APPENDIX A
STATISTICAL TABLES
- A.1 Area of the Unit Normal Distribution
- A.2 Quantiles of the Unit Normal Distribution
- A.3 Commonly Used Normal Quantiles
- A.4 Quantiles of the t Distribution
- A.5 Quantiles of the ChiSquare Distribution
- A.6 90Percentiles of the F(n, m) Distribution
- A.7 95Percentiles of the F(n, m) Distribution
- A.8 99Percentiles of the F(n, m) Distribution
- A.9 Quantiles of the KS Distribution
- A.10 Approximation Formulas for Statistical Tables
A.1 AREA OF THE UNIT NORMAL DISTRIBUTION
Table A.1 lists area between 0 and z. For example, the area between z = 0 and z = 1.03 is 0.3485. Due to symmetry of the normal distribution, the area between z = 0 and z = 1.03 is also the same.

TABLE A.1 Area or the Unit Normal Distribution
|
|
z
| 0.00
| 0.01
| 0.02
| 0.03
| 0.04
| 0.05
| 0.06
| 0.07
| 0.08
| 0.09
|
|
0.0
| 0.0000
| 0.0040
| 0.0080
| 0.0120
| 0.0160
| 0.0199
| 0.0239
| 0.0279
| 0.0319
| 0.0359
|
0.1
| 0.0398
| 0.0438
| 0.0478
| 0.0517
| 0.0557
| 0.0596
| 0.0636
| 0.0675
| 0.0714
| 0.0753
|
0.2
| 0.0793
| 0.0832
| 0.0871
| 0.0910
| 0.0948
| 0.0987
| 0.1026
| 0.1064
| 0.1103
| 0.1141
|
0.3
| 0.1179
| 0.1217
| 0.1255
| 0.1293
| 0.1331
| 0.1368
| 0.1406
| 0.1443
| 0.1480
| 0.1517
|
0.4
| 0.1554
| 0.1591
| 0.1628
| 0.1664
| 0.1700
| 0.1736
| 0.1772
| 0.1808
| 0.1844
| 0.1879
|
0.5
| 0.1915
| 0.1950
| 0.1985
| 0.2019
| 0.2054
| 0.2088
| 0.2123
| 0.2157
| 0.2190
| 0.2224
|
0.6
| 0.2257
| 0.2291
| 0.2324
| 0.2357
| 0.2389
| 0.2422
| 0.2454
| 0.2486
| 0.2517
| 0.2549
|
0.7
| 0.2580
| 0.2611
| 0.2642
| 0.2673
| 0.2703
| 0.2734
| 0.2764
| 0.2794
| 0.2823
| 0.2852
|
0.8
| 0.2881
| 0.2910
| 0.2939
| 0.2967
| 0.2995
| 0.3023
| 0.3051
| 0.3078
| 0.3106
| 0.3133
|
0.9
| 0.3159
| 0.3186
| 0.3212
| 0.3238
| 0.3264
| 0.3289
| 0.3315
| 0.3340
| 0.3365
| 0.3389
|
1.0
| 0.3413
| 0.3438
| 0.3461
| 0.3485
| 0.3508
| 0.3531
| 0.3554
| 0.3577
| 0.3599
| 0.3621
|
1.1
| 0.3643
| 0.3665
| 0.3686
| 0.3708
| 0.3729
| 0.3749
| 0.3770
| 0.3790
| 0.3810
| 0.3830
|
1.2
| 0.3849
| 0.3869
| 0.3888
| 0.3907
| 0.3925
| 0.3944
| 0.3962
| 0.3980
| 0.3997
| 0.4015
|
1.3
| 0.4032
| 0.4049
| 0.4066
| 0.4082
| 0.4099
| 0.4115
| 0.4131
| 0.4147
| 0.4162
| 0.4177
|
1.4
| 0.4192
| 0.4207
| 0.4222
| 0.4236
| 0.4251
| 0.4265
| 0.4279
| 0.4292
| 0.4306
| 0.4319
|
1.5
| 0.4332
| 0.4345
| 0.4357
| 0.4370
| 0.4382
| 0.4394
| 0.4406
| 0.4418
| 0.4429
| 0.4441
|
1.6
| 0.4452
| 0.4463
| 0.4474
| 0.4484
| 0.4495
| 0.4505
| 0.4515
| 0.4525
| 0.4535
| 0.4545
|
1.7
| 0.4554
| 0.4564
| 0.4573
| 0.4582
| 0.4591
| 0.4599
| 0.4608
| 0.4616
| 0.4625
| 0.4633
|
1.8
| 0.4641
| 0.4649
| 0.4656
| 0.4664
| 0.4671
| 0.4678
| 0.4686
| 0.4693
| 0.4699
| 0.4706
|
1.9
| 0.4713
| 0.4719
| 0.4726
| 0.4732
| 0.4738
| 0.4744
| 0.4750
| 0.4756
| 0.4761
| 0.4767
|
2.0
| 0.4772
| 0.4778
| 0.4783
| 0.4788
| 0.4793
| 0.4798
| 0.4803
| 0.4808
| 0.4812
| 0.4817
|
2.1
| 0.4821
| 0.4826
| 0.4830
| 0.4834
| 0.4838
| 0.4842
| 0.4846
| 0.4850
| 0.4854
| 0.4857
|
2.2
| 0.4861
| 0.4864
| 0.4868
| 0.4871
| 0.4875
| 0.4878
| 0.4881
| 0.4884
| 0.4887
| 0.4890
|
2.3
| 0.4893
| 0.4896
| 0.4898
| 0.4901
| 0.4904
| 0.4906
| 0.4909
| 0.4911
| 0.4913
| 0.4916
|
2.4
| 0.4918
| 0.4920
| 0.4922
| 0.4925
| 0.4927
| 0.4929
| 0.4931
| 0.4932
| 0.4934
| 0.4936
|
2.5
| 0.4938
| 0.4940
| 0.4941
| 0.4943
| 0.4945
| 0.4946
| 0.4948
| 0.4949
| 0.4951
| 0.4952
|
2.6
| 0.4953
| 0.4955
| 0.4956
| 0.4957
| 0.4959
| 0.4960
| 0.4961
| 0.4962
| 0.4963
| 0.4964
|
2.7
| 0.4965
| 0.4966
| 0.4967
| 0.4968
| 0.4969
| 0.4970
| 0.4971
| 0.4972
| 0.4973
| 0.4974
|
2.8
| 0.4974
| 0.4975
| 0.4976
| 0.4977
| 0.4977
| 0.4978
| 0.4979
| 0.4979
| 0.4980
| 0.4981
|
2.9
| 0.4981
| 0.4982
| 0.4982
| 0.4983
| 0.4984
| 0.4984
| 0.4985
| 0.4985
| 0.4986
| 0.4986
|
3.0
| 0.4987
| 0.4987
| 0.4987
| 0.4988
| 0.4988
| 0.4989
| 0.4989
| 0.4989
| 0.4990
| 0.4990
|
|
A.2 QUANTITIES OF THE UNIT NORMAL DISTRIBUTION
Table A.2 lists zp for a given p. For example, for a twosided confidence interval at 95%, α= 0.05 and p = 1 α/2 = 0.975. The entry in the row labeled 0.97 and column labeled 0.005 gives zp = 1.960.

TABLE A.2 Quantiles of the Unit Normal Distribution
|
|
p
| 0.00
| 0.01
| 0.02
| 0.03
| 0.04
| 0.05
| 0.06
| 0.07
| 0.08
| 0.09
|
|
0.5
| 0.000
| 0.025
| 0.050
| 0.075
| 0.100
| 0.126
| 0.151
| 0.176
| 0.202
| 0.228
|
0.6
| 0.253
| 0.279
| 0.305
| 0.332
| 0.358
| 0.385
| 0.412
| 0.440
| 0.468
| 0.496
|
0.7
| 0.524
| 0.553
| 0.583
| 0.613
| 0.643
| 0.674
| 0.706
| 0.739
| 0.772
| 0.806
|
0.8
| 0.842
| 0.878
| 0.915
| 0.954
| 0.994
| 1.036
| 1.080
| 1.126
| 1.175
| 1.227
|
|
|
p
| 0.000
| 0.001
| 0.002
| 0.003
| 0.004
| 0.005
| 0.006
| 0.007
| 0.008
| 0.009
|
|
0.90
| 1.282
| 1.287
| 1.293
| 1.299
| 1.305
| 1.311
| 1.317
| 1.323
| 1.329
| 1.335
|
0.91
| 1.341
| 1.347
| 1.353
| 1.359
| 1.366
| 1.372
| 1.379
| 1.385
| 1.392
| 1.398
|
0.92
| 1.405
| 1.412
| 1.419
| 1.426
| 1.433
| 1.440
| 1.447
| 1.454
| 1.461
| 1.468
|
0.93
| 1.476
| 1.483
| 1.491
| 1.499
| 1.506
| 1.514
| 1.522
| 1.530
| 1.538
| 1.546
|
0.94
| 1.555
| 1.563
| 1.572
| 1.580
| 1.589
| 1.598
| 1.607
| 1.616
| 1.626
| 1.635
|
0.95
| 1.645
| 1.655
| 1.665
| 1.675
| 1.685
| 1.695
| 1.706
| 1.717
| 1.728
| 1.739
|
0.96
| 1.751
| 1.762
| 1.774
| 1.787
| 1.799
| 1.812
| 1.825
| 1.838
| 1.852
| 1.866
|
0.97
| 1.881
| 1.896
| 1.911
| 1.927
| 1.943
| 1.960
| 1.977
| 1.995
| 2.014
| 2.034
|
0.98
| 2.054
| 2.075
| 2.097
| 2.120
| 2.144
| 2.170
| 2.197
| 2.226
| 2.257
| 2.290
|
|
|
p
| 0.0000
| 0.0001
| 0.0002
| 0.0003
| 0.0004
| 0.0005
| 0.0006
| 0.0007
| 0.0008
| 0.0009
|
|
0.990
| 2.326
| 2.330
| 2.334
| 2.338
| 2.342
| 2.346
| 2.349
| 2.353
| 2.357
| 2.362
|
0.991
| 2.366
| 2.370
| 2.374
| 2.378
| 2.382
| 2.387
| 2.391
| 2.395
| 2.400
| 2.404
|
0.992
| 2.409
| 2.414
| 2.418
| 2.423
| 2.428
| 2.432
| 2.437
| 2.442
| 2.447
| 2.452
|
0.993
| 2.457
| 2.462
| 2.468
| 2.473
| 2.478
| 2.484
| 2.489
| 2.495
| 2.501
| 2.506
|
0.994
| 2.512
| 2.518
| 2.524
| 2.530
| 2.536
| 2.543
| 2.549
| 2.556
| 2.562
| 2.569
|
0.995
| 2.576
| 2.583
| 2.590
| 2.597
| 2.605
| 2.612
| 2.620
| 2.628
| 2.636
| 2.644
|
0.996
| 2.652
| 2.661
| 2.669
| 2.678
| 2.687
| 2.697
| 2.706
| 2.716
| 2.727
| 2.737
|
0.997
| 2.748
| 2.759
| 2.770
| 2.782
| 2.794
| 2.807
| 2.820
| 2.834
| 2.848
| 2.863
|
0.998
| 2.878
| 2.894
| 2.911
| 2.929
| 2.948
| 2.968
| 2.989
| 3.011
| 3.036
| 3.062
|
0.999
| 3.090
| 3.121
| 3.156
| 3.195
| 3.239
| 3.291
| 3.353
| 3.432
| 3.540
| 3.719
|
|
See Table A.3 for commonly used values.
A.3 COMMONLY USED NORMAL QUANTILES
Table A.3 lists commonly used normal quantiles. The confidence levels listed in the first column are for a twosided confidence intervals. For example, for a twosided confidence interval at 99%, α= 0.01, α/2 = 0.005 and z0.995 = 2.576. For a onesided confidence interval at 99%, α= 0.01, and z1α = 2.326.
TABLE A.3 Commonly Used Normal Quantiles
|
|
Confidence Level (%)
| α
| α/2
| z1α/2
|
|
20
| 0.8
| 0.4
| 0.253
|
40
| 0.6
| 0.3
| 0.524
|
60
| 0.4
| 0.2
| 0.842
|
68.26
| 0.3174
| 0.1587
| 1.000
|
80
| 0.2
| 0.1
| 1.282
|
90
| 0.1
| 0.05
| 1.645
|
95
| 0.05
| 0.025
| 1.960
|
95.46
| 0.0454
| 0.0228
| 2.000
|
98
| 0.02
| 0.01
| 2.326
|
99
| 0.01
| 0.005
| 2.576
|
99.74
| 0.0026
| 0.0013
| 3.000
|
99.8
| 0.002
| 0.001
| 3.090
|
99.9
| 0.001
| 0.0005
| 3.29
|
99.98
| 0.0002
| 0.0001
| 3.72
|
|
A.4 QUANTILES OF THE t DISTRIBUTION
Table A.4 lists t[p;n]. For example, the t[0.95;13] required for a twosided 90% confidence interval of the mean of a sample of 14 observation is 1.771.

TABLE A.4 Quantiles of the t Distribution
|
|
| p
|
|
|
n
| 0.6000
| 0.7000
| 0.8000
| 0.9000
| 0.9500
| 0.9750
| 0.9950
| 0.9995
|
|
1
| 0.325
| 0.727
| 1.377
| 3.078
| 6.314
| 12.706
| 63.657
| 636.619
|
2
| 0.289
| 0.617
| 1.061
| 1.886
| 2.920
| 4.303
| 9.925
| 31.599
|
3
| 0.277
| 0.584
| 0.978
| 1.638
| 2.353
| 3.182
| 5.841
| 12.924
|
4
| 0.271
| 0.569
| 0.941
| 1.533
| 2.132
| 2.776
| 4.604
| 8.610
|
5
| 0.267
| 0.559
| 0.920
| 1.476
| 2.015
| 2.571
| 4.032
| 6.869
|
6
| 0.265
| 0.553
| 0.906
| 1.440
| 1.943
| 2.447
| 3.707
| 5.959
|
7
| 0.263
| 0.549
| 0.896
| 1.415
| 1.895
| 2.365
| 3.499
| 5.408
|
8
| 0.262
| 0.546
| 0.889
| 1.397
| 1.860
| 2.306
| 3.355
| 5.041
|
9
| 0.261
| 0.543
| 0.883
| 1.383
| 1.833
| 2.262
| 3.250
| 4.781
|
10
| 0.260
| 0.542
| 0.879
| 1.372
| 1.812
| 2.228
| 3.169
| 4.587
|
11
| 0.260
| 0.540
| 0.876
| 1.363
| 1.796
| 2.201
| 3.106
| 4.437
|
12
| 0.259
| 0.539
| 0.873
| 1.356
| 1.782
| 2.179
| 3.055
| 4.318
|
13
| 0.259
| 0.538
| 0.870
| 1.350
| 1.771
| 2.160
| 3.012
| 4.221
|
14
| 0.258
| 0.537
| 0.868
| 1.345
| 1.761
| 2.145
| 2.977
| 4.140
|
15
| 0.258
| 0.536
| 0.866
| 1.341
| 1.753
| 2.131
| 2.947
| 4.073
|
16
| 0.258
| 0.535
| 0.865
| 1.337
| 1.746
| 2.120
| 2.921
| 4.015
|
17
| 0.257
| 0.534
| 0.863
| 1.333
| 1.740
| 2.110
| 2.898
| 3.965
|
18
| 0.257
| 0.534
| 0.862
| 1.330
| 1.734
| 2.101
| 2.878
| 3.922
|
19
| 0.257
| 0.533
| 0.861
| 1.328
| 1.729
| 2.093
| 2.861
| 3.883
|
20
| 0.257
| 0.533
| 0.860
| 1.325
| 1.725
| 2.086
| 2.845
| 3.850
|
21
| 0.257
| 0.532
| 0.859
| 1.323
| 1.721
| 2.080
| 2.831
| 3.819
|
22
| 0.256
| 0.532
| 0.858
| 1.321
| 1.717
| 2.074
| 2.819
| 3.792
|
23
| 0.256
| 0.532
| 0.858
| 1.319
| 1.714
| 2.069
| 2.807
| 3.768
|
24
| 0.256
| 0.531
| 0.857
| 1.318
| 1.711
| 2.064
| 2.797
| 3.745
|
25
| 0.256
| 0.531
| 0.856
| 1.316
| 1.708
| 2.060
| 2.787
| 3.725
|
26
| 0.256
| 0.531
| 0.856
| 1.315
| 1.706
| 2.056
| 2.779
| 3.707
|
27
| 0.256
| 0.531
| 0.855
| 1.314
| 1.703
| 2.052
| 2.771
| 3.690
|
28
| 0.256
| 0.530
| 0.855
| 1.313
| 1.701
| 2.048
| 2.763
| 3.674
|
29
| 0.256
| 0.530
| 0.854
| 1.311
| 1.699
| 2.045
| 2.756
| 3.659
|
30
| 0.256
| 0.530
| 0.854
| 1.310
| 1.697
| 2.042
| 2.750
| 3.646
|
60
| 0.254
| 0.527
| 0.848
| 1.296
| 1.671
| 2.000
| 2.660
| 3.460
|
90
| 0.254
| 0.526
| 0.846
| 1.291
| 1.662
| 1.987
| 2.632
| 3.402
|
120
| 0.254
| 0.526
| 0.845
| 1.289
| 1.658
| 1.980
| 2.617
| 3.373
|
|
A.5 QUANTILES OF THE CHISQUARE DISTRIBUTION
Table A.5 lists X2[p;n]. For example, the X2[0.95;13] required for a chisquare test at 95% confidence using 14 cells is 22.362.

TABLE A.5 Quantiles of the ChiSquare Distribution
|
|
| p
|
|
|
n
| 0.005
| 0.010
| 0.050
| 0.100
| 0.200
| 0.500
| 0.800
| 0.900
| 0.950
| 0.990
| 0.995
|
|
1
| a | b | c | d | 0.064
| 0.455
| 1.642
| 2.706
| 3.841
| 6.635
| 7.879
|
2
| 0.010
| 0.020
| 0.103
| 0.211
| 0.446
| 1.386
| 3.219
| 4.605
| 5.991
| 9.210
| 10.596
|
3
| 0.072
| 0.115
| 0.352
| 0.585
| 1.005
| 2.366
| 4.642
| 6.253
| 7.817
| 11.356
| 12.861
|
4
| 0.207
| 0.297
| 0.711
| 1.064
| 1.649
| 3.357
| 5.989
| 7.779
| 9.488
| 13.277
| 14.861
|
5
| 0.412
| 0.554
| 1.145
| 1.610
| 2.343
| 4.351
| 7.289
| 9.236
| 11.071
| 15.086
| 16.750
|
6
| 0.676
| 0.872
| 1.635
| 2.204
| 3.070
| 5.348
| 8.558
| 10.645
| 12.592
| 16.812
| 18.548
|
7
| 0.989
| 1.239
| 2.167
| 2.833
| 3.822
| 6.346
| 9.803
| 12.017
| 14.067
| 18.475
| 20.278
|
8
| 1.344
| 1.646
| 2.733
| 3.490
| 4.594
| 7.344
| 11.030
| 13.362
| 15.507
| 20.090
| 21.955
|
9
| 1.735
| 2.088
| 3.325
| 4.168
| 5.380
| 8.343
| 12.242
| 14.684
| 16.919
| 21.666
| 23.589
|
10
| 2.156
| 2.558
| 3.940
| 4.865
| 6.179
| 9.342
| 13.442
| 15.987
| 18.307
| 23.209
| 25.188
|
11
| 2.603
| 3.053
| 4.575
| 5.578
| 6.989
| 10.341
| 14.631
| 17.275
| 19.675
| 24.725
| 26.757
|
12
| 3.074
| 3.571
| 5.226
| 6.304
| 7.807
| 11.340
| 15.812
| 18.549
| 21.026
| 26.217
| 28.300
|
13
| 3.565
| 4.107
| 5.892
| 7.041
| 8.634
| 12.340
| 16.985
| 19.812
| 22.362
| 27.688
| 29.820
|
14
| 4.075
| 4.660
| 6.571
| 7.790
| 9.467
| 13.339
| 18.151
| 21.064
| 23.685
| 29.141
| 31.319
|
15
| 4.601
| 5.229
| 7.261
| 8.547
| 10.307
| 14.339
| 19.311
| 22.307
| 24.996
| 30.578
| 32.801
|
16
| 5.142
| 5.812
| 7.962
| 9.312
| 11.152
| 15.339
| 20.465
| 23.542
| 26.296
| 32.000
| 34.267
|
17
| 5.697
| 6.408
| 8.672
| 10.085
| 12.002
| 16.338
| 21.615
| 24.769
| 27.587
| 33.409
| 35.719
|
18
| 6.265
| 7.015
| 9.390
| 10.865
| 12.857
| 17.338
| 22.760
| 25.989
| 28.869
| 34.805
| 37.156
|
19
| 6.844
| 7.633
| 10.117
| 11.651
| 13.716
| 18.338
| 23.900
| 27.204
| 30.144
| 36.191
| 38.582
|
20
| 7.434
| 8.260
| 10.851
| 12.443
| 14.578
| 19.337
| 25.038
| 28.412
| 31.410
| 37.566
| 39.997
|
21
| 8.034
| 8.897
| 11.591
| 13.240
| 15.445
| 20.337
| 26.171
| 29.615
| 32.671
| 38.932
| 41.401
|
22
| 8.643
| 9.542
| 12.338
| 14.041
| 16.314
| 21.337
| 27.301
| 30.813
| 33.924
| 40.289
| 42.796
|
23
| 9.260
| 10.196
| 13.090
| 14.848
| 17.186
| 22.337
| 28.429
| 32.007
| 35.172
| 41.638
| 44.181
|
24
| 9.886
| 10.856
| 13.848
| 15.659
| 18.062
| 23.337
| 29.553
| 33.196
| 36.415
| 42.980
| 45.559
|
25
| 10.520
| 11.524
| 14.611
| 16.473
| 18.940
| 24.337
| 30.675
| 34.382
| 37.653
| 44.314
| 46.928
|
26
| 11.160
| 12.198
| 15.379
| 17.292
| 19.820
| 25.336
| 31.795
| 35.563
| 38.885
| 45.642
| 48.290
|
27
| 11.808
| 12.878
| 16.151
| 18.114
| 20.703
| 26.336
| 32.912
| 36.741
| 40.113
| 46.963
| 49.645
|
28
| 12.461
| 13.565
| 16.928
| 18.939
| 21.588
| 27.336
| 34.027
| 37.916
| 41.337
| 48.278
| 50.993
|
29
| 13.121
| 14.256
| 17.708
| 19.768
| 22.475
| 28.336
| 35.139
| 39.088
| 42.557
| 49.588
| 52.336
|
30
| 13.787
| 14.953
| 18.493
| 20.599
| 23.364
| 29.336
| 36.250
| 40.256
| 43.773
| 50.892
| 53.672
|
31
| 14.458
| 15.655
| 19.281
| 21.434
| 24.255
| 30.336
| 37.359
| 41.422
| 44.985
| 52.191
| 55.003
|
32
| 15.134
| 16.362
| 20.072
| 22.271
| 25.148
| 31.336
| 38.466
| 42.585
| 46.194
| 53.486
| 56.328
|
33
| 15.815
| 17.073
| 20.866
| 23.110
| 26.042
| 32.336
| 39.572
| 43.745
| 47.400
| 54.776
| 57.649
|
34
| 16.501
| 17.789
| 21.664
| 23.952
| 26.938
| 33.336
| 40.676
| 44.903
| 48.602
| 56.061
| 58.964
|
35
| 17.192
| 18.509
| 22.465
| 24.797
| 27.836
| 34.336
| 41.778
| 46.059
| 49.802
| 57.342
| 60.275
|
36
| 17.887
| 19.233
| 23.269
| 25.643
| 28.735
| 35.336
| 42.879
| 47.212
| 50.998
| 58.619
| 61.581
|
37
| 18.586
| 19.960
| 24.075
| 26.492
| 29.635
| 36.336
| 43.978
| 48.363
| 52.192
| 59.893
| 62.883
|
38
| 19.289
| 20.691
| 24.884
| 27.343
| 30.537
| 37.335
| 45.076
| 49.513
| 53.384
| 61.162
| 64.181
|
39
| 19.996
| 21.426
| 25.695
| 28.196
| 31.440
| 38.335
| 46.173
| 50.660
| 54.572
| 62.428
| 65.476
|
40
| 20.706
| 22.164
| 26.509
| 29.050
| 32.345
| 39.335
| 47.269
| 51.805
| 55.759
| 63.691
| 66.766
|
|
a3.93 × 105
b1.57 × 104
c3.93 × 103
d1.58 × 102
A.6 90PERCENTILES OF THE F(n, m) DISTRIBUTION
Table A.6 lists F[0.90;n,m]. For example, the F[0.90;9,18] required for an Ftest at 90% confidence level is 2.00.

TABLE A.6 90Pereentiles of the F(n, m) Distribution
|
Numerator Degrees of Freedom n
|
|
|
m
| 1
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
| 10
|
|
1
| 39.86
| 49.50
| 53.59
| 55.83
| 57.24
| 58.20
| 58.90
| 59.44
| 59.86
| 60.19
|
2
| 8.53
| 9.00
| 9.16
| 9.24
| 9.29
| 9.33
| 9.35
| 9.37
| 9.38
| 9.39
|
3
| 5.54
| 5.46
| 5.39
| 5.34
| 5.31
| 5.28
| 5.27
| 5.25
| 5.24
| 5.23
|
4
| 4.54
| 4.32
| 4.19
| 4.11
| 4.05
| 4.01
| 3.98
| 3.95
| 3.94
| 3.92
|
5
| 4.06
| 3.78
| 3.62
| 3.52
| 3.45
| 3.40
| 3.37
| 3.34
| 3.32
| 3.30
|
6
| 3.78
| 3.46
| 3.29
| 3.18
| 3.11
| 3.05
| 3.01
| 2.98
| 2.96
| 2.94
|
7
| 3.59
| 3.26
| 3.07
| 2.96
| 2.88
| 2.83
| 2.78
| 2.75
| 2.72
| 2.70
|
8
| 3.46
| 3.11
| 2.92
| 2.81
| 2.73
| 2.67
| 2.62
| 2.59
| 2.56
| 2.54
|
9
| 3.36
| 3.01
| 2.81
| 2.69
| 2.61
| 2.55
| 2.51
| 2.47
| 2.44
| 2.42
|
10
| 3.29
| 2.92
| 2.73
| 2.61
| 2.52
| 2.46
| 2.41
| 2.38
| 2.35
| 2.32
|
12
| 3.18
| 2.81
| 2.61
| 2.48
| 2.39
| 2.33
| 2.28
| 2.24
| 2.21
| 2.19
|
14
| 3.10
| 2.73
| 2.52
| 2.39
| 2.31
| 2.24
| 2.19
| 2.15
| 2.12
| 2.10
|
16
| 3.05
| 2.67
| 2.46
| 2.33
| 2.24
| 2.18
| 2.13
| 2.09
| 2.06
| 2.03
|
18
| 3.01
| 2.62
| 2.42
| 2.29
| 2.20
| 2.13
| 2.08
| 2.04
| 2.00
| 1.98
|
20
| 2.97
| 2.59
| 2.38
| 2.25
| 2.16
| 2.09
| 2.04
| 2.00
| 1.96
| 1.94
|
25
| 2.92
| 2.53
| 2.32
| 2.18
| 2.09
| 2.02
| 1.97
| 1.93
| 1.89
| 1.87
|
30
| 2.88
| 2.49
| 2.28
| 2.14
| 2.05
| 1.98
| 1.93
| 1.88
| 1.85
| 1.82
|
35
| 2.85
| 2.46
| 2.25
| 2.11
| 2.02
| 1.95
| 1.90
| 1.85
| 1.82
| 1.79
|
40
| 2.84
| 2.44
| 2.23
| 2.09
| 2.00
| 1.93
| 1.87
| 1.83
| 1.79
| 1.76
|
500
| 2.72
| 2.31
| 2.09
| 1.96
| 1.86
| 1.79
| 1.73
| 1.68
| 1.64
| 1.61
|
|
|
Numerator Degrees of Freedom n
|
|
|
m
| 12
| 14
| 16
| 18
| 20
| 25
| 30
| 35
| 40
| 500
|
|
1
| 60.70
| 61.07
| 61.35
| 61.56
| 61.74
| 62.05
| 62.26
| 62.41
| 62.53
| 63.26
|
2
| 9.41
| 9.42
| 9.43
| 9.44
| 9.44
| 9.45
| 9.46
| 9.46
| 9.47
| 9.49
|
3
| 5.22
| 5.20
| 5.20
| 5.19
| 5.18
| 5.17
| 5.17
| 5.16
| 5.16
| 5.13
|
4
| 3.90
| 3.88
| 3.86
| 3.85
| 3.84
| 3.83
| 3.82
| 3.81
| 3.80
| 3.76
|
5
| 3.27
| 3.25
| 3.23
| 3.22
| 3.21
| 3.19
| 3.17
| 3.16
| 3.16
| 3.10
|
6
| 2.90
| 2.88
| 2.86
| 2.85
| 2.84
| 2.81
| 2.80
| 2.79
| 2.78
| 2.72
|
7
| 2.67
| 2.64
| 2.62
| 2.61
| 2.59
| 2.57
| 2.56
| 2.54
| 2.54
| 2.47
|
8
| 2.50
| 2.48
| 2.45
| 2.44
| 2.42
| 2.40
| 2.38
| 2.37
| 2.36
| 2.29
|
9
| 2.38
| 2.35
| 2.33
| 2.31
| 2.30
| 2.27
| 2.25
| 2.24
| 2.23
| 2.16
|
10
| 2.28
| 2.26
| 2.23
| 2.22
| 2.20
| 2.17
| 2.16
| 2.14
| 2.13
| 2.06
|
12
| 2.15
| 2.12
| 2.09
| 2.08
| 2.06
| 2.03
| 2.01
| 2.00
| 1.99
| 1.90
|
14
| 2.05
| 2.02
| 2.00
| 1.98
| 1.96
| 1.93
| 1.91
| 1.90
| 1.89
| 1.80
|
16
| 1.99
| 1.95
| 1.93
| 1.91
| 1.89
| 1.86
| 1.84
| 1.82
| 1.81
| 1.72
|
18
| 1.93
| 1.90
| 1.87
| 1.85
| 1.84
| 1.80
| 1.78
| 1.77
| 1.75
| 1.66
|
20
| 1.89
| 1.86
| 1.83
| 1.81
| 1.79
| 1.76
| 1.74
| 1.72
| 1.71
| 1.61
|
25
| 1.82
| 1.79
| 1.76
| 1.74
| 1.72
| 1.68
| 1.66
| 1.64
| 1.63
| 1.52
|
30
| 1.77
| 1.74
| 1.71
| 1.69
| 1.67
| 1.63
| 1.61
| 1.59
| 1.57
| 1.46
|
35
| 1.74
| 1.70
| 1.67
| 1.65
| 1.63
| 1.60
| 1.57
| 1.55
| 1.53
| 1.41
|
40
| 1.71
| 1.68
| 1.65
| 1.62
| 1.61
| 1.57
| 1.54
| 1.52
| 1.51
| 1.38
|
500
| 1.56
| 1.52
| 1.49
| 1.46
| 1.44
| 1.39
| 1.36
| 1.33
| 1.31
| 2.16
|
|
A.7 95PERCENTILES OF THE F(n, m) DISTRIBUTION
Table A.7 lists F[0.95;n,m]. For example, the F[0.95;9,14] required for an Ftest at 95% confidence level is 2.70.

TABLE A.7 95Percentiles or the F(n, m) Distribution
|
|
| Numerator Degrees of Freedom n
|
|
|
m
| 1
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
| 10
|
|
1
| 161.45
| 199.50
| 215.70
| 224.57
| 230.15
| 233.97
| 236.76
| 238.87
| 240.53
| 241.87
|
2
| 18.51
| 19.00
| 19.16
| 19.25
| 19.30
| 19.33
| 19.35
| 19.37
| 19.38
| 19.40
|
3
| 10.13
| 9.55
| 9.28
| 9.12
| 9.01
| 8.94
| 8.89
| 8.85
| 8.81
| 8.79
|
4
| 7.71
| 6.94
| 6.59
| 6.39
| 6.26
| 6.16
| 6.09
| 6.04
| 6.00
| 5.96
|
5
| 6.61
| 5.79
| 5.41
| 5.19
| 5.05
| 4.95
| 4.88
| 4.82
| 4.77
| 4.74
|
6
| 5.99
| 5.14
| 4.76
| 4.53
| 4.39
| 4.28
| 4.21
| 4.15
| 4.10
| 4.06
|
7
| 5.59
| 4.74
| 4.35
| 4.12
| 3.97
| 3.87
| 3.79
| 3.73
| 3.68
| 3.64
|
8
| 5.32
| 4.46
| 4.07
| 3.84
| 3.69
| 3.58
| 3.50
| 3.44
| 3.39
| 3.35
|
9
| 5.12
| 4.26
| 3.86
| 3.63
| 3.48
| 3.37
| 3.29
| 3.23
| 3.18
| 3.14
|
10
| 4.96
| 4.10
| 3.71
| 3.48
| 3.33
| 3.22
| 3.14
| 3.07
| 3.02
| 2.98
|
12
| 4.75
| 3.89
| 3.49
| 3.26
| 3.11
| 3.00
| 2.91
| 2.85
| 2.80
| 2.75
|
14
| 4.60
| 3.74
| 3.34
| 3.11
| 2.96
| 2.85
| 2.76
| 2.70
| 2.65
| 2.60
|
16
| 4.49
| 3.63
| 3.24
| 3.01
| 2.85
| 2.74
| 2.66
| 2.59
| 2.54
| 2.49
|
18
| 4.41
| 3.55
| 3.16
| 2.93
| 2.77
| 2.66
| 2.58
| 2.51
| 2.46
| 2.41
|
20
| 4.35
| 3.49
| 3.10
| 2.87
| 2.71
| 2.60
| 2.51
| 2.45
| 2.39
| 2.35
|
25
| 4.24
| 3.39
| 2.99
| 2.76
| 2.60
| 2.49
| 2.40
| 2.34
| 2.28
| 2.24
|
30
| 4.17
| 3.32
| 2.92
| 2.69
| 2.53
| 2.42
| 2.33
| 2.27
| 2.21
| 2.16
|
35
| 4.12
| 3.27
| 2.87
| 2.64
| 2.49
| 2.37
| 2.29
| 2.22
| 2.16
| 2.11
|
40
| 4.08
| 3.23
| 2.84
| 2.61
| 2.45
| 2.34
| 2.25
| 2.18
| 2.12
| 2.08
|
500
| 3.86
| 3.01
| 2.62
| 2.39
| 2.23
| 2.12
| 2.03
| 1.96
| 1.90
| 1.85
|
|
| Numerator Degrees of Freedom n
|
|
|
m
| 12
| 14
| 16
| 18
| 20
| 25
| 30
| 35
| 40
| 500
|
|
1
| 243.90
| 245.35
| 246.45
| 247.31
| 248.00
| 249.25
| 250.09
| 250.68
| 251.13
| 254.05
|
2
| 19.41
| 19.42
| 19.43
| 19.44
| 19.45
| 19.46
| 19.46
| 19.47
| 19.47
| 19.49
|
3
| 8.74
| 8.71
| 8.69
| 8.67
| 8.66
| 8.63
| 8.62
| 8.60
| 8.59
| 8.53
|
4
| 5.91
| 5.87
| 5.84
| 5.82
| 5.80
| 5.77
| 5.75
| 5.73
| 5.72
| 5.63
|
5
| 4.68
| 4.64
| 4.60
| 4.58
| 4.56
| 4.52
| 4.50
| 4.48
| 4.46
| 4.36
|
6
| 4.00
| 3.96
| 3.92
| 3.90
| 3.87
| 3.83
| 3.81
| 3.79
| 3.77
| 3.67
|
7
| 3.57
| 3.53
| 3.49
| 3.47
| 3.44
| 3.40
| 3.38
| 3.36
| 3.34
| 3.23
|
8
| 3.28
| 3.24
| 3.20
| 3.17
| 3.15
| 3.11
| 3.08
| 3.06
| 3.04
| 2.93
|
9
| 3.07
| 3.03
| 2.99
| 2.96
| 2.94
| 2.89
| 2.86
| 2.84
| 2.83
| 2.71
|
10
| 2.91
| 2.86
| 2.83
| 2.80
| 2.77
| 2.73
| 2.70
| 2.68
| 2.66
| 2.54
|
12
| 2.69
| 2.64
| 2.60
| 2.57
| 2.54
| 2.50
| 2.47
| 2.44
| 2.43
| 2.30
|
14
| 2.53
| 2.48
| 2.44
| 2.41
| 2.39
| 2.34
| 2.31
| 2.28
| 2.27
| 2.13
|
16
| 2.42
| 2.37
| 2.33
| 2.30
| 2.28
| 2.23
| 2.19
| 2.17
| 2.15
| 2.01
|
18
| 2.34
| 2.29
| 2.25
| 2.22
| 2.19
| 2.14
| 2.11
| 2.08
| 2.06
| 1.92
|
20
| 2.28
| 2.22
| 2.18
| 2.15
| 2.12
| 2.07
| 2.04
| 2.01
| 1.99
| 1.84
|
25
| 2.16
| 2.11
| 2.07
| 2.04
| 2.01
| 1.96
| 1.92
| 1.89
| 1.87
| 1.71
|
30
| 2.09
| 2.04
| 1.99
| 1.96
| 1.93
| 1.88
| 1.84
| 1.81
| 1.79
| 1.62
|
35
| 2.04
| 1.99
| 1.94
| 1.91
| 1.88
| 1.82
| 1.79
| 1.76
| 1.74
| 1.56
|
40
| 2.00
| 1.95
| 1.90
| 1.87
| 1.84
| 1.78
| 1.74
| 1.72
| 1.69
| 1.51
|
500
| 1.77
| 1.71
| 1.66
| 1.62
| 1.59
| 1.53
| 1.48
| 1.45
| 1.42
| 2.21
|
|
A.8 99PERCENTILES OF THE F(n, m) DISTRIBUTION
Table A.8 lists F[0.99;n,m]. For example, the F[0.99;6,12] required for an Ftest at 99% confidence level is 4.82.

TABLE A.8 99Percentiles or the F(n, m) Distribution
|
|
| Numerator Degrees of Freedom n
|
|
|
m
| 1
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
| 10
|
|
1
| 4052.18
| 4999.50
| 5403.05
| 5624.30
| 5763.37
| 5858.71
| 5928.09
| 5980.80
| 6022.21
| 6055.58
|
2
| 98.50
| 99.00
| 99.17
| 99.25
| 99.30
| 99.33
| 99.36
| 99.37
| 99.39
| 99.40
|
3
| 34.12
| 30.82
| 29.46
| 28.71
| 28.24
| 27.91
| 27.67
| 27.49
| 27.34
| 27.23
|
4
| 21.20
| 18.00
| 16.69
| 15.98
| 15.52
| 15.21
| 14.98
| 14.80
| 14.66
| 14.55
|
5
| 16.26
| 13.27
| 12.06
| 11.39
| 10.97
| 10.67
| 10.46
| 10.29
| 10.16
| 10.05
|
6
| 13.75
| 10.92
| 9.78
| 9.15
| 8.75
| 8.47
| 8.26
| 8.10
| 7.98
| 7.87
|
7
| 12.25
| 9.55
| 8.45
| 7.85
| 7.46
| 7.19
| 6.99
| 6.84
| 6.72
| 6.62
|
8
| 11.26
| 8.65
| 7.59
| 7.01
| 6.63
| 6.37
| 6.18
| 6.03
| 5.91
| 5.81
|
9
| 10.56
| 8.02
| 6.99
| 6.42
| 6.06
| 5.80
| 5.61
| 5.47
| 5.35
| 5.26
|
10
| 10.04
| 7.56
| 6.55
| 5.99
| 5.64
| 5.39
| 5.20
| 5.06
| 4.94
| 4.85
|
12
| 9.33
| 6.93
| 5.95
| 5.41
| 5.06
| 4.82
| 4.64
| 4.50
| 4.39
| 4.30
|
14
| 8.86
| 6.51
| 5.56
| 5.04
| 4.69
| 4.46
| 4.28
| 4.14
| 4.03
| 3.94
|
16
| 8.53
| 6.23
| 5.29
| 4.77
| 4.44
| 4.20
| 4.03
| 3.89
| 3.78
| 3.69
|
18
| 8.29
| 6.01
| 5.09
| 4.58
| 4.25
| 4.01
| 3.84
| 3.71
| 3.60
| 3.51
|
20
| 8.10
| 5.85
| 4.94
| 4.43
| 4.10
| 3.87
| 3.70
| 3.56
| 3.46
| 3.37
|
25
| 7.77
| 5.57
| 4.68
| 4.18
| 3.85
| 3.63
| 3.46
| 3.32
| 3.22
| 3.13
|
30
| 7.56
| 5.39
| 4.51
| 4.02
| 3.70
| 3.47
| 3.30
| 3.17
| 3.07
| 2.98
|
35
| 7.42
| 5.27
| 4.40
| 3.91
| 3.59
| 3.37
| 3.20
| 3.07
| 2.96
| 2.88
|
40
| 7.31
| 5.18
| 4.31
| 3.83
| 3.51
| 3.29
| 3.12
| 2.99
| 2.89
| 2.80
|
500
| 6.69
| 4.65
| 3.82
| 3.36
| 3.05
| 2.84
| 2.68
| 2.55
| 2.44
| 2.36
|
|
| Numerator Degrees of Freedom n
|
|
|
m
| 12
| 14
| 16
| 18
| 20
| 25
| 30
| 35
| 40
| 500
|
|
1
| 6106.06
| 6142.42
| 6169.85
| 6191.28
| 6208.48
| 6239.57
| 6260.40
| 6275.32
| 6286.53
| 6359.26
|
2
| 99.42
| 99.43
| 99.44
| 99.44
| 99.45
| 99.46
| 99.47
| 99.47
| 99.47
| 99.50
|
3
| 27.05
| 26.92
| 26.83
| 26.75
| 26.69
| 26.58
| 26.50
| 26.45
| 26.41
| 26.12
|
4
| 14.37
| 14.25
| 14.15
| 14.08
| 14.02
| 13.91
| 13.84
| 13.79
| 13.75
| 13.46
|
5
| 9.89
| 9.77
| 9.68
| 9.61
| 9.55
| 9.45
| 9.38
| 9.33
| 9.29
| 9.02
|
6
| 7.72
| 7.60
| 7.52
| 7.45
| 7.40
| 7.30
| 7.23
| 7.18
| 7.14
| 6.88
|
7
| 6.47
| 6.36
| 6.28
| 6.21
| 6.16
| 6.06
| 5.99
| 5.94
| 5.91
| 5.65
|
8
| 5.67
| 5.56
| 5.48
| 5.41
| 5.36
| 5.26
| 5.20
| 5.15
| 5.12
| 4.86
|
9
| 5.11
| 5.01
| 4.92
| 4.86
| 4.81
| 4.71
| 4.65
| 4.60
| 4.57
| 4.31
|
10
| 4.71
| 4.60
| 4.52
| 4.46
| 4.41
| 4.31
| 4.25
| 4.20
| 4.17
| 3.91
|
12
| 4.16
| 4.05
| 3.97
| 3.91
| 3.86
| 3.76
| 3.70
| 3.65
| 3.62
| 3.36
|
14
| 3.80
| 3.70
| 3.62
| 3.56
| 3.51
| 3.41
| 3.35
| 3.30
| 3.27
| 3.00
|
16
| 3.55
| 3.45
| 3.37
| 3.31
| 3.26
| 3.16
| 3.10
| 3.05
| 3.02
| 2.75
|
18
| 3.37
| 3.27
| 3.19
| 3.13
| 3.08
| 2.98
| 2.92
| 2.87
| 2.84
| 2.57
|
20
| 3.23
| 3.13
| 3.05
| 2.99
| 2.94
| 2.84
| 2.78
| 2.73
| 2.69
| 2.42
|
25
| 2.99
| 2.89
| 2.81
| 2.75
| 2.70
| 2.60
| 2.54
| 2.49
| 2.45
| 2.17
|
30
| 2.84
| 2.74
| 2.66
| 2.60
| 2.55
| 2.45
| 2.39
| 2.34
| 2.30
| 2.01
|
35
| 2.74
| 2.64
| 2.56
| 2.50
| 2.44
| 2.35
| 2.28
| 2.23
| 2.19
| 1.89
|
40
| 2.66
| 2.56
| 2.48
| 2.42
| 2.37
| 2.27
| 2.20
| 2.15
| 2.11
| 1.80
|
500
| 2.22
| 2.12
| 2.04
| 1.97
| 1.92
| 1.81
| 1.74
| 1.68
| 1.63
| 2.30
|
|
A.9 QUANTILES OF THE KS DISTRIBUTION
Table A.9 lists quantiles K[p;n] of the KS distribution. For example, the K[0.99;12] required for a KS test at 99% confidence level is 1.4521.
TABLE A.9 Quantiles of the KS Distribution
|
|
| p
|
|
|
n
| 0.00
| 0.01
| 0.05
| 0.10
| 0.20
| 0.50
| 0.80
| 0.90
| 0.95
| 0.99
| 0.995
|
|
1
| 0.0050
| 0.0100
| 0.0500
| 0.1000
| 0.2000
| 0.5000
| 0.8000
| 0.9000
| 0.9500
| 0.9900
| 0.9950
|
2
| 0.0067
| 0.0135
| 0.0673
| 0.1296
| 0.2416
| 0.5176
| 0.7818
| 0.9670
| 1.0980
| 1.2728
| 1.3142
|
3
| 0.0081
| 0.0162
| 0.0792
| 0.1471
| 0.2615
| 0.5147
| 0.8187
| 0.9783
| 1.1017
| 1.3589
| 1.4359
|
4
| 0.0093
| 0.0186
| 0.0879
| 0.1590
| 0.2726
| 0.5110
| 0.8248
| 0.9853
| 1.1304
| 1.3777
| 1.4685
|
5
| 0.0103
| 0.0207
| 0.0947
| 0.1675
| 0.2793
| 0.5245
| 0.8277
| 0.9995
| 1.1392
| 1.4024
| 1.4949
|
6
| 0.0113
| 0.0226
| 0.1002
| 0.1739
| 0.2834
| 0.5319
| 0.8343
| 1.0052
| 1.1463
| 1.4144
| 1.5104
|
7
| 0.0121
| 0.0243
| 0.1048
| 0.1787
| 0.2859
| 0.5364
| 0.8398
| 1.0093
| 1.1537
| 1.4246
| 1.5235
|
8
| 0.0130
| 0.0259
| 0.1086
| 0.1826
| 0.2874
| 0.5392
| 0.8431
| 1.0135
| 1.1586
| 1.4327
| 1.5324
|
9
| 0.0137
| 0.0275
| 0.1119
| 0.1856
| 0.2881
| 0.5411
| 0.8455
| 1.0173
| 1.1624
| 1.4388
| 1.5400
|
10
| 0.0145
| 0.0289
| 0.1147
| 0.1880
| 0.2884
| 0.5426
| 0.8477
| 1.0202
| 1.1658
| 1.4440
| 1.5461
|
11
| 0.0151
| 0.0303
| 0.1172
| 0.1900
| 0.2883
| 0.5439
| 0.8498
| 1.0225
| 1.1688
| 1.4484
| 1.5512
|
12
| 0.0158
| 0.0314
| 0.1193
| 0.1916
| 0.2879
| 0.5453
| 0.8519
| 1.0246
| 1.1714
| 1.4521
| 1.5555
|
13
| 0.0164
| 0.0324
| 0.1212
| 0.1929
| 0.2903
| 0.5468
| 0.8537
| 1.0265
| 1.1736
| 1.4553
| 1.5593
|
14
| 0.0171
| 0.0333
| 0.1229
| 0.1940
| 0.2925
| 0.5486
| 0.8551
| 1.0282
| 1.1755
| 1.4581
| 1.5626
|
15
| 0.0176
| 0.0342
| 0.1244
| 0.1948
| 0.2944
| 0.5500
| 0.8564
| 1.0298
| 1.1773
| 1.4606
| 1.5655
|
16
| 0.0182
| 0.0351
| 0.1257
| 0.1955
| 0.2961
| 0.5512
| 0.8576
| 1.0311
| 1.1789
| 1.4629
| 1.5681
|
17
| 0.0188
| 0.0359
| 0.1269
| 0.1961
| 0.2975
| 0.5523
| 0.8587
| 1.0324
| 1.1803
| 1.4649
| 1.5704
|
18
| 0.0193
| 0.0367
| 0.1280
| 0.1965
| 0.2987
| 0.5532
| 0.8597
| 1.0335
| 1.1816
| 1.4667
| 1.5725
|
19
| 0.0198
| 0.0374
| 0.1290
| 0.1968
| 0.2998
| 0.5540
| 0.8607
| 1.0346
| 1.1828
| 1.4683
| 1.5744
|
20
| 0.0203
| 0.0381
| 0.1298
| 0.1971
| 0.3007
| 0.5547
| 0.8616
| 1.0355
| 1.1839
| 1.4699
| 1.5761
|
21
| 0.0208
| 0.0387
| 0.1306
| 0.1973
| 0.3015
| 0.5554
| 0.8624
| 1.0365
| 1.1850
| 1.4712
| 1.5777
|
22
| 0.0213
| 0.0394
| 0.1313
| 0.1974
| 0.3023
| 0.5561
| 0.8631
| 1.0373
| 1.1859
| 1.4725
| 1.5792
|
23
| 0.0217
| 0.0400
| 0.1320
| 0.1974
| 0.3030
| 0.5567
| 0.8639
| 1.0381
| 1.1868
| 1.4737
| 1.5806
|
24
| 0.0221
| 0.0405
| 0.1326
| 0.1974
| 0.3035
| 0.5573
| 0.8645
| 1.0388
| 1.1876
| 1.4748
| 1.5816
|
25
| 0.0225
| 0.0411
| 0.1331
| 0.1974
| 0.3041
| 0.5579
| 0.8651
| 1.0395
| 1.1884
| 1.4758
| 1.5829
|
26
| 0.0228
| 0.0416
| 0.1336
| 0.1977
| 0.3046
| 0.5585
| 0.8657
| 1.0402
| 1.1891
| 1.4768
| 1.5840
|
27
| 0.0231
| 0.0421
| 0.1340
| 0.1985
| 0.3050
| 0.5590
| 0.8663
| 1.0408
| 1.1898
| 1.4777
| 1.5850
|
28
| 0.0235
| 0.0426
| 0.1344
| 0.1992
| 0.3054
| 0.5595
| 0.8668
| 1.0414
| 1.1905
| 1.4786
| 1.5860
|
29
| 0.0238
| 0.0431
| 0.1348
| 0.2000
| 0.3058
| 0.5600
| 0.8673
| 1.0419
| 1.1911
| 1.4794
| 1.5969
|
30
| 0.0241
| 0.0435
| 0.1351
| 0.2006
| 0.3062
| 0.5605
| 0.8678
| 1.0424
| 1.1916
| 1.4801
| 1.5878
|
|
A.10 APPROXIMATION FORMULAS FOR STATISTICAL TABLES
In computer programs, the following approximate formulas may be used in place of statistical tables:
- 1. Area Under the Normal Distribution: The area under the unit normal pdf between 0 and z is given approximately by (Hastings, Jr. (1955)):
p = ½ - ½(1+0.196854z + 0.115194z2 + 0.000344z3 + 0.019527z4)-4
Given zκ, this formula can be used to find κ (κ = 0.5 + p).
- 2. Unit Normal Quantiles: The unit normal quantile zp for a given p can be calculated approximately by the following formula (Hastings, Jr. (1955)):

where

A simpler but more approximate formula is
Zp = 4.91[p0.14 (1 p)0.14]
- 3. ChiSquare Quantiles: For large degrees of freedom, the X2(v) quantiles can be calculated approximately from the unit normal quantiles zκ as follows:

Given a X2κ value, this formula can also be used to compute zκ and hence the significance κ.
- 4. FQuantiles: For large degrees of freedoms, the following approximation can be used to compute Fκ from zκ:

Again, given an Fκ value, this formula can also be used to to compute zκ and hence the significance κ.