1.60 1.36 1.62
85 1.48 1.53 4.16 1.55 1.43 1.58 1.41 1.60 1.39 1.63
90 1.50 1.54 1.47 1.56 1.45 1.59 1.43 1.61 1.41 1.64
95 1.51 1.55 1.49 1.57 1.47 1.60 1.45 1.62 1.42 1.64
100 1.52 1.56 1.50 1.58 1.48 1.60 1.46 1.63 1.44 1.65
