Statistical Tables
by Bill Raynor
braynor@kcc.com

Chi-Square Upper tails
df 0.25 0.20 0.15 0.10 0.05 0.01
==|=======================
1 | 1.32 1.64 2.07 2.71 3.84 6.63
2 | 2.77 3.22 3.79 4.61 5.99 9.21
3 | 4.11 4.64 5.32 6.25 7.81 11.3
4 | 5.39 5.99 6.74 7.78 9.49 13.3
5 | 6.63 7.29 8.12 9.24 11.1 15.1
6 | 7.84 8.56 9.45 10.6 12.6 16.8
7 | 9.04 9.80 10.7 12.0 14.1 18.5
8 | 10.2 11.0 12.0 13.4 15.5 20.1
9 | 11.4 12.2 13.3 14.7 16.9 21.7
10| 12.5 13.4 14.5 16.0 18.3 23.2
11| 13.7 14.6 15.8 17.3 19.7 24.7
12| 14.8 15.8 17.0 18.5 21.0 26.2
13| 16.0 17.0 18.2 19.8 22.4 27.7
14| 17.1 18.2 19.4 21.1 23.7 29.1
15| 18.2 19.3 20.6 22.3 25.0 30.6
16| 19.4 20.5 21.8 23.5 26.3 32.0
17| 20.5 21.6 23.0 24.8 27.6 33.4
18| 21.6 22.8 24.2 26.0 28.9 34.8
19| 22.7 23.9 25.3 27.2 30.1 36.2
20| 23.8 25.0 26.5 28.4 31.4 37.6
21| 24.9 26.2 27.7 29.6 32.7 38.9
22| 26.0 27.3 28.8 30.8 33.9 40.3
23| 27.1 28.4 30.0 32.0 35.2 41.6
24| 28.2 29.6 31.1 33.2 36.4 43.0
25| 29.3 30.7 32.3 34.4 37.7 44.3
30| 34.8 36.3 38.0 40.3 43.8 50.9
35| 40.2 41.8 43.6 46.1 49.8 57.3
40| 45.6 47.3 49.2 51.8 55.8 63.7
45| 51.0 52.7 54.8 57.5 61.7 70.0
50| 56.3 58.2 60.3 63.2 67.5 76.2
60| 67.0 69.0 71.3 74.4 79.1 88.4
70| 77.6 79.7 82.3 85.5 90.5 100
80| 88.1 90.4 93.1 96.6 102 112
90| 98.6 101. 104 108 113 124
100| 109 112 115 118 124 136
= =|=======================

F tails alpha=.01 [2/2:v1=12--infinity]
v2 | 12 14 16 20 24
==+=======================
1| 6106 6143 6170 6209 6235
2| 99.42 99.43 99.44 99.45 99.46
3| 27.05 26.92 26.83 26.69 26.60
4| 14.37 14.25 14.15 14.02 13.93
5| 9.888 9.770 9.680 9.553 9.466
6| 7.718 7.605 7.519 7.396 7.313
7| 6.469 6.359 6.275 6.155 6.074
8| 5.667 5.559 5.477 5.359 5.279
9| 5.111 5.005 4.924 4.808 4.729
10| 4.706 4.601 4.520 4.405 4.327
11| 4.397 4.293 4.213 4.099 4.021
12| 4.155 4.052 3.972 3.858 3.780
13| 3.960 3.857 3.778 3.665 3.587
14| 3.800 3.698 3.619 3.505 3.427
15| 3.666 3.564 3.485 3.372 3.294
16| 3.553 3.451 3.372 3.259 3.181
17| 3.455 3.353 3.275 3.162 3.084
18| 3.371 3.269 3.190 3.077 2.999
19| 3.297 3.195 3.116 3.003 2.925
20| 3.231 3.130 3.051 2.938 2.859
21| 3.173 3.072 2.993 2.880 2.801
22| 3.121 3.019 2.941 2.827 2.749
23| 3.074 2.973 2.894 2.781 2.702
24| 3.032 2.930 2.852 2.738 2.659
25| 2.993 2.892 2.813 2.699 2.620
26| 2.958 2.857 2.778 2.664 2.585
27| 2.926 2.824 2.746 2.632 2.552
28| 2.896 2.795 2.716 2.602 2.522
29| 2.868 2.767 2.689 2.574 2.495
30| 2.843 2.742 2.663 2.549 2.469
40| 2.665 2.563 2.484 2.369 2.288
50| 2.562 2.461 2.382 2.265 2.183
60| 2.496 2.394 2.315 2.198 2.115
120| 2.336 2.234 2.154 2.035 1.950
inf| 2.203 2.099 2.018 1.897 1.810
==+=======================

F tails alpha=.01 v1=30--infinity
v2 | 30 40 60 120 inf
==+=======================
1| 6261 6287 6313 6339 6365.5
2| 99.47 99.47 99.48 99.49 99.50
3| 26.50 26.41 26.32 26.22 26.13
4| 13.84 13.75 13.65 13.56 13.46
5| 9.379 9.291 9.202 9.112 9.022
6| 7.229 7.143 7.057 6.969 6.881
7| 5.992 5.908 5.824 5.737 5.651
8| 5.198 5.116 5.032 4.946 4.860
9| 4.649 4.567 4.483 4.398 4.312
10| 4.247 4.165 4.082 3.996 3.910
11| 3.941 3.860 3.776 3.690 3.604
12| 3.701 3.619 3.535 3.449 3.362
13| 3.507 3.425 3.341 3.255 3.166
14| 3.348 3.266 3.181 3.094 3.005
15| 3.214 3.132 3.047 2.959 2.870
16| 3.101 3.018 2.933 2.845 2.754
17| 3.003 2.920 2.835 2.746 2.654
18| 2.919 2.835 2.749 2.660 2.567
19| 2.844 2.761 2.674 2.584 2.490
20| 2.778 2.695 2.608 2.517 2.422
21| 2.720 2.636 2.548 2.457 2.361
22| 2.667 2.583 2.495 2.403 2.307
23| 2.620 2.535 2.447 2.354 2.257
24| 2.577 2.492 2.403 2.310 2.212
25| 2.538 2.453 2.364 2.270 2.171
26| 2.503 2.417 2.327 2.233 2.133
27| 2.470 2.384 2.294 2.198 2.098
28| 2.440 2.354 2.263 2.167 2.065
29| 2.412 2.325 2.234 2.138 2.035
30| 2.386 2.299 2.208 2.111 2.008
40| 2.203 2.114 2.019 1.917 1.806
60| 2.028 1.936 1.836 1.726 1.602
120| 1.860 1.763 1.656 1.533 1.383
inf| 1.716 1.613 1.495 1.351 1.159
==+=======================

Student's T Distribution Upper Tails

df| .10 .05 .025 .01 .005
--+=======================
1| 3.078 6.314 12.71 31.82 63.66
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
50| 1.299 1.676 2.009 2.403 2.678
60| 1.296 1.671 2.000 2.390 2.660
70| 1.294 1.667 1.994 2.381 2.648
80| 1.292 1.664 1.990 2.374 2.639
100| 1.290 1.660 1.984 2.364 2.626
120| 1.289 1.658 1.980 2.358 2.617
inf | 1.282 1.645 1.960 2.326 2.576
----|=======================

F tails alpha=.05 [1/2: v1=1(1)10]
v2 | 1 2 3 4 5
==+=======================
1| 161.4 199.5 215.7 224.6 230.2
2| 18.51 19.00 19.16 19.25 19.30
3| 10.13 9.552 9.277 9.117 9.013
4| 7.709 6.944 6.591 6.388 6.256
5| 6.608 5.786 5.409 5.192 5.050
6| 5.987 5.143 4.757 4.534 4.387
7| 5.591 4.737 4.347 4.120 3.972
8| 5.318 4.459 4.066 3.838 3.687
9| 5.117 4.256 3.863 3.633 3.482
10| 4.965 4.103 3.708 3.478 3.326
11| 4.844 3.982 3.587 3.357 3.204
12| 4.747 3.885 3.490 3.259 3.106
13| 4.667 3.806 3.411 3.179 3.025
14| 4.600 3.739 3.344 3.112 2.958
15| 4.543 3.682 3.287 3.056 2.901
16| 4.494 3.634 3.239 3.007 2.852
17| 4.451 3.592 3.197 2.965 2.810
18| 4.414 3.555 3.160 2.928 2.773
19| 4.381 3.522 3.127 2.895 2.740
20| 4.351 3.493 3.098 2.866 2.711
21| 4.325 3.467 3.072 2.840 2.685
22| 4.301 3.443 3.049 2.817 2.661
23| 4.279 3.422 3.028 2.796 2.640
24| 4.260 3.403 3.009 2.776 2.621
25| 4.242 3.385 2.991 2.759 2.603
26| 4.225 3.369 2.975 2.743 2.587
27| 4.210 3.354 2.960 2.728 2.572
28| 4.196 3.340 2.947 2.714 2.558
29| 4.183 3.328 2.934 2.701 2.545
30| 4.171 3.316 2.922 2.690 2.534
40| 4.085 3.232 2.839 2.606 2.449
50| 4.034 3.183 2.790 2.557 2.400
60| 4.001 3.150 2.758 2.525 2.368
120| 3.920 3.072 2.680 2.447 2.290
inf| 3.851 3.005 2.614 2.381 2.223
==+=======================

F tails alpha=.05 [v1=6(1)10]
v2 | 6 7 8 9 10
==+=======================
1| 234.0 236.8 238.9 240.5 241.9
2| 19.33 19.35 19.37 19.38 19.40
3| 8.941 8.887 8.845 8.812 8.786
4| 6.163 6.094 6.041 5.999 5.964
5| 4.950 4.876 4.818 4.772 4.735
6| 4.284 4.207 4.147 4.099 4.060
7| 3.866 3.787 3.726 3.677 3.637
8| 3.581 3.500 3.438 3.388 3.347
9| 3.374 3.293 3.230 3.179 3.137
10| 3.217 3.135 3.072 3.020 2.978
11| 3.095 3.012 2.948 2.896 2.854
12| 2.996 2.913 2.849 2.796 2.753
13| 2.915 2.832 2.767 2.714 2.671
14| 2.848 2.764 2.699 2.646 2.602
15| 2.790 2.707 2.641 2.588 2.544
16| 2.741 2.657 2.591 2.538 2.494
17| 2.699 2.614 2.548 2.494 2.450
18| 2.661 2.577 2.510 2.456 2.412
19| 2.628 2.544 2.477 2.423 2.378
20| 2.599 2.514 2.447 2.393 2.348
21| 2.573 2.488 2.420 2.366 2.321
22| 2.549 2.464 2.397 2.342 2.297
23| 2.528 2.442 2.375 2.320 2.275
24| 2.508 2.423 2.355 2.300 2.255
25| 2.490 2.405 2.337 2.282 2.236
26| 2.474 2.388 2.321 2.265 2.220
27| 2.459 2.373 2.305 2.250 2.204
28| 2.445 2.359 2.291 2.236 2.190
29| 2.432 2.346 2.278 2.223 2.177
30| 2.421 2.334 2.266 2.211 2.165
40| 2.336 2.249 2.180 2.124 2.077
50| 2.286 2.199 2.130 2.073 2.026
60| 2.254 2.167 2.097 2.040 1.993
120| 2.175 2.087 2.016 1.959 1.910
inf| 2.108 2.019 1.948 1.889 1.840
==+=======================

F tails alpha=.05 [2/2:v1=12--infinity]
v2 | 12 14 16 20 24
==+=======================
1| 243.9 245.4 246.5 248.0 249.1
2| 19.41 19.42 19.43 19.45 19.45
3| 8.745 8.715 8.692 8.660 8.639
4| 5.912 5.873 5.844 5.803 5.774
5| 4.678 4.636 4.604 4.558 4.527
6| 4.000 3.956 3.922 3.874 3.841
7| 3.575 3.529 3.494 3.445 3.410
8| 3.284 3.237 3.202 3.150 3.115
9| 3.073 3.025 2.989 2.936 2.900
10| 2.913 2.865 2.828 2.774 2.737
11| 2.788 2.739 2.701 2.646 2.609
12| 2.687 2.637 2.599 2.544 2.505
13| 2.604 2.554 2.515 2.459 2.420
14| 2.534 2.484 2.445 2.388 2.349
15| 2.475 2.424 2.385 2.328 2.288
16| 2.425 2.373 2.333 2.276 2.235
17| 2.381 2.329 2.289 2.230 2.190
18| 2.342 2.290 2.250 2.191 2.150
19| 2.308 2.256 2.215 2.155 2.114
20| 2.278 2.225 2.184 2.124 2.082
21| 2.250 2.197 2.156 2.096 2.054
22| 2.226 2.173 2.131 2.071 2.028
23| 2.204 2.150 2.109 2.048 2.005
24| 2.183 2.130 2.088 2.027 1.984
25| 2.165 2.111 2.069 2.007 1.964
26| 2.148 2.094 2.052 1.990 1.946
27| 2.132 2.078 2.036 1.974 1.930
28| 2.118 2.064 2.021 1.959 1.915
29| 2.104 2.050 2.007 1.945 1.901
30| 2.092 2.037 1.995 1.932 1.887
40| 2.003 1.948 1.904 1.839 1.793
50| 1.952 1.895 1.850 1.784 1.737
60| 1.917 1.860 1.815 1.748 1.700
120| 1.834 1.775 1.728 1.659 1.608
inf| 1.762 1.702 1.654 1.581 1.528
==+=======================

F tails alpha=.05 v1=30--infinity
v2 | 30 40 60 120 inf
==+=======================
1| 250.1 251.1 252.2 253.3 254.30
2| 19.46 19.47 19.48 19.49 19.50
3| 8.617 8.594 8.572 8.549 8.527
4| 5.746 5.717 5.688 5.658 5.628
5| 4.496 4.464 4.431 4.398 4.365
6| 3.808 3.774 3.740 3.705 3.669
7| 3.376 3.340 3.304 3.267 3.230
8| 3.079 3.043 3.005 2.967 2.928
9| 2.864 2.826 2.787 2.748 2.707
10| 2.700 2.661 2.621 2.580 2.538
11| 2.570 2.531 2.490 2.448 2.405
12| 2.466 2.426 2.384 2.341 2.297
13| 2.380 2.339 2.297 2.252 2.207
14| 2.308 2.266 2.223 2.178 2.131
15| 2.247 2.204 2.160 2.114 2.066
16| 2.194 2.151 2.106 2.059 2.010
17| 2.148 2.104 2.058 2.011 1.961
18| 2.107 2.063 2.017 1.968 1.917
19| 2.071 2.026 1.980 1.930 1.879
20| 2.039 1.994 1.946 1.896 1.844
21| 2.010 1.965 1.916 1.866 1.812
22| 1.984 1.938 1.889 1.838 1.784
23| 1.961 1.914 1.865 1.813 1.758
24| 1.939 1.892 1.842 1.790 1.734
25| 1.919 1.872 1.822 1.768 1.712
26| 1.901 1.853 1.803 1.749 1.691
27| 1.884 1.836 1.785 1.731 1.672
28| 1.869 1.820 1.769 1.714 1.655
29| 1.854 1.806 1.754 1.698 1.638
30| 1.841 1.792 1.740 1.683 1.623
40| 1.744 1.693 1.637 1.577 1.510
60| 1.649 1.594 1.534 1.467 1.390
120| 1.554 1.495 1.429 1.352 1.255
inf| 1.471 1.406 1.332 1.239 1.110
==+=======================

Probability -> Odds&Logits (logOdds)
log apprx prob
prob odds odds odds (%)
---- ---- ---- ------ -----
0.50 1.00 0.00 ( 1/1 50% )
0.51 1.04 0.04 (24/23 51% )
0.52 1.08 0.08 (13/12 52% )
0.53 1.13 0.12 ( 9/8 53% )
0.54 1.17 0.16 ( 7/6 54% )
0.55 1.22 0.20 (11/9 55% )
0.56 1.27 0.24 (14/11 56% )
0.57 1.33 0.28 ( 4/3 57% )
0.58 1.38 0.32 (11/8 58% )
0.59 1.44 0.36 (13/9 59% )
0.60 1.50 0.41 ( 3/2 60% )
0.61 1.56 0.45 (14/9 61% )
0.62 1.63 0.49 (13/8 62% )
0.63 1.70 0.53 (17/10 63% )
0.64 1.78 0.58 (16/9 64% )
0.65 1.86 0.62 (13/7 65% )
0.66 1.94 0.66 (31/16 66% )
0.67 2.03 0.71 (59/29 67% )
0.68 2.13 0.75 (17/8 68% )
0.69 2.23 0.80 (29/13 69% )
0.70 2.33 0.85 ( 7/3 70% )
0.71 2.45 0.90 (27/11 71% )
0.72 2.57 0.94 (18/7 72% )
0.73 2.70 0.99 (27/10 73% )
0.74 2.85 1.05 (37/13 74% )
0.75 3.00 1.10 ( 3/1 75% )
0.76 3.17 1.15 (19/6 76% )
0.77 3.35 1.21 (57/17 77% )
0.78 3.55 1.27 (39/11 78% )
0.79 3.76 1.32 (64/17 79% )
0.80 4.00 1.39 ( 4/1 80% )
0.81 4.26 1.45 (81/19 81% )
0.82 4.56 1.52 (41/9 82% )
0.83 4.88 1.59 (39/8 83% )
0.84 5.25 1.66 (21/4 84% )
0.85 5.67 1.73 (17/3 85% )
0.86 6.14 1.82 (43/7 86% )
0.87 6.69 1.90 (87/13 87% )
0.88 7.33 1.99 (22/3 88% )
0.89 8.09 2.09 (89/11 89% )
0.90 9.00 2.20 ( 9/1 90% )
0.91 10.11 2.31 (91/9 91% )
0.92 11.50 2.44 (23/2 92% )
0.93 13.29 2.59 (93/7 93% )
0.94 15.67 2.75 (47/3 94% )
0.95 19.00 2.94 (19/1 95% )
0.96 24.00 3.18 (24/1 96% )
0.97 32.33 3.48 (97/3 97% )
0.98 49.00 3.89 (49/1 98% )
0.99 99.00 4.60 (99/1 99% )
----------------------------------------

Log-Odds -> Prob & Odds

Log- Approx
Odds Prob. Odds
----- -------- --------
0.000 50.00% 1/1
0.025 50.62% 30/29
0.050 51.25% 20/19
0.075 51.87% 13/12
0.100 52.50% 10/9
0.125 53.12% 9/8
0.150 53.74% 22/19
0.175 54.36% 19/16
0.200 54.98% 11/9
0.225 55.60% 5/4
0.250 56.22% 23/18
0.275 56.83% 25/19
0.300 57.44% 23/17
0.325 58.05% 11/8
0.350 58.66% 17/12
0.375 59.27% 16/11
0.400 59.87% 52/35
0.425 60.47% 23/15
0.450 61.06% 11/7
0.475 61.66% 29/18
0.500 62.25% 28/17
0.525 62.83% 22/13
0.550 63.41% 19/11
0.575 63.99% 16/9
0.600 64.57% 20/11
0.625 65.14% 28/15
0.650 65.70% 23/12
0.675 66.26% 45/23
0.700 66.82% 2/1
0.725 67.37% 33/16
0.750 67.92% 36/17
0.775 68.46% 13/6
0.800 69.00% 29/13
0.825 69.53% 41/18
0.850 70.06% 68/29
0.875 70.58% 12/5
0.900 71.09% 32/13
0.925 71.61% 53/21
0.950 72.11% 44/17
0.975 72.61% 45/17
1.000 73.11% 49/18
1.100 75.03% 3/1
1.200 76.85% 63/19
1.300 78.58% 11/3
1.400 80.22% 65/16
1.500 81.76% 94/21
1.600 83.20% 94/19
1.700 84.55% 82/15
1.800 85.81% 97/16
1.900 86.99% 87/13
2.000 88.08% 59/8
2.100 89.09% 49/6
2.200 90.02% 9/1
2.300 90.89% 10/1
2.400 91.68% 11/1
2.500 92.41% 73/6
2.600 93.09% 94/7
2.700 93.70% 89/6
2.800 94.27% 82/5
2.900 94.78% 91/5
3.000 95.26% 20/1
3.100 95.69% 89/4
3.200 96.08% 49/2
3.300 96.44% 27/1
3.400 96.77% 30/1
3.500 97.07% 33/1
3.600 97.34% 73/2
3.700 97.59% 81/2
3.800 97.81% 89/2
3.900 98.02% 99/2
4.000 98.20% 55/1
4.100 98.37% 61/1
4.200 98.52% 67/1
4.300 98.66% 74/1
4.400 98.79% 82/1
4.500 98.90% 90/1
4.600 99.00% 100
4.700 99.10% 110
4.800 99.18% 122
4.900 99.26% 135
5.000 99.33% 149
---------------------------------------
Notes:
1. This table is primarily of use in
dealing with probabilities, which
are often modeled as if they were
linear on a logit (log-odds) scale.

2. For negative log-odds, simply take
the complement of the prob and
invert the odds.

Normal Quantiles
Quick tails
-%- Z ò -%- Z ò -%- Z ò
.010 3.719 ò .025 3.481 ò .050 3.291
.100 3.090 ò .250 2.807 ò .500 2.576
1.00 2.326 ò 2.50 1.960 ò 5.00 1.645
10.0 1.282 ò 25.0 0.674 ò 50.0 0.000

Extended tails ( 0.0<p<0.5)
P P+000 P+002 p+004 p+006 p+008
0% . -2.88 -2.65 -2.51 -2.41
1% -2.33 -2.26 -2.20 -2.14 -2.10
2% -2.05 -2.01 -1.98 -1.94 -1.91
3% -1.88 -1.85 -1.83 -1.80 -1.77
4% -1.75 -1.73 -1.71 -1.68 -1.66
5% -1.64 -1.63 -1.61 -1.59 -1.57
6% -1.55 -1.54 -1.52 -1.51 -1.49
7% -1.48 -1.46 -1.45 -1.43 -1.42
8% -1.41 -1.39 -1.38 -1.37 -1.35
9% -1.34 -1.33 -1.32 -1.30 -1.29
10% -1.28 -1.27 -1.26 -1.25 -1.24
11% -1.23 -1.22 -1.21 -1.20 -1.19
12% -1.17 -1.17 -1.16 -1.15 -1.14
13% -1.13 -1.12 -1.11 -1.10 -1.09
14% -1.08 -1.07 -1.06 -1.05 -1.05
15% -1.04 -1.03 -1.02 -1.01 -1.00
16% -0.99 -0.99 -0.98 -0.97 -0.96
17% -0.95 -0.95 -0.94 -0.93 -0.92
18% -0.92 -0.91 -0.90 -0.89 -0.89
19% -0.88 -0.87 -0.86 -0.86 -0.85
20% -0.84 -0.83 -0.83 -0.82 -0.81
21% -0.81 -0.80 -0.79 -0.79 -0.78
22% -0.77 -0.77 -0.76 -0.75 -0.75
23% -0.74 -0.73 -0.73 -0.72 -0.71
24% -0.71 -0.70 -0.69 -0.69 -0.68
25% -0.67 -0.67 -0.66 -0.66 -0.65
26% -0.64 -0.64 -0.63 -0.62 -0.62
27% -0.61 -0.61 -0.60 -0.59 -0.59
28% -0.58 -0.58 -0.57 -0.57 -0.56
29% -0.55 -0.55 -0.54 -0.54 -0.53
30% -0.52 -0.52 -0.51 -0.51 -0.50
31% -0.50 -0.49 -0.48 -0.48 -0.47
32% -0.47 -0.46 -0.46 -0.45 -0.45
33% -0.44 -0.43 -0.43 -0.42 -0.42
34% -0.41 -0.41 -0.40 -0.40 -0.39
35% -0.39 -0.38 -0.37 -0.37 -0.36
36% -0.36 -0.35 -0.35 -0.34 -0.34
37% -0.33 -0.33 -0.32 -0.32 -0.31
38% -0.31 -0.30 -0.29 -0.29 -0.28
39% -0.28 -0.27 -0.27 -0.26 -0.26
40% -0.25 -0.25 -0.24 -0.24 -0.23
41% -0.23 -0.22 -0.22 -0.21 -0.21
42% -0.20 -0.20 -0.19 -0.19 -0.18
43% -0.18 -0.17 -0.17 -0.16 -0.16
44% -0.15 -0.15 -0.14 -0.14 -0.13
45% -0.13 -0.12 -0.12 -0.11 -0.11
46% -0.10 -0.10 -0.09 -0.09 -0.08
47% -0.08 -0.07 -0.07 -0.06 -0.06
48% -0.05 -0.05 -0.04 -0.04 -0.03
49% -0.03 -0.02 -0.02 -0.01 -0.01

Normal Percentiles
Z <Z >Z |Z| pdf
-4.0 0.000 1.000 0.000 0.000
-3.9 0.000 1.000 0.000 0.000
-3.8 0.000 1.000 0.000 0.000
-3.7 0.000 1.000 0.000 0.000
-3.6 0.000 1.000 0.000 0.001
-3.5 0.000 1.000 0.000 0.001
-3.4 0.000 1.000 0.001 0.001
-3.3 0.000 1.000 0.001 0.002
-3.2 0.001 0.999 0.001 0.002
-3.1 0.001 0.999 0.002 0.003
-3.0 0.001 0.999 0.003 0.004
-2.9 0.002 0.998 0.004 0.006
-2.8 0.003 0.997 0.005 0.008
-2.7 0.003 0.997 0.007 0.010
-2.6 0.005 0.995 0.009 0.014
-2.5 0.006 0.994 0.012 0.018
-2.4 0.008 0.992 0.016 0.022
-2.3 0.011 0.989 0.021 0.028
-2.2 0.014 0.986 0.028 0.035
-2.1 0.018 0.982 0.036 0.044
-2.0 0.023 0.977 0.046 0.054
-1.9 0.029 0.971 0.057 0.066
-1.8 0.036 0.964 0.072 0.079
-1.7 0.045 0.955 0.089 0.094
-1.6 0.055 0.945 0.110 0.111
-1.5 0.067 0.933 0.134 0.130
-1.4 0.081 0.919 0.162 0.150
-1.3 0.097 0.903 0.194 0.171
-1.2 0.115 0.885 0.230 0.194
-1.1 0.136 0.864 0.271 0.218
-1.0 0.159 0.841 0.317 0.242
-0.9 0.184 0.816 0.368 0.266
-0.8 0.212 0.788 0.424 0.290
-0.7 0.242 0.758 0.484 0.312
-0.6 0.274 0.726 0.549 0.333
-0.5 0.309 0.691 0.617 0.352
-0.4 0.345 0.655 0.689 0.368
-0.3 0.382 0.618 0.764 0.381
-0.2 0.421 0.579 0.841 0.391
-0.1 0.460 0.540 0.920 0.397
0.0 0.500 0.500 1.000 0.399
0.1 0.540 0.460 0.920 0.397
0.2 0.579 0.421 0.841 0.391
0.3 0.618 0.382 0.764 0.381
0.4 0.655 0.345 0.689 0.368
0.5 0.691 0.309 0.617 0.352
0.6 0.726 0.274 0.549 0.333
0.7 0.758 0.242 0.484 0.312
0.8 0.788 0.212 0.424 0.290
0.9 0.816 0.184 0.368 0.266
1.0 0.841 0.159 0.317 0.242
1.1 0.864 0.136 0.271 0.218
1.2 0.885 0.115 0.230 0.194
1.3 0.903 0.097 0.194 0.171
1.4 0.919 0.081 0.162 0.150
1.5 0.933 0.067 0.134 0.130
1.6 0.945 0.055 0.110 0.111
1.7 0.955 0.045 0.089 0.094
1.8 0.964 0.036 0.072 0.079
1.9 0.971 0.029 0.057 0.066
2.0 0.977 0.023 0.046 0.054
2.1 0.982 0.018 0.036 0.044
2.2 0.986 0.014 0.028 0.035
2.3 0.989 0.011 0.021 0.028
2.4 0.992 0.008 0.016 0.022
2.5 0.994 0.006 0.012 0.018
2.6 0.995 0.005 0.009 0.014
2.7 0.997 0.003 0.007 0.010
2.8 0.997 0.003 0.005 0.008
2.9 0.998 0.002 0.004 0.006
3.0 0.999 0.001 0.003 0.004
3.1 0.999 0.001 0.002 0.003
3.2 0.999 0.001 0.001 0.002
3.3 1.000 0.000 0.001 0.002
3.4 1.000 0.000 0.001 0.001
3.5 1.000 0.000 0.000 0.001
3.6 1.000 0.000 0.000 0.001
3.7 1.000 0.000 0.000 0.000
3.8 1.000 0.000 0.000 0.000
3.9 1.000 0.000 0.000 0.000
4.0 1.000 0.000 0.000 0.000

F tails alpha=.10 [2/2 v1=12--infinity]
v2 | 12 14 16 20 24
==+=======================
1| 60.71 61.07 61.35 61.74 62.00
2| 9.408 9.420 9.429 9.441 9.450
3| 5.216 5.205 5.196 5.184 5.176
4| 3.896 3.878 3.864 3.844 3.831
5| 3.268 3.247 3.230 3.207 3.191
6| 2.905 2.881 2.863 2.836 2.818
7| 2.668 2.643 2.623 2.595 2.575
8| 2.502 2.475 2.455 2.425 2.404
9| 2.379 2.351 2.329 2.298 2.277
10| 2.284 2.255 2.233 2.201 2.178
11| 2.209 2.179 2.156 2.123 2.100
12| 2.147 2.117 2.094 2.060 2.036
13| 2.097 2.066 2.042 2.007 1.983
14| 2.054 2.022 1.998 1.962 1.938
15| 2.017 1.985 1.961 1.924 1.899
16| 1.985 1.953 1.928 1.891 1.866
17| 1.958 1.925 1.900 1.862 1.836
18| 1.933 1.900 1.875 1.837 1.810
19| 1.912 1.878 1.852 1.814 1.787
20| 1.892 1.859 1.833 1.794 1.767
21| 1.875 1.841 1.815 1.776 1.748
22| 1.859 1.825 1.798 1.759 1.731
23| 1.845 1.811 1.784 1.744 1.716
24| 1.832 1.797 1.770 1.730 1.702
25| 1.820 1.785 1.758 1.718 1.689
26| 1.809 1.774 1.747 1.706 1.677
27| 1.799 1.764 1.736 1.695 1.666
28| 1.790 1.754 1.726 1.685 1.656
29| 1.781 1.745 1.717 1.676 1.647
30| 1.773 1.737 1.709 1.667 1.638
40| 1.715 1.678 1.649 1.605 1.574
50| 1.680 1.643 1.613 1.568 1.536
60| 1.657 1.619 1.589 1.543 1.511
120| 1.601 1.562 1.530 1.482 1.447
inf| 1.552 1.511 1.478 1.428 1.391
==+=======================

F tails alpha=.10 (2/2)
v2 | 30 40 60 120 inf
==+=======================
1| 62.26 62.53 62.79 63.06 63.32
2| 9.458 9.466 9.475 9.483 9.491
3| 5.168 5.160 5.151 5.143 5.134
4| 3.817 3.804 3.790 3.775 3.761
5| 3.174 3.157 3.140 3.123 3.105
6| 2.800 2.781 2.762 2.742 2.722
7| 2.555 2.535 2.514 2.493 2.471
8| 2.383 2.361 2.339 2.316 2.293
9| 2.255 2.232 2.208 2.184 2.160
10| 2.155 2.132 2.107 2.082 2.056
11| 2.076 2.052 2.026 2.000 1.972
12| 2.011 1.986 1.960 1.932 1.904
13| 1.958 1.931 1.904 1.876 1.847
14| 1.912 1.885 1.857 1.828 1.798
15| 1.873 1.845 1.817 1.787 1.755
16| 1.839 1.811 1.782 1.751 1.719
17| 1.809 1.781 1.751 1.719 1.686
18| 1.783 1.754 1.723 1.691 1.657
19| 1.759 1.730 1.699 1.666 1.631
20| 1.738 1.708 1.677 1.643 1.608
21| 1.719 1.689 1.657 1.623 1.587
22| 1.702 1.671 1.639 1.604 1.567
23| 1.686 1.655 1.622 1.587 1.550
24| 1.672 1.641 1.607 1.571 1.533
25| 1.659 1.627 1.593 1.557 1.518
26| 1.647 1.615 1.581 1.544 1.504
27| 1.636 1.603 1.569 1.531 1.491
28| 1.625 1.592 1.558 1.520 1.479
29| 1.616 1.583 1.547 1.509 1.468
30| 1.606 1.573 1.538 1.499 1.457
40| 1.541 1.506 1.467 1.425 1.378
60| 1.476 1.437 1.395 1.348 1.292
120| 1.409 1.368 1.320 1.265 1.194
inf| 1.350 1.304 1.250 1.181 1.084
==+=======================

F tails alpha=.01 [1/2: v1=1(1)10]
v2 | 1 2 3 4 5
==+=======================
1| 4052 5000 5403 5625 5764
2| 98.50 99.00 99.17 99.25 99.30
3| 34.12 30.82 29.46 28.71 28.24
4| 21.20 18.00 16.69 15.98 15.52
5| 16.26 13.27 12.06 11.39 10.97
6| 13.75 10.92 9.780 9.148 8.746
7| 12.25 9.547 8.451 7.847 7.460
8| 11.26 8.649 7.591 7.006 6.632
9| 10.56 8.022 6.992 6.422 6.057
10| 10.04 7.559 6.552 5.994 5.636
11| 9.646 7.206 6.217 5.668 5.316
12| 9.330 6.927 5.953 5.412 5.064
13| 9.074 6.701 5.739 5.205 4.862
14| 8.862 6.515 5.564 5.035 4.695
15| 8.683 6.359 5.417 4.893 4.556
16| 8.531 6.226 5.292 4.773 4.437
17| 8.400 6.112 5.185 4.669 4.336
18| 8.285 6.013 5.092 4.579 4.248
19| 8.185 5.926 5.010 4.500 4.171
20| 8.096 5.849 4.938 4.431 4.103
21| 8.017 5.780 4.874 4.369 4.042
22| 7.945 5.719 4.817 4.313 3.988
23| 7.881 5.664 4.765 4.264 3.939
24| 7.823 5.614 4.718 4.218 3.895
25| 7.770 5.568 4.675 4.177 3.855
26| 7.721 5.526 4.637 4.140 3.818
27| 7.677 5.488 4.601 4.106 3.785
28| 7.636 5.453 4.568 4.074 3.754
29| 7.598 5.420 4.538 4.045 3.725
30| 7.562 5.390 4.510 4.018 3.699
40| 7.314 5.179 4.313 3.828 3.514
50| 7.171 5.057 4.199 3.720 3.408
60| 7.077 4.977 4.126 3.649 3.339
120| 6.851 4.787 3.949 3.480 3.174
inf| 6.660 4.626 3.801 3.338 3.036
==+=======================

F tails alpha=.01 [v1=6(1)10]
v2 | 6 7 8 9 10
==+=======================
1| 5859 5928 5981 6022 6056
2| 99.33 99.36 99.37 99.39 99.40
3| 27.91 27.67 27.49 27.35 27.23
4| 15.21 14.98 14.80 14.66 14.55
5| 10.67 10.46 10.29 10.16 10.05
6| 8.466 8.260 8.102 7.976 7.874
7| 7.191 6.993 6.840 6.719 6.620
8| 6.371 6.178 6.029 5.911 5.814
9| 5.802 5.613 5.467 5.351 5.257
10| 5.386 5.200 5.057 4.942 4.849
11| 5.069 4.886 4.744 4.632 4.539
12| 4.821 4.640 4.499 4.388 4.296
13| 4.620 4.441 4.302 4.191 4.100
14| 4.456 4.278 4.140 4.030 3.939
15| 4.318 4.142 4.004 3.895 3.805
16| 4.202 4.026 3.890 3.780 3.691
17| 4.102 3.927 3.791 3.682 3.593
18| 4.015 3.841 3.705 3.597 3.508
19| 3.939 3.765 3.631 3.523 3.434
20| 3.871 3.699 3.564 3.457 3.368
21| 3.812 3.640 3.506 3.398 3.310
22| 3.758 3.587 3.453 3.346 3.258
23| 3.710 3.539 3.406 3.299 3.211
24| 3.667 3.496 3.363 3.256 3.168
25| 3.627 3.457 3.324 3.217 3.129
26| 3.591 3.421 3.288 3.182 3.094
27| 3.558 3.388 3.256 3.149 3.062
28| 3.528 3.358 3.226 3.120 3.032
29| 3.499 3.330 3.198 3.092 3.005
30| 3.473 3.304 3.173 3.067 2.979
40| 3.291 3.124 2.993 2.888 2.801
50| 3.186 3.020 2.890 2.785 2.698
60| 3.119 2.953 2.823 2.718 2.632
120| 2.956 2.792 2.663 2.559 2.472
inf| 2.820 2.657 2.529 2.425 2.339
==+=======================

F tails alpha=.10 [1/2 : v1= 1, (1)10]
v2 | 1 2 3 4 5
==+=======================
1| 39.86 49.50 53.59 55.83 57.24
2| 8.526 9.000 9.162 9.243 9.293
3| 5.538 5.462 5.391 5.343 5.309
4| 4.545 4.325 4.191 4.107 4.051
5| 4.060 3.780 3.619 3.520 3.453
6| 3.776 3.463 3.289 3.181 3.108
7| 3.589 3.257 3.074 2.961 2.883
8| 3.458 3.113 2.924 2.806 2.726
9| 3.360 3.006 2.813 2.693 2.611
10| 3.285 2.924 2.728 2.605 2.522
11| 3.225 2.860 2.660 2.536 2.451
12| 3.177 2.807 2.606 2.480 2.394
13| 3.136 2.763 2.560 2.434 2.347
14| 3.102 2.726 2.522 2.395 2.307
15| 3.073 2.695 2.490 2.361 2.273
16| 3.048 2.668 2.462 2.333 2.244
17| 3.026 2.645 2.437 2.308 2.218
18| 3.007 2.624 2.416 2.286 2.196
19| 2.990 2.606 2.397 2.266 2.176
20| 2.975 2.589 2.380 2.249 2.158
21| 2.961 2.575 2.365 2.233 2.142
22| 2.949 2.561 2.351 2.219 2.128
23| 2.937 2.549 2.339 2.207 2.115
24| 2.927 2.538 2.327 2.195 2.103
25| 2.918 2.528 2.317 2.184 2.092
26| 2.909 2.519 2.307 2.174 2.082
27| 2.901 2.511 2.299 2.165 2.073
28| 2.894 2.503 2.291 2.157 2.064
29| 2.887 2.495 2.283 2.149 2.057
30| 2.881 2.489 2.276 2.142 2.049
40| 2.835 2.440 2.226 2.091 1.997
50| 2.809 2.412 2.197 2.061 1.966
60| 2.791 2.393 2.177 2.041 1.946
120| 2.748 2.347 2.130 1.992 1.896
inf| 2.711 2.308 2.089 1.950 1.853
==+=======================

F tails alpha=.10 v1=6,10
v2 | 6 7 8 9 10
==+=======================
1| 58.20 58.91 59.44 59.86 60.19
2| 9.326 9.349 9.367 9.381 9.392
3| 5.285 5.266 5.252 5.240 5.230
4| 4.010 3.979 3.955 3.936 3.920
5| 3.405 3.368 3.339 3.316 3.297
6| 3.055 3.014 2.983 2.958 2.937
7| 2.827 2.785 2.752 2.725 2.703
8| 2.668 2.624 2.589 2.561 2.538
9| 2.551 2.505 2.469 2.440 2.416
10| 2.461 2.414 2.377 2.347 2.323
11| 2.389 2.342 2.304 2.274 2.248
12| 2.331 2.283 2.245 2.214 2.188
13| 2.283 2.234 2.195 2.164 2.138
14| 2.243 2.193 2.154 2.122 2.095
15| 2.208 2.158 2.119 2.086 2.059
16| 2.178 2.128 2.088 2.055 2.028
17| 2.152 2.102 2.061 2.028 2.001
18| 2.130 2.079 2.038 2.005 1.977
19| 2.109 2.058 2.017 1.984 1.956
20| 2.091 2.040 1.999 1.965 1.937
21| 2.075 2.023 1.982 1.948 1.920
22| 2.060 2.008 1.967 1.933 1.904
23| 2.047 1.995 1.953 1.919 1.890
24| 2.035 1.983 1.941 1.906 1.877
25| 2.024 1.971 1.929 1.895 1.866
26| 2.014 1.961 1.919 1.884 1.855
27| 2.005 1.952 1.909 1.874 1.845
28| 1.996 1.943 1.900 1.865 1.836
29| 1.988 1.935 1.892 1.857 1.827
30| 1.980 1.927 1.884 1.849 1.819
40| 1.927 1.873 1.829 1.793 1.763
50| 1.895 1.840 1.796 1.760 1.729
60| 1.875 1.819 1.775 1.738 1.707
120| 1.824 1.767 1.722 1.684 1.652
inf| 1.780 1.723 1.676 1.638 1.605
==+=======================