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Appendix Tables
663
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Appendix Tables
Table A.1
x
Cumulative Binomial Probabilities
B(x; n, p) b(y; n, p)
a. n 5
y0
p
x
0
1
2
3
4
0.01
0.05
0.10
0.20
0.25
0.30
0.40
0.50
0.60
0.70
0.75
0.80
0.90
0.95
0.99
.951
.999
1.000
1.000
1.000
.774
.977
.999
1.000
1.000
.590
.919
.991
1.000
1.000
.328
.737
.942
.993
1.000
.237
.633
.896
.984
.999
.168
.528
.837
.969
.998
.078
.337
.683
.913
.990
.031
.188
.500
.812
.969
.010
.087
.317
.663
.922
.002
.031
.163
.472
.832
.001
.016
.104
.367
.763
.000
.007
.058
.263
.672
.000
.000
.009
.081
.410
.000
.000
.001
.023
.226
.000
.000
.000
.001
.049
b. n 10
p
x
0.01
0.05
0.10
0.20
0.25
0.30
0.40
0.50
0.60
0.70
0.75
0.80
0.90
0.95
0.99
0
1
2
3
4
.904
.996
1.000
1.000
1.000
.599
.914
.988
.999
1.000
.349
.736
.930
.987
.998
.107
.376
.678
.879
.967
.056
.244
.526
.776
.922
.028
.149
.383
.650
.850
.006
.046
.167
.382
.633
.001
.011
.055
.172
.377
.000
.002
.012
.055
.166
.000
.000
.002
.011
.047
.000
.000
.000
.004
.020
.000
.000
.000
.001
.006
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
5
6
7
8
9
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.994
.999
1.000
1.000
1.000
.980
.996
1.000
1.000
1.000
.953
.989
.998
1.000
1.000
.834
.945
.988
.998
1.000
.623
.828
.945
.989
.999
.367
.618
.833
.954
.994
.150
.350
.617
.851
.972
.078
.224
.474
.756
.944
.033
.121
.322
.624
.893
.002
.013
.070
.264
.651
.000
.001
.012
.086
.401
.000
.000
.000
.004
.096
c. n 15
p
x
0.01
0.05
0.10
0.20
0.25
0.30
0.40
0.50
0.60
0.70
0.75
0.80
0.90
0.95
0.99
0
1
2
3
4
.860
.990
1.000
1.000
1.000
.463
.829
.964
.995
.999
.206
.549
.816
.944
.987
.035
.167
.398
.648
.836
.013
.080
.236
.461
.686
.005
.035
.127
.297
.515
.000
.005
.027
.091
.217
.000
.000
.004
.018
.059
.000
.000
.000
.002
.009
.000
.000
.000
.000
.001
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
5
6
7
8
9
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.998
1.000
1.000
1.000
1.000
.939
.982
.996
.999
1.000
.852
.943
.983
.996
.999
.722
.869
.950
.985
.996
.402
.610
.787
.905
.966
.151
.304
.500
.696
.849
.034
.095
.213
.390
.597
.004
.015
.050
.131
.278
.001
.004
.017
.057
.148
.000
.001
.004
.018
.061
.000
.000
.000
.000
.002
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
10
11
12
13
14
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.999
1.000
1.000
1.000
1.000
.991
.998
1.000
1.000
1.000
.941
.982
.996
1.000
1.000
.783
.909
.973
.995
1.000
.485
.703
.873
.965
.995
.314
.539
.764
.920
.987
.164
.352
.602
.833
.965
.013
.056
.184
.451
.794
.001
.005
.036
.171
.537
.000
.000
.000
.010
.140
(continued )
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Appendix Tables
Table A.1
665
x
Cumulative Binomial Probabilities (cont.)
B(x; n, p) b(y; n, p)
d. n 20
y0
p
x
0.01
0.05
0.10
0.20
0.25
0.30
0.40
0.50
0.60
0.70
0.75
0.80
0.90
0.95
0.99
0
1
2
3
4
.818
.983
.999
1.000
1.000
.358
.736
.925
.984
.997
.122
.392
.677
.867
.957
.012
.069
.206
.411
.630
.003
.024
.091
.225
.415
.001
.008
.035
.107
.238
.000
.001
.004
.016
.051
.000
.000
.000
.001
.006
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
5
6
7
8
9
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.989
.998
1.000
1.000
1.000
.804
.913
.968
.990
.997
.617
.786
.898
.959
.986
.416
.608
.772
.887
.952
.126
.250
.416
.596
.755
.021
.058
.132
.252
.412
.002
.006
.021
.057
.128
.000
.000
.001
.005
.017
.000
.000
.000
.001
.004
.000
.000
.000
.000
.001
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
10
11
12
13
14
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.999
1.000
1.000
1.000
1.000
.996
.999
1.000
1.000
1.000
.983
.995
.999
1.000
1.000
.872
.943
.979
.994
.998
.588
.748
.868
.942
.979
.245
.404
.584
.750
.874
.048
.113
.228
.392
.584
.014
.041
.102
.214
.383
.003
.010
.032
.087
.196
.000
.000
.000
.002
.011
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
15
16
17
18
19
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.994
.999
1.000
1.000
1.000
.949
.984
.996
.999
1.000
.762
.893
.965
.992
.999
.585
.775
.909
.976
.997
.370
.589
.794
.931
.988
.043
.133
.323
.608
.878
.003
.016
.075
.264
.642
.000
.000
.001
.017
.182
(continued )
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Appendix Tables
Table A.1
x
Cumulative Binomial Probabilities (cont.)
B(x; n, p) b(y; n, p)
e. n 25
y0
p
x
0.01
0.05
0.10
0.20
0.25
0.30
0.40
0.50
0.60
0.70
0.75
0.80
0.90
0.95
0.99
0
1
2
3
4
.778
.974
.998
1.000
1.000
.277
.642
.873
.966
.993
.072
.271
.537
.764
.902
.004
.027
.098
.234
.421
.001
.007
.032
.096
.214
.000
.002
.009
.033
.090
.000
.000
.000
.002
.009
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
5
6
7
8
9
1.000
1.000
1.000
1.000
1.000
.999
1.000
1.000
1.000
1.000
.967
.991
.998
1.000
1.000
.617
.780
.891
.953
.983
.378
.561
.727
.851
.929
.193
.341
.512
.677
.811
.029
.074
.154
.274
.425
.002
.007
.022
.054
.115
.000
.000
.001
.004
.013
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
10
11
12
13
14
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.994
.998
1.000
1.000
1.000
.970
.980
.997
.999
1.000
.902
.956
.983
.994
.998
.586
.732
.846
.922
.966
.212
.345
.500
.655
.788
.034
.078
.154
.268
.414
.002
.006
.017
.044
.098
.000
.001
.003
.020
.030
.000
.000
.000
.002
.006
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
15
16
17
18
19
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.987
.996
.999
1.000
1.000
.885
.946
.978
.993
.998
.575
.726
.846
.926
.971
.189
.323
.488
.659
.807
.071
.149
.273
.439
.622
.017
.047
.109
.220
.383
.000
.000
.002
.009
.033
.000
.000
.000
.000
.001
.000
.000
.000
.000
.000
20
21
22
23
24
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.991
.998
1.000
1.000
1.000
.910
.967
.991
.998
1.000
.786
.904
.968
.993
.999
.579
.766
.902
.973
.996
.098
.236
.463
.729
.928
.007
.034
.127
.358
.723
.000
.000
.002
.026
.222
x
e y
F(x; ) y0 y!
Table A.2 Cumulative Poisson Probabilities
x
0
1
2
3
4
5
6
.1
.2
.3
.4
.5
.6
.7
.8
.9
1.0
.905
.995
1.000
.819
.982
.999
1.000
.741
.963
.996
1.000
.670
.938
.992
.999
1.000
.607
.910
.986
.998
1.000
.549
.878
.977
.997
1.000
.497
.844
.966
.994
.999
1.000
.449
.809
.953
.991
.999
1.000
.407
.772
.937
.987
.998
1.000
.368
.736
.920
.981
.996
.999
1.000
(continued )
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Appendix Tables
Table A.2
667
x
Cumulative Poisson Probabilities (cont.)
e y
F(x; ) y0 y!
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
15.0
20.0
0
1
2
3
4
.135
.406
.677
.857
.947
.050
.199
.423
.647
.815
.018
.092
.238
.433
.629
.007
.040
.125
.265
.440
.002
.017
.062
.151
.285
.001
.007
.030
.082
.173
.000
.003
.014
.042
.100
.000
.001
.006
.021
.055
.000
.000
.003
.010
.029
.000
.000
.000
.000
.001
.000
.000
.000
.000
.000
5
6
7
8
9
.983
.995
.999
1.000
.916
.966
.988
.996
.999
.785
.889
.949
.979
.992
.616
.762
.867
.932
.968
.446
.606
.744
.847
.916
.301
.450
.599
.729
.830
.191
.313
.453
.593
.717
.116
.207
.324
.456
.587
.067
.130
.220
.333
.458
.003
.008
.018
.037
.070
.000
.000
.001
.002
.005
1.000
.997
.999
1.000
.986
.995
.998
.999
1.000
.957
.980
.991
.996
.999
.901
.947
.973
.987
.994
.816
.888
.936
.966
.983
.706
.803
.876
.926
.959
.583
.697
.792
.864
.917
.118
.185
.268
.363
.466
.011
.021
.039
.066
.105
.999
1.000
.998
.999
1.000
.992
.996
.998
.999
1.000
.978
.989
.995
.998
.999
.951
.973
.986
.993
.997
.568
.664
.749
.819
.875
.157
.221
.297
.381
.470
1.000
.998
.999
1.000
.917
.947
.967
.981
.989
.559
.644
.721
.787
.843
.994
.997
.998
.999
1.000
.888
.922
.948
.966
.978
10
11
12
13
14
x
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
.987
.992
.995
.997
.999
35
36
.999
1.000
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Appendix Tables
Table A.3
Standard Normal Curve Areas
Φ(z) P(Z z)
Standard normal density function
Shaded area = Φ(z)
0
z
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
3.4
3.3
3.2
3.1
3.0
.0003
.0005
.0007
.0010
.0013
.0003
.0005
.0007
.0009
.0013
.0003
.0005
.0006
.0009
.0013
.0003
.0004
.0006
.0009
.0012
.0003
.0004
.0006
.0008
.0012
.0003
.0004
.0006
.0008
.0011
.0003
.0004
.0006
.0008
.0011
.0003
.0004
.0005
.0008
.0011
.0003
.0004
.0005
.0007
.0010
.0002
.0003
.0005
.0007
.0010
2.9
2.8
2.7
2.6
2.5
.0019
.0026
.0035
.0047
.0062
.0018
.0025
.0034
.0045
.0060
.0017
.0024
.0033
.0044
.0059
.0017
.0023
.0032
.0043
.0057
.0016
.0023
.0031
.0041
.0055
.0016
.0022
.0030
.0040
.0054
.0015
.0021
.0029
.0039
.0052
.0015
.0021
.0028
.0038
.0051
.0014
.0020
.0027
.0037
.0049
.0014
.0019
.0026
.0036
.0038
2.4
2.3
2.2
2.1
2.0
.0082
.0107
.0139
.0179
.0228
.0080
.0104
.0136
.0174
.0222
.0078
.0102
.0132
.0170
.0217
.0075
.0099
.0129
.0166
.0212
.0073
.0096
.0125
.0162
.0207
.0071
.0094
.0122
.0158
.0202
.0069
.0091
.0119
.0154
.0197
.0068
.0089
.0116
.0150
.0192
.0066
.0087
.0113
.0146
.0188
.0064
.0084
.0110
.0143
.0183
1.9
1.8
1.7
1.6
1.5
.0287
.0359
.0446
.0548
.0668
.0281
.0352
.0436
.0537
.0655
.0274
.0344
.0427
.0526
.0643
.0268
.0336
.0418
.0516
.0630
.0262
.0329
.0409
.0505
.0618
.0256
.0322
.0401
.0495
.0606
.0250
.0314
.0392
.0485
.0594
.0244
.0307
.0384
.0475
.0582
.0239
.0301
.0375
.0465
.0571
.0233
.0294
.0367
.0455
.0559
1.4
1.3
1.2
1.1
1.0
.0808
.0968
.1151
.1357
.1587
.0793
.0951
.1131
.1335
.1562
.0778
.0934
.1112
.1314
.1539
.0764
.0918
.1093
.1292
.1515
.0749
.0901
.1075
.1271
.1492
.0735
.0885
.1056
.1251
.1469
.0722
.0869
.1038
.1230
.1446
.0708
.0853
.1020
.1210
.1423
.0694
.0838
.1003
.1190
.1401
.0681
.0823
.0985
.1170
.1379
0.9
0.8
0.7
0.6
0.5
.1841
.2119
.2420
.2743
.3085
.1814
.2090
.2389
.2709
.3050
.1788
.2061
.2358
.2676
.3015
.1762
.2033
.2327
.2643
.2981
.1736
.2005
.2296
.2611
.2946
.1711
.1977
.2266
.2578
.2912
.1685
.1949
.2236
.2546
.2877
.1660
.1922
.2206
.2514
.2843
.1635
.1894
.2177
.2483
.2810
.1611
.1867
.2148
.2451
.2776
0.4
0.3
0.2
0.1
0.0
.3446
.3821
.4207
.4602
.5000
.3409
.3783
.4168
.4562
.4960
.3372
.3745
.4129
.4522
.4920
.3336
.3707
.4090
.4483
.4880
.3300
.3669
.4052
.4443
.4840
.3264
.3632
.4013
.4404
.4801
.3228
.3594
.3974
.4364
.4761
.3192
.3557
.3936
.4325
.4721
.3156
.3520
.3897
.4286
.4681
.3121
.3482
.3859
.4247
.4641
(continued )
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Appendix Tables
669
(z) P(Z z)
Table A.3 Standard Normal Curve Areas (cont.)
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
0.1
0.2
0.3
0.4
.5000
.5398
.5793
.6179
.6554
.5040
.5438
.5832
.6217
.6591
.5080
.5478
.5871
.6255
.6628
.5120
.5517
.5910
.6293
.6664
.5160
.5557
.5948
.6331
.6700
.5199
.5596
.5987
.6368
.6736
.5239
.5636
.6026
.6406
.6772
.5279
.5675
.6064
.6443
.6808
.5319
.5714
.6103
.6480
.6844
.5359
.5753
.6141
.6517
.6879
0.5
0.6
0.7
0.8
0.9
.6915
.7257
.7580
.7881
.8159
.6950
.7291
.7611
.7910
.8186
.6985
.7324
.7642
.7939
.8212
.7019
.7357
.7673
.7967
.8238
.7054
.7389
.7704
.7995
.8264
.7088
.7422
.7734
.8023
.8289
.7123
.7454
.7764
.8051
.8315
.7157
.7486
.7794
.8078
.8340
.7190
.7517
.7823
.8106
.8365
.7224
.7549
.7852
.8133
.8389
1.0
1.1
1.2
1.3
1.4
.8413
.8643
.8849
.9032
.9192
.8438
.8665
.8869
.9049
.9207
.8461
.8686
.8888
.9066
.9222
.8485
.8708
.8907
.9082
.9236
.8508
.8729
.8925
.9099
.9251
.8531
.8749
.8944
.9115
.9265
.8554
.8770
.8962
.9131
.9278
.8577
.8790
.8980
.9147
.9292
.8599
.8810
.8997
.9162
.9306
.8621
.8830
.9015
.9177
.9319
1.5
1.6
1.7
1.8
1.9
.9332
.9452
.9554
.9641
.9713
.9345
.9463
.9564
.9649
.9719
.9357
.9474
.9573
.9656
.9726
.9370
.9484
.9582
.9664
.9732
.9382
.9495
.9591
.9671
.9738
.9394
.9505
.9599
.9678
.9744
.9406
.9515
.9608
.9686
.9750
.9418
.9525
.9616
.9693
.9756
.9429
.9535
.9625
.9699
.9761
.9441
.9545
.9633
.9706
.9767
2.0
2.1
2.2
2.3
2.4
.9772
.9821
.9861
.9893
.9918
.9778
.9826
.9864
.9896
.9920
.9783
.9830
.9868
.9898
.9922
.9788
.9834
.9871
.9901
.9925
.9793
.9838
.9875
.9904
.9927
.9798
.9842
.9878
.9906
.9929
.9803
.9846
.9881
.9909
.9931
.9808
.9850
.9884
.9911
.9932
.9812
.9854
.9887
.9913
.9934
.9817
.9857
.9890
.9916
.9936
2.5
2.6
2.7
2.8
2.9
.9938
.9953
.9965
.9974
.9981
.9940
.9955
.9966
.9975
.9982
.9941
.9956
.9967
.9976
.9982
.9943
.9957
.9968
.9977
.9983
.9945
.9959
.9969
.9977
.9984
.9946
.9960
.9970
.9978
.9984
.9948
.9961
.9971
.9979
.9985
.9949
.9962
.9972
.9979
.9985
.9951
.9963
.9973
.9980
.9986
.9952
.9964
.9974
.9981
.9986
3.0
3.1
3.2
3.3
3.4
.9987
.9990
.9993
.9995
.9997
.9987
.9991
.9993
.9995
.9997
.9987
.9991
.9994
.9995
.9997
.9988
.9991
.9994
.9996
.9997
.9988
.9992
.9994
.9996
.9997
.9989
.9992
.9994
.9996
.9997
.9989
.9992
.9994
.9996
.9997
.9989
.9992
.9995
.9996
.9997
.9990
.9993
.9995
.9996
.9997
.9990
.9993
.9995
.9997
.9998
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Appendix Tables
Table A.4
The Incomplete Gamma Function
F(x; ) (1)y
x
1 y
e
dy
0
x
1
2
3
4
5
6
7
8
9
10
1
2
3
4
.632
.865
.950
.982
.264
.594
.801
.908
.080
.323
.577
.762
.019
.143
.353
.567
.004
.053
.185
.371
.001
.017
.084
.215
.000
.005
.034
.111
.000
.001
.012
.051
.000
.000
.004
.021
.000
.000
.001
.008
5
6
7
8
9
.993
.998
.999
1.000
.960
.983
.993
.997
.999
.875
.938
.970
.986
.994
.735
.849
.918
.958
.979
.560
.715
.827
.900
.945
.384
.554
.699
.809
.884
.238
.394
.550
.687
.793
.133
.256
.401
.547
.676
.068
.153
.271
.407
.544
.032
.084
.170
.283
.413
1.000
.997
.999
1.000
.990
.995
.998
.999
1.000
.971
.985
.992
.996
.998
.933
.962
.980
.989
.994
.870
.921
.954
.974
.986
.780
.857
.911
.946
.968
.667
.768
.845
.900
.938
.542
.659
.758
.834
.891
.999
.997
.992
.982
.963
.930
10
11
12
13
14
15
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671
Appendix Tables
Table A.5 Critical Values for t Distributions
t density curve
Shaded area = 0
t,
v
.10
.05
.025
.01
.005
.001
.0005
1
2
3
4
3.078
1.886
1.638
1.533
6.314
2.920
2.353
2.132
12.706
4.303
3.182
2.776
31.821
6.965
4.541
3.747
63.657
9.925
5.841
4.604
318.31
22.326
10.213
7.173
636.62
31.598
12.924
8.610
5
6
7
8
9
1.476
1.440
1.415
1.397
1.383
2.015
1.943
1.895
1.860
1.833
2.571
2.447
2.365
2.306
2.262
3.365
3.143
2.998
2.896
2.821
4.032
3.707
3.499
3.355
3.250
5.893
5.208
4.785
4.501
4.297
6.869
5.959
5.408
5.041
4.781
10
11
12
13
14
1.372
1.363
1.356
1.350
1.345
1.812
1.796
1.782
1.771
1.761
2.228
2.201
2.179
2.160
2.145
2.764
2.718
2.681
2.650
2.624
3.169
3.106
3.055
3.012
2.977
4.144
4.025
3.930
3.852
3.787
4.587
4.437
4.318
4.221
4.140
15
16
17
18
19
1.341
1.337
1.333
1.330
1.328
1.753
1.746
1.740
1.734
1.729
2.131
2.120
2.110
2.101
2.093
2.602
2.583
2.567
2.552
2.539
2.947
2.921
2.898
2.878
2.861
3.733
3.686
3.646
3.610
3.579
4.073
4.015
3.965
3.922
3.883
20
21
22
23
24
1.325
1.323
1.321
1.319
1.318
1.725
1.721
1.717
1.714
1.711
2.086
2.080
2.074
2.069
2.064
2.528
2.518
2.508
2.500
2.492
2.845
2.831
2.819
2.807
2.797
3.552
3.527
3.505
3.485
3.467
3.850
3.819
3.792
3.767
3.745
25
26
27
28
29
1.316
1.315
1.314
1.313
1.311
1.708
1.706
1.703
1.701
1.699
2.060
2.056
2.052
2.048
2.045
2.485
2.479
2.473
2.467
2.462
2.787
2.779
2.771
2.763
2.756
3.450
3.435
3.421
3.408
3.396
3.725
3.707
3.690
3.674
3.659
30
32
34
36
38
1.310
1.309
1.307
1.306
1.304
1.697
1.694
1.691
1.688
1.686
2.042
2.037
2.032
2.028
2.024
2.457
2.449
2.441
2.434
2.429
2.750
2.738
2.728
2.719
2.712
3.385
3.365
3.348
3.333
3.319
3.646
3.622
3.601
3.582
3.566
40
50
60
120
∞
1.303
1.299
1.296
1.289
1.282
1.684
1.676
1.671
1.658
1.645
2.021
2.009
2.000
1.980
1.960
2.423
2.403
2.390
2.358
2.326
2.704
2.678
2.660
2.617
2.576
3.307
3.262
3.232
3.160
3.090
3.551
3.496
3.460
3.373
3.291
32.019
8.380
5.369
4.275
3.712
3.369
3.136
2.967
2.839
2.737
2.655
2.587
2.529
2.480
2.437
2.400
2.366
2.337
2.310
2.208
2.140
2.090
2.052
2.021
1.996
1.958
1.929
1.907
1.889
1.874
1.825
1.798
1.780
1.767
1.645
37.674
9.916
6.370
5.079
4.414
4.007
3.732
3.532
3.379
3.259
3.162
3.081
3.012
2.954
2.903
2.858
2.819
2.784
2.752
2.631
2.549
2.490
2.445
2.408
2.379
2.333
2.299
2.272
2.251
2.233
2.175
2.143
2.121
2.106
1.960
95%
% of Population Captured 90%
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Sample Size n 17
18
19
20
25
30
35
40
45
50
60
70
80
90
100
150
200
250
300
95%
48.430
12.861
8.299
6.634
5.775
5.248
4.891
4.631
4.433
4.277
4.150
4.044
3.955
3.878
3.812
3.754
3.702
3.656
3.615
3.457
3.350
3.272
3.213
3.165
3.126
3.066
3.021
2.986
2.958
2.934
2.859
2.816
2.788
2.767
2.576
99%
160.193
18.930
9.398
6.612
5.337
4.613
4.147
3.822
3.582
3.397
3.250
3.130
3.029
2.945
2.872
2.808
2.753
2.703
2.659
2.494
2.385
2.306
2.247
2.200
2.162
2.103
2.060
2.026
1.999
1.977
1.905
1.865
1.839
1.820
1.645
90%
Two-sided Intervals
188.491
22.401
11.150
7.855
6.345
5.488
4.936
4.550
4.265
4.045
3.870
3.727
3.608
3.507
3.421
3.345
3.279
3.221
3.168
2.972
2.841
2.748
2.677
2.621
2.576
2.506
2.454
2.414
2.382
2.355
2.270
2.222
2.191
2.169
1.960
95%
99%
242.300
29.055
14.527
10.260
8.301
7.187
6.468
5.966
5.594
5.308
5.079
4.893
4.737
4.605
4.492
4.393
4.307
4.230
4.161
3.904
3.733
3.611
3.518
3.444
3.385
3.293
3.225
3.173
3.130
3.096
2.983
2.921
2.880
2.850
2.576
99%
Tolerance Critical Values for Normal Population Distributions
20.581
6.156
4.162
3.407
3.006
2.756
2.582
2.454
2.355
2.275
2.210
2.155
2.109
2.068
2.033
2.002
1.974
1.949
1.926
1.838
1.777
1.732
1.697
1.669
1.646
1.609
1.581
1.559
1.542
1.527
1.478
1.450
1.431
1.417
1.282
90%
26.260
7.656
5.144
4.203
3.708
3.400
3.187
3.031
2.911
2.815
2.736
2.671
2.615
2.566
2.524
2.486
2.453
2.423
2.396
2.292
2.220
2.167
2.126
2.092
2.065
2.022
1.990
1.965
1.944
1.927
1.870
1.837
1.815
1.800
1.645
95%
95%
37.094
10.553
7.042
5.741
5.062
4.642
4.354
4.143
3.981
3.852
3.747
3.659
3.585
3.520
3.464
3.414
3.370
3.331
3.295
3.158
3.064
2.995
2.941
2.898
2.863
2.807
2.765
2.733
2.706
2.684
2.611
2.570
2.542
2.522
2.326
99%
103.029
13.995
7.380
5.362
4.411
3.859
3.497
3.241
3.048
2.898
2.777
2.677
2.593
2.522
2.460
2.405
2.357
2.314
2.276
2.129
2.030
1.957
1.902
1.857
1.821
1.764
1.722
1.688
1.661
1.639
1.566
1.524
1.496
1.476
1.282
90%
One-sided Intervals
131.426
17.370
9.083
6.578
5.406
4.728
4.285
3.972
3.738
3.556
3.410
3.290
3.189
3.102
3.028
2.963
2.905
2.854
2.808
2.633
2.516
2.430
2.364
2.312
2.269
2.202
2.153
2.114
2.082
2.056
1.971
1.923
1.891
1.868
1.645
95%
99%
185.617
23.896
12.387
8.939
7.335
6.412
5.812
5.389
5.074
4.829
4.633
4.472
4.337
4.222
4.123
4.037
3.960
3.892
3.832
3.601
3.447
3.334
3.249
3.180
3.125
3.038
2.974
2.924
2.883
2.850
2.741
2.679
2.638
2.608
2.326
99%
672
Confidence Level
Table A.6
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Appendix Tables
38217_App_p662-690.qxd
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Page 673
673
Appendix Tables
Table A.7
2 density curve
Critical Values for Chi-Squared Distributions
Shaded area = 0
2,
.995
.99
.975
.95
.90
.10
.05
.025
.01
.005
1
2
3
4
5
0.000
0.010
0.072
0.207
0.412
0.000
0.020
0.115
0.297
0.554
0.001
0.051
0.216
0.484
0.831
0.004
0.103
0.352
0.711
1.145
0.016
0.211
0.584
1.064
1.610
2.706
4.605
6.251
7.779
9.236
3.843
5.992
7.815
9.488
11.070
5.025
7.378
9.348
11.143
12.832
6.637
9.210
11.344
13.277
15.085
7.882
10.597
12.837
14.860
16.748
6
7
8
9
10
0.676
0.989
1.344
1.735
2.156
0.872
1.239
1.646
2.088
2.558
1.237
1.690
2.180
2.700
3.247
1.635
2.167
2.733
3.325
3.940
2.204
2.833
3.490
4.168
4.865
10.645
12.017
13.362
14.684
15.987
12.592
14.067
15.507
16.919
18.307
14.440
16.012
17.534
19.022
20.483
16.812
18.474
20.090
21.665
23.209
18.548
20.276
21.954
23.587
25.188
11
12
13
14
15
2.603
3.074
3.565
4.075
4.600
3.053
3.571
4.107
4.660
5.229
3.816
4.404
5.009
5.629
6.262
4.575
5.226
5.892
6.571
7.261
5.578
6.304
7.041
7.790
8.547
17.275
18.549
19.812
21.064
22.307
19.675
21.026
22.362
23.685
24.996
21.920
23.337
24.735
26.119
27.488
24.724
26.217
27.687
29.141
30.577
26.755
28.300
29.817
31.319
32.799
16
17
18
19
20
5.142
5.697
6.265
6.843
7.434
5.812
6.407
7.015
7.632
8.260
6.908
7.564
8.231
8.906
9.591
7.962
8.682
9.390
10.117
10.851
9.312
10.085
10.865
11.651
12.443
23.542
24.769
25.989
27.203
28.412
26.296
27.587
28.869
30.143
31.410
28.845
30.190
31.526
32.852
34.170
32.000
33.408
34.805
36.190
37.566
34.267
35.716
37.156
38.580
39.997
21
22
23
24
25
8.033
8.643
9.260
9.886
10.519
8.897
9.542
10.195
10.856
11.523
10.283
10.982
11.688
12.401
13.120
11.591
12.338
13.090
13.848
14.611
13.240
14.042
14.848
15.659
16.473
29.615
30.813
32.007
33.196
34.381
32.670
33.924
35.172
36.415
37.652
35.478
36.781
38.075
39.364
40.646
38.930
40.289
41.637
42.980
44.313
41.399
42.796
44.179
45.558
46.925
26
27
28
29
30
11.160
11.807
12.461
13.120
13.787
12.198
12.878
13.565
14.256
14.954
13.844
14.573
15.308
16.147
16.791
15.379
16.151
16.928
17.708
18.493
17.292
18.114
18.939
19.768
20.599
35.563
36.741
37.916
39.087
40.256
38.885
40.113
41.337
42.557
43.773
41.923
43.194
44.461
45.772
46.979
45.642
46.962
48.278
49.586
50.892
48.290
49.642
50.993
52.333
53.672
31
32
33
34
35
14.457
15.134
15.814
16.501
17.191
15.655
16.362
17.073
17.789
18.508
17.538
18.291
19.046
19.806
20.569
19.280
20.072
20.866
21.664
22.465
21.433
22.271
23.110
23.952
24.796
41.422
42.585
43.745
44.903
46.059
44.985
46.194
47.400
48.602
49.802
48.231
49.480
50.724
51.966
53.203
52.190
53.486
54.774
56.061
57.340
55.000
56.328
57.646
58.964
60.272
36
37
38
39
40
17.887
18.584
19.289
19.994
20.706
19.233
19.960
20.691
21.425
22.164
21.336
22.105
22.878
23.654
24.433
23.269
24.075
24.884
25.695
26.509
25.643
26.492
27.343
28.196
29.050
47.212
48.363
49.513
50.660
51.805
50.998
52.192
53.384
54.572
55.758
54.437
55.667
56.896
58.119
59.342
58.619
59.891
61.162
62.426
63.691
61.581
62.880
64.181
65.473
66.766
2
For 40, 2, 1 z
9
2
9
3
38217_App_p662-690.qxd
674
12/20/06
09:48
Page 674
Appendix Tables
Table A.8
t Curve Tail Areas
t curve
Area to the
right of t
0
t
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0.0
0.1
0.2
0.3
0.4
0.5
.500
.468
.437
.407
.379
.352
.500
.465
.430
.396
.364
.333
.500
.463
.427
.392
.358
.326
.500
.463
.426
.390
.355
.322
.500
.462.
.425
.388
.353
.319
.500
.462
.424
.387
.352
.317
.500
.462
.424
.386
.351
.316
.500
.461
.423
.386
.350
.315
.500
.461
.423
.386
.349
.315
.500
.461
.423
.385
.349
.314
.500
.461
.423
.385
.348
.313
.500
.461
.422
.385
.348
.313
.500
.461
.422
.384
.348
.313
.500
.461
.422
.384
.347
.312
.500
.461
.422
.384
.347
.312
.500
.461
.422
.384
.347
.312
.500
.461
.422
.384
.347
.312
.500
.461
.422
.384
.347
.312
0.6
0.7
0.8
0.9
1.0
.328
.306
.285
.267
.250
.305
.278
.254
.232
.211
.295
.267
.241
.217
.196
.290
.261
.234
.210
.187
.287
.258
.230
.205
.182
.285
.255
.227
.201
.178
.284
.253
.225
.199
.175
.283
.252
.223
.197
.173
.282
.251
.222
.196
.172
.281
.250
.221
.195
.170
.280
.249
.220
.194
.169
.280
.249
.220
.193
.169
.279
.248
.219
.192
.168
.279
.247
.218
.191
.167
.279
.247
.218
.191
.167
.278
.247
.218
.191
.166
.278
.247
.217
.190
.166
.278
.246
.217
.190
.165
1.1
1.2
1.3
1.4
1.5
.235
.221
.209
.197
.187
.193
.177
.162
.148
.136
.176
.158
.142
.128
.115
.167
.148
.132
.117
.104
.162
.142
.125
.110
.097
.157
.138
.121
.106
.092
.154
.135
.117
.102
.089
.152
.132
.115
.100
.086
.150
.130
.113
.098
.084
.149
.129
.111
.096
.082
.147
.128
.110
.095
.081
.146
.127
.109
.093
.080
.146
.126
.108
.092
.079
.144
.124
.107
.091
.077
.144
.124
.107
.091
.077
.144
.124
.106
.090
.077
.143
.123
.105
.090
.076
.143
.123
.105
.089
.075
1.6
1.7
1.8
1.9
2.0
.178
.169
.161
.154
.148
.125
.116
.107
.099
.092
.104
.094
.085
.077
.070
.092
.082
.073
.065
.058
.085
.075
.066
.058
.051
.080
.070
.061
.053
.046
.077
.065
.057
.050
.043
.074
.064
.055
.047
.040
.072
.062
.053
.045
.038
.070
.060
.051
.043
.037
.069
.059
.050
.042
.035
.068
.057
.049
.041
.034
.067
.056
.048
.040
.033
.065
.055
.046
.038
.032
.065
.055
.046
.038
.032
.065
.054
.045
.038
.031
.064
.054
.045
.037
.031
.064
.053
.044
.037
.030
2.1
2.2
2.3
2.4
2.5
.141
.136
.131
.126
.121
.085
.079
.074
.069
.065
.063
.058
.052
.048
.044
.052
.046
.041
.037
.033
.045
.040
.035
.031
.027
.040
.035
.031
.027
.023
.037
.032
.027
.024
.020
.034
.029
.025
.022
.018
.033
.028
.023
.020
.017
.031
.026
.022
.019
.016
.030
.025
.021
.018
.015
.029
.024
.020
.017
.014
.028
.023
.019
.016
.013
.027
.022
.018
.015
.012
.027
.022
.018
.015
.012
.026
.021
.018
.014
.012
.025
.021
.017
.014
.011
.025
.021
.017
.014
.011
2.6
2.7
2.8
2.9
3.0
.117
.113
.109
.106
.102
.061
.057
.054
.051
.048
.040
.037
.034
.031
.029
.030
.027
.024
.022
.020
.024
.021
.019
.017
.015
.020
.018
.016
.014
.012
.018
.015
.013
.011
.010
.016
.014
.012
.010
.009
.014
.012
.010
.009
.007
.013
.011
.009
.008
.007
.012
.010
.009
.007
.006
.012
.010
.008
.007
.006
.011
.009
.008
.006
.005
.010
.008
.007
.005
.004
.010
.008
.007
.005
.004
.010
.008
.006
.005
.004
.009
.008
.006
.005
.004
.009
.007
.006
.005
.004
3.1
3.2
3.3
3.4
3.5
.099
.096
.094
.091
.089
.045
.043
.040
.038
.036
.027
.025
.023
.021
.020
.018
.016
.015
.014
.012
.013
.012
.011
.010
.009
.011
.009
.008
.007
.006
.009
.008
.007
.006
.005
.007
.006
.005
.005
.004
.006
.005
.005
.004
.003
.006
.005
.004
.003
.003
.005
.004
.004
.003
.002
.005
.004
.003
.003
.002
.004
.003
.003
.002
.002
.004
.003
.002
.002
.002
.004
.003
.002
.002
.002
.003
.003
.002
.002
.001
.003
.003
.002
.002
.001
.003
.002
.002
.002
.001
3.6
3.7
3.8
3.9
4.0
.086
.084
.082
.080
.078
.035
.033
.031
.030
.029
.018
.017
.016
.015
.014
.011
.010
.010
.009
.008
.008
.007
.006
.006
.005
.006
.005
.004
.004
.004
.004
.004
.003
.003
.003
.004
.003
.003
.002
.002
.003
.002
.002
.002
.002
.002
.002
.002
.001
.001
.002
.002
.001
.001
.001
.002
.002
.001
.001
.001
.002
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.000
.001
.001
.001
.001
.000
(continued )
38217_App_p662-690.qxd
12/20/06
09:48
Page 675
Appendix Tables
Table A.8
675
t Curve Tail Areas (cont.)
t curve
Area to the
right of t
0
t
19
20
21
22
23
24
25
26
27
28
29
30
35
40
60
120
( z)
0.0
0.1
0.2
0.3
0.4
0.5
.500
.461
.422
.384
.347
.311
.500
.461
.422
.384
.347
.311
.500
.461
.422
.384
.347
.311
.500
.461
.422
.383
.347
.311
.500
.461
.422
.383
.346
.311
.500
.461
.422
.383
.346
.311
.500
.461
.422
.383
.346
.311
.500
.461
.422
.383
.346
.311
.500
.461
.421
.383
.346
.311
.500
.461
.421
.383
.346
.310
.500
.461
.421
.383
.346
.310
.500
.461
.421
.383
.346
.310
.500
.460
.421
.383
.346
.310
.500
.460
.421
.383
.346
.310
.500
.460
.421
.383
.345
.309
.500
.460
.421
.382
.345
.309
.500
.460
.421
.382
.345
.309
0.6
0.7
0.8
0.9
1.0
.278
.246
.217
.190
.165
.278
.246
.217
.189
.165
.278
.246
.216
.189
.164
.277
.246
.216
.189
.164
.277
.245
.216
.189
.164
.277
.245
.216
.189
.164
.277
.245
.216
.188
.163
.277
.245
.215
.188
.163
.277
.245
.215
.188
.163
.277
.245
.215
.188
.163
.277
.245
.215
.188
.163
.277
.245
.215
.188
.163
.276
.244
.215
.187
.162
.276
.244
.214
.187
.162
.275
.243
.213
.186
.161
.275
.243
.213
.185
.160
.274
.242
.212
.184
.159
1.1
1.2
1.3
1.4
1.5
.143
.122
.105
.089
.075
.142
.122
.104
.089
.075
.142
.122
.104
.088
.074
.142
.121
.104
.088
.074
.141
.121
.103
.087
.074
.141
.121
.103
.087
.073
.141
.121
.103
.087
.073
.141
.120
.103
.087
.073
.141
.120
.102
.086
.073
.140
.120
.102
.086
.072
.140
.120
.102
.086
.072
.140
.120
.102
.086
.072
.139
.119
.101
.085
.071
.139
.119
.101
.085
.071
.138
.117
.099
.083
.069
.137
.116
.098
.082
.068
.136
.115
.097
.081
.067
1.6
1.7
1.8
1.9
2.0
.063
.053
.044
.036
.030
.063
.052
.043
.036
.030
.062
.052
.043
.036
.029
.062
.052
.043
.035
.029
.062
.051
.042
.035
.029
.061
.051
.042
.035
.028
.061
.051
.042
.035
.028
.061
.051
.042
.034
.028
.061
.050
.042
.034
.028
.060
.050
.041
.034
.028
.060
.050
.041
.034
.027
.060
.050
.041
.034
.027
.059
.049
.040
.033
.027
.059
.048
.040
.032
.026
.057
.047
.038
.031
.025
.056
.046
.037
.030
.024
.055
.045
.036
.029
.023
2.1
2.2
2.3
2.4
2.5
.025
.020
.016
.013
.011
.024
.020
.016
.013
.011
.024
.020
.016
.013
.010
.024
.019
.016
.013
.010
.023
.019
.015
.012
.010
.023
.019
.015
.012
.010
.023
.019
.015
.012
.010
.023
.018
.015
.012
.010
.023
.018
.015
.012
.009
.022
.018
.015
.012
.009
.022
.018
.014
.012
.009
.022
.018
.014
.011
.009
.022
.017
.014
.011
.009
.021
.017
.013
.011
.008
.020
.016
.012
.010
.008
.019
.015
.012
.009
.007
.018
.014
.011
.008
.006
2.6
2.7
2.8
2.9
3.0
.009
.007
.006
.005
.004
.009
.007
.006
.004
.004
.008
.007
.005
.004
.003
.008
.007
.005
.004
.003
.008
.006
.005
.004
.003
.008
.006
.005
.004
.003
.008
.006
.005
.004
.003
.008
.006
.005
.004
.003
.007
.006
.005
.004
.003
.007
.006
.005
.004
.003
.007
.006
.005
.004
.003
.007
.006
.004
.003
.003
.007
.005
.004
.003
.002
.007
.005
.004
.003
.002
.006
.004
.003
.003
.002
.005
.004
.003
.002
.002
.005
.003
.003
.002
.001
3.1
3.2
3.3
3.4
3.5
.003
.002
.002
.002
.001
.003
.002
.002
.001
.001
.003
.002
.002
.001
.001
.003
.002
.002
.001
.001
.003
.002
.002
.001
.001
.002
.002
.001
.001
.001
.002
.002
.001
.001
.001
.002
.002
.001
.001
.001
.002
.002
.001
.001
.001
.002
.002
.001
.001
.001
.002
.002
.001
.001
.001
.002
.002
.001
.001
.001
.002
.001
.001
.001
.001
.002
.001
.001
.001
.001
.001
.001
.001
.001
.000
.001
.001
.001
.000
.000
.001
.001
.000
.000
.000
3.6
3.7
3.8
3.9
4.0
.001
.001
.001
.000
.000
.001
.001
.001
.000
.000
.001
.001
.001
.000
.000
.001
.001
.000
.000
.000
.001
.001
.000
.000
.000
.001
.001
.000
.000
.000
.001
.001
.000
.000
.000
.001
.001
.000
.000
.000
.001
.000
.000
.000
.000
.001
.000
.000
.000
.000
.001
.000
.000
.000
.000
.001
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
t
38217_App_p662-690.qxd
676
12/20/06
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Page 676
Appendix Tables
Table A.9 Critical Values for F Distributions
2 denominator df
1 numerator df
1
2
3
4
5
6
7
8
9
1
.100
.050
.010
.001
39.86
161.45
4052.2
405284
49.50
199.50
4999.5
500000
53.59
215.71
5403.4
540379
55.83
224.58
5624.6
562500
57.24
230.16
5763.6
576405
58.20
233.99
5859.0
585937
58.91
236.77
5928.4
592873
59.44
238.88
5981.1
598144
59.86
240.54
6022.5
602284
2
.100
.050
.010
.001
8.53
18.51
98.50
998.50
9.00
19.00
99.00
999.00
9.16
19.16
99.17
999.17
9.24
19.25
99.25
999.25
9.29
19.30
99.30
999.30
9.33
19.33
99.33
999.33
9.35
19.35
99.36
999.36
9.37
19.37
99.37
999.37
9.38
19.38
99.39
999.39
3
.100
.050
.010
.001
5.54
10.13
34.12
167.03
5.46
9.55
30.82
148.50
5.39
9.28
29.46
141.11
5.34
9.12
28.71
137.10
5.31
9.01
28.24
134.58
5.28
8.94
27.91
132.85
5.27
8.89
27.67
131.58
5.25
8.85
27.49
130.62
5.24
8.81
27.35
129.86
4
.100
.050
.010
.001
4.54
7.71
21.20
74.14
4.32
6.94
18.00
61.25
4.19
6.59
16.69
56.18
4.11
6.39
15.98
53.44
4.05
6.26
15.52
51.71
4.01
6.16
15.21
50.53
3.98
6.09
14.98
49.66
3.95
6.04
14.80
49.00
3.94
6.00
14.66
48.47
5
.100
.050
.010
.001
4.06
6.61
16.26
47.18
3.78
5.79
13.27
37.12
3.62
5.41
12.06
33.20
3.52
5.19
11.39
31.09
3.45
5.05
10.97
29.75
3.40
4.95
10.67
28.83
3.37
4.88
10.46
28.16
3.34
4.82
10.29
27.65
3.32
4.77
10.16
27.24
6
.100
.050
.010
.001
3.78
5.99
13.75
35.51
3.46
5.14
10.92
27.00
3.29
4.76
9.78
23.70
3.18
4.53
9.15
21.92
3.11
4.39
8.75
20.80
3.05
4.28
8.47
20.03
3.01
4.21
8.26
19.46
2.98
4.15
8.10
19.03
2.96
4.10
7.98
18.69
7
.100
.050
.010
.001
3.59
5.59
12.25
29.25
3.26
4.74
9.55
21.69
3.07
4.35
8.45
18.77
2.96
4.12
7.85
17.20
2.88
3.97
7.46
16.21
2.83
3.87
7.19
15.52
2.78
3.79
6.99
15.02
2.75
3.73
6.84
14.63
2.72
3.68
6.72
14.33
8
.100
.050
.010
.001
3.46
5.32
11.26
25.41
3.11
4.46
8.65
18.49
2.92
4.07
7.59
15.83
2.81
3.84
7.01
14.39
2.73
3.69
6.63
13.48
2.67
3.58
6.37
12.86
2.62
3.50
6.18
12.40
2.59
3.44
6.03
12.05
2.56
3.39
5.91
11.77
9
.100
.050
.010
.001
3.36
5.12
10.56
22.86
3.01
4.26
8.02
16.39
2.81
3.86
6.99
13.90
2.69
3.63
6.42
12.56
2.61
3.48
6.06
11.71
2.55
3.37
5.80
11.13
2.51
3.29
5.61
10.70
2.47
3.23
5.47
10.37
2.44
3.18
5.35
10.11
10
.100
.050
.010
.001
3.29
4.96
10.04
21.04
2.92
4.10
7.56
14.91
2.73
3.71
6.55
12.55
2.61
3.48
5.99
11.28
2.52
3.33
5.64
10.48
2.46
3.22
5.39
9.93
2.41
3.14
5.20
9.52
2.38
3.07
5.06
9.20
2.35
3.02
4.94
8.96
11
.100
.050
.010
.001
3.23
4.84
9.65
19.69
2.86
3.98
7.21
13.81
2.66
3.59
6.22
11.56
2.54
3.36
5.67
10.35
2.45
3.20
5.32
9.58
2.39
3.09
5.07
9.05
2.34
3.01
4.89
8.66
2.30
2.95
4.74
8.35
2.27
2.90
4.63
8.12
12
.100
.050
.010
.001
3.18
4.75
9.33
18.64
2.81
3.89
6.93
12.97
2.61
3.49
5.95
10.80
2.48
3.26
5.41
9.63
2.39
3.11
5.06
8.89
2.33
3.00
4.82
8.38
2.28
2.91
4.64
8.00
2.24
2.85
4.50
7.71
2.21
2.80
4.39
7.48
(continued )
38217_App_p662-690.qxd
12/20/06
09:48
Page 677
Appendix Tables
Table A.9
677
Critical Values for F Distributions (cont.)
1 numerator df
10
12
15
20
25
30
40
50
60
120
1000
60.19
241.88
6055.8
605621
60.71
243.91
6106.3
610668
61.22
245.95
6157.3
615764
61.74
248.01
6208.7
620908
62.05
249.26
6239.8
624017
62.26
250.10
6260.6
626099
62.53
251.14
6286.8
628712
62.69
251.77
6302.5
630285
62.79
252.20
6313.0
631337
63.06
253.25
6339.4
633972
63.30
254.19
6362.7
636301
9.39
19.40
99.40
999.40
9.41
19.41
99.42
999.42
9.42
19.43
99.43
999.43
9.44
19.45
99.45
999.45
9.45
19.46
99.46
999.46
9.46
19.46
99.47
999.47
9.47
19.47
99.47
999.47
9.47
19.48
99.48
999.48
9.47
19.48
99.48
999.48
9.48
19.49
99.49
999.49
9.49
19.49
99.50
999.50
5.23
8.79
27.23
129.25
5.22
8.74
27.05
128.32
5.20
8.70
26.87
127.37
5.18
8.66
26.69
126.42
5.17
8.63
26.58
125.84
5.17
8.62
26.50
125.45
5.16
8.59
26.41
124.96
5.15
8.58
26.35
124.66
5.15
8.57
26.32
124.47
5.14
8.55
26.22
123.97
5.13
8.53
26.14
123.53
3.92
5.96
14.55
48.05
3.90
5.91
14.37
47.41
3.87
5.86
14.20
46.76
3.84
5.80
14.02
46.10
3.83
5.77
13.91
45.70
3.82
5.75
13.84
45.43
3.80
5.72
13.75
45.09
3.80
5.70
13.69
44.88
3.79
5.69
13.65
44.75
3.78
5.66
13.56
44.40
3.76
5.63
13.47
44.09
3.30
4.74
10.05
26.92
3.27
4.68
9.89
26.42
3.24
4.62
9.72
25.91
3.21
4.56
9.55
25.39
3.19
4.52
9.45
25.08
3.17
4.50
9.38
24.87
3.16
4.46
9.29
24.60
3.15
4.44
9.24
24.44
3.14
4.43
9.20
24.33
3.12
4.40
9.11
24.06
3.11
4.37
9.03
23.82
2.94
4.06
7.87
18.41
2.90
4.00
7.72
17.99
2.87
3.94
7.56
17.56
2.84
3.87
7.40
17.12
2.81
3.83
7.30
16.85
2.80
3.81
7.23
16.67
2.78
3.77
7.14
16.44
2.77
3.75
7.09
16.31
2.76
3.74
7.06
16.21
2.74
3.70
6.97
15.98
2.72
3.67
6.89
15.77
2.70
3.64
6.62
14.08
2.67
3.57
6.47
13.71
2.63
3.51
6.31
13.32
2.59
3.44
6.16
12.93
2.57
3.40
6.06
12.69
2.56
3.38
5.99
12.53
2.54
3.34
5.91
12.33
2.52
3.32
5.86
12.20
2.51
3.30
5.82
12.12
2.49
3.27
5.74
11.91
2.47
3.23
5.66
11.72
2.54
3.35
5.81
11.54
2.50
3.28
5.67
11.19
2.46
3.22
5.52
10.84
2.42
3.15
5.36
10.48
2.40
3.11
5.26
10.26
2.38
3.08
5.20
10.11
2.36
3.04
5.12
9.92
2.35
3.02
5.07
9.80
2.34
3.01
5.03
9.73
2.32
2.97
4.95
9.53
2.30
2.93
4.87
9.36
2.42
3.14
5.26
9.89
2.38
3.07
5.11
9.57
2.34
3.01
4.96
9.24
2.30
2.94
4.81
8.90
2.27
2.89
4.71
8.69
2.25
2.86
4.65
8.55
2.23
2.83
4.57
8.37
2.22
2.80
4.52
8.26
2.21
2.79
4.48
8.19
2.18
2.75
4.40
8.00
2.16
2.71
4.32
7.84
2.32
2.98
4.85
8.75
2.28
2.91
4.71
8.45
2.24
2.85
4.56
8.13
2.20
2.77
4.41
7.80
2.17
2.73
4.31
7.60
2.16
2.70
4.25
7.47
2.13
2.66
4.17
7.30
2.12
2.64
4.12
7.19
2.11
2.62
4.08
7.12
2.08
2.58
4.00
6.94
2.06
2.54
3.92
6.78
2.25
2.85
4.54
7.92
2.21
2.79
4.40
7.63
2.17
2.72
4.25
7.32
2.12
2.65
4.10
7.01
2.10
2.60
4.01
6.81
2.08
2.57
3.94
6.68
2.05
2.53
3.86
6.52
2.04
2.51
3.81
6.42
2.03
2.49
3.78
6.35
2.00
2.45
3.69
6.18
1.98
2.41
3.61
6.02
2.19
2.75
4.30
7.29
2.15
2.69
4.16
7.00
2.10
2.62
4.01
6.71
2.06
2.54
3.86
6.40
2.03
2.50
3.76
6.22
2.01
2.47
3.70
6.09
1.99
2.43
3.62
5.93
1.97
2.40
3.57
5.83
1.96
2.38
3.54
5.76
1.93
2.34
3.45
5.59
1.91
2.30
3.37
5.44
(continued )
38217_App_p662-690.qxd
678
12/20/06
09:48
Page 678
Appendix Tables
Table A.9
Critical Values for F Distributions (cont.)
2 denominator df
1 numerator df
1
2
3
4
5
6
7
8
9
13
.100
.050
.010
.001
3.14
4.67
9.07
17.82
2.76
3.81
6.70
12.31
2.56
3.41
5.74
10.21
2.43
3.18
5.21
9.07
2.35
3.03
4.86
8.35
2.28
2.92
4.62
7.86
2.23
2.83
4.44
7.49
2.20
2.77
4.30
7.21
2.16
2.71
4.19
6.98
14
.100
.050
.010
.001
3.10
4.60
8.86
17.14
2.73
3.74
6.51
11.78
2.52
3.34
5.56
9.73
2.39
3.11
5.04
8.62
2.31
2.96
4.69
7.92
2.24
2.85
4.46
7.44
2.19
2.76
4.28
7.08
2.15
2.70
4.14
6.80
2.12
2.65
4.03
6.58
15
.100
.050
.010
.001
3.07
4.54
8.68
16.59
2.70
3.68
6.36
11.34
2.49
3.29
5.42
9.34
2.36
3.06
4.89
8.25
2.27
2.90
4.56
7.57
2.21
2.79
4.32
7.09
2.16
2.71
4.14
6.74
2.12
2.64
4.00
6.47
2.09
2.59
3.89
6.26
16
.100
.050
.010
.001
3.05
4.49
8.53
16.12
2.67
3.63
6.23
10.97
2.46
3.24
5.29
9.01
2.33
3.01
4.77
7.94
2.24
2.85
4.44
7.27
2.18
2.74
4.20
6.80
2.13
2.66
4.03
6.46
2.09
2.59
3.89
6.19
2.06
2.54
3.78
5.98
17
.100
.050
.010
.001
3.03
4.45
8.40
15.72
2.64
3.59
6.11
10.66
2.44
3.20
5.19
8.73
2.31
2.96
4.67
7.68
2.22
2.81
4.34
7.02
2.15
2.70
4.10
6.56
2.10
2.61
3.93
6.22
2.06
2.55
3.79
5.96
2.03
2.49
3.68
5.75
18
.100
.050
.010
.001
3.01
4.41
8.29
15.38
2.62
3.55
6.01
10.39
2.42
3.16
5.09
8.49
2.29
2.93
4.58
7.46
2.20
2.77
4.25
6.81
2.13
2.66
4.01
6.35
2.08
2.58
3.84
6.02
2.04
2.51
3.71
5.76
2.00
2.46
3.60
5.56
19
.100
.050
.010
.001
2.99
4.38
8.18
15.08
2.61
3.52
5.93
10.16
2.40
3.13
5.01
8.28
2.27
2.90
4.50
7.27
2.18
2.74
4.17
6.62
2.11
2.63
3.94
6.18
2.06
2.54
3.77
5.85
2.02
2.48
3.63
5.59
1.98
2.42
3.52
5.39
20
.100
.050
.010
.001
2.97
4.35
8.10
14.82
2.59
3.49
5.85
9.95
2.38
3.10
4.94
8.10
2.25
2.87
4.43
7.10
2.16
2.71
4.10
6.46
2.09
2.60
3.87
6.02
2.04
2.51
3.70
5.69
2.00
2.45
3.56
5.44
1.96
2.39
3.46
5.24
21
.100
.050
.010
.001
2.96
4.32
8.02
14.59
2.57
3.47
5.78
9.77
2.36
3.07
4.87
7.94
2.23
2.84
4.37
6.95
2.14
2.68
4.04
6.32
2.08
2.57
3.81
5.88
2.02
2.49
3.64
5.56
1.98
2.42
3.51
5.31
1.95
2.37
3.40
5.11
22
.100
.050
.010
.001
2.95
4.30
7.95
14.38
2.56
3.44
5.72
9.61
2.35
3.05
4.82
7.80
2.22
2.82
4.31
6.81
2.13
2.66
3.99
6.19
2.06
2.55
3.76
5.76
2.01
2.46
3.59
5.44
1.97
2.40
3.45
5.19
1.93
2.34
3.35
4.99
23
.100
.050
.010
.001
2.94
4.28
7.88
14.20
2.55
3.42
5.66
9.47
2.34
3.03
4.76
7.67
2.21
2.80
4.26
6.70
2.11
2.64
3.94
6.08
2.05
2.53
3.71
5.65
1.99
2.44
3.54
5.33
1.95
2.37
3.41
5.09
1.92
2.32
3.30
4.89
24
.100
.050
.010
.001
2.93
4.26
7.82
14.03
2.54
3.40
5.61
9.34
2.33
3.01
4.72
7.55
2.19
2.78
4.22
6.59
2.10
2.62
3.90
5.98
2.04
2.51
3.67
5.55
1.98
2.42
3.50
5.23
1.94
2.36
3.36
4.99
1.91
2.30
3.26
4.80
(continued )
38217_App_p662-690.qxd
Table A.9
12/20/06
09:48
Page 679
Appendix Tables
679
Critical Values for F Distributions (cont.)
1 numerator df
10
12
15
20
25
30
40
50
60
120
1000
2.14
2.67
4.10
6.80
2.10
2.60
3.96
6.52
2.05
2.53
3.82
6.23
2.01
2.46
3.66
5.93
1.98
2.41
3.57
5.75
1.96
2.38
3.51
5.63
1.93
2.34
3.43
5.47
1.92
2.31
3.38
5.37
1.90
2.30
3.34
5.30
1.88
2.25
3.25
5.14
1.85
2.21
3.18
4.99
2.10
2.60
3.94
6.40
2.05
2.53
3.80
6.13
2.01
2.46
3.66
5.85
1.96
2.39
3.51
5.56
1.93
2.34
3.41
5.38
1.91
2.31
3.35
5.25
1.89
2.27
3.27
5.10
1.87
2.24
3.22
5.00
1.86
2.22
3.18
4.94
1.83
2.18
3.09
4.77
1.80
2.14
3.02
4.62
2.06
2.54
3.80
6.08
2.02
2.48
3.67
5.81
1.97
2.40
3.52
5.54
1.92
2.33
3.37
5.25
1.89
2.28
3.28
5.07
1.87
2.25
3.21
4.95
1.85
2.20
3.13
4.80
1.83
2.18
3.08
4.70
1.82
2.16
3.05
4.64
1.79
2.11
2.96
4.47
1.76
2.07
2.88
4.33
2.03
2.49
3.69
5.81
1.99
2.42
3.55
5.55
1.94
2.35
3.41
5.27
1.89
2.28
3.26
4.99
1.86
2.23
3.16
4.82
1.84
2.19
3.10
4.70
1.81
2.15
3.02
4.54
1.79
2.12
2.97
4.45
1.78
2.11
2.93
4.39
1.75
2.06
2.84
4.23
1.72
2.02
2.76
4.08
2.00
2.45
3.59
5.58
1.96
2.38
3.46
5.32
1.91
2.31
3.31
5.05
1.86
2.23
3.16
4.78
1.83
2.18
3.07
4.60
1.81
2.15
3.00
4.48
1.78
2.10
2.92
4.33
1.76
2.08
2.87
4.24
1.75
2.06
2.83
4.18
1.72
2.01
2.75
4.02
1.69
1.97
2.66
3.87
1.98
2.41
3.51
5.39
1.93
2.34
3.37
5.13
1.89
2.27
3.23
4.87
1.84
2.19
3.08
4.59
1.80
2.14
2.98
4.42
1.78
2.11
2.92
4.30
1.75
2.06
2.84
4.15
1.74
2.04
2.78
4.06
1.72
2.02
2.75
4.00
1.69
1.97
2.66
3.84
1.66
1.92
2.58
3.69
1.96
2.38
3.43
5.22
1.91
2.31
3.30
4.97
1.86
2.23
3.15
4.70
1.81
2.16
3.00
4.43
1.78
2.11
2.91
4.26
1.76
2.07
2.84
4.14
1.73
2.03
2.76
3.99
1.71
2.00
2.71
3.90
1.70
1.98
2.67
3.84
1.67
1.93
2.58
3.68
1.64
1.88
2.50
3.53
1.94
2.35
3.37
5.08
1.89
2.28
3.23
4.82
1.84
2.20
3.09
4.56
1.79
2.12
2.94
4.29
1.76
2.07
2.84
4.12
1.74
2.04
2.78
4.00
1.71
1.99
2.69
3.86
1.69
1.97
2.64
3.77
1.68
1.95
2.61
3.70
1.64
1.90
2.52
3.54
1.61
1.85
2.43
3.40
1.92
2.32
3.31
4.95
1.87
2.25
3.17
4.70
1.83
2.18
3.03
4.44
1.78
2.10
2.88
4.17
1.74
2.05
2.79
4.00
1.72
2.01
2.72
3.88
1.69
1.96
2.64
3.74
1.67
1.94
2.58
3.64
1.66
1.92
2.55
3.58
1.62
1.87
2.46
3.42
1.59
1.82
2.37
3.28
1.90
2.30
3.26
4.83
1.86
2.23
3.12
4.58
1.81
2.15
2.98
4.33
1.76
2.07
2.83
4.06
1.73
2.02
2.73
3.89
1.70
1.98
2.67
3.78
1.67
1.94
2.58
3.63
1.65
1.91
2.53
3.54
1.64
1.89
2.50
3.48
1.60
1.84
2.40
3.32
1.57
1.79
2.32
3.17
1.89
2.27
3.21
4.73
1.84
2.20
3.07
4.48
1.80
2.13
2.93
4.23
1.74
2.05
2.78
3.96
1.71
2.00
2.69
3.79
1.69
1.96
2.62
3.68
1.66
1.91
2.54
3.53
1.64
1.88
2.48
3.44
1.62
1.86
2.45
3.38
1.59
1.81
2.35
3.22
1.55
1.76
2.27
3.08
1.88
2.25
3.17
4.64
1.83
2.18
3.03
4.39
1.78
2.11
2.89
4.14
1.73
2.03
2.74
3.87
1.70
1.97
2.64
3.71
1.67
1.94
2.58
3.59
1.64
1.89
2.49
3.45
1.62
1.86
2.44
3.36
1.61
1.84
2.40
3.29
1.57
1.79
2.31
3.14
1.54
1.74
2.22
2.99
(continued )
38217_App_p662-690.qxd
680
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09:48
Page 680
Appendix Tables
Table A.9
Critical Values for F Distributions (cont.)
2 denominator df
1 numerator df
1
2
3
4
5
6
7
8
9
25
.100
.050
.010
.001
2.92
4.24
7.77
13.88
2.53
3.39
5.57
9.22
2.32
2.99
4.68
7.45
2.18
2.76
4.18
6.49
2.09
2.60
3.85
5.89
2.02
2.49
3.63
5.46
1.97
2.40
3.46
5.15
1.93
2.34
3.32
4.91
1.89
2.28
3.22
4.71
26
.100
.050
.010
.001
2.91
4.23
7.72
13.74
2.52
3.37
5.53
9.12
2.31
2.98
4.64
7.36
2.17
2.74
4.14
6.41
2.08
2.59
3.82
5.80
2.01
2.47
3.59
5.38
1.96
2.39
3.42
5.07
1.92
2.32
3.29
4.83
1.88
2.27
3.18
4.64
27
.100
.050
.010
.001
2.90
4.21
7.68
13.61
2.51
3.35
5.49
9.02
2.30
2.96
4.60
7.27
2.17
2.73
4.11
6.33
2.07
2.57
3.78
5.73
2.00
2.46
3.56
5.31
1.95
2.37
3.39
5.00
1.91
2.31
3.26
4.76
1.87
2.25
3.15
4.57
28
.100
.050
.010
.001
2.89
4.20
7.64
13.50
2.50
3.34
5.45
8.93
2.29
2.95
4.57
7.19
2.16
2.71
4.07
6.25
2.06
2.56
3.75
5.66
2.00
2.45
3.53
5.24
1.94
2.36
3.36
4.93
1.90
2.29
3.23
4.69
1.87
2.24
3.12
4.50
29
.100
.050
.010
.001
2.89
4.18
7.60
13.39
2.50
3.33
5.42
8.85
2.28
2.93
4.54
7.12
2.15
2.70
4.04
6.19
2.06
2.55
3.73
5.59
1.99
2.43
3.50
5.18
1.93
2.35
3.33
4.87
1.89
2.28
3.20
4.64
1.86
2.22
3.09
4.45
30
.100
.050
.010
.001
2.88
4.17
7.56
13.29
2.49
3.32
5.39
8.77
2.28
2.92
4.51
7.05
2.14
2.69
4.02
6.12
2.05
2.53
3.70
5.53
1.98
2.42
3.47
5.12
1.93
2.33
3.30
4.82
1.88
2.27
3.17
4.58
1.85
2.21
3.07
4.39
40
.100
.050
.010
.001
2.84
4.08
7.31
12.61
2.44
3.23
5.18
8.25
2.23
2.84
4.31
6.59
2.09
2.61
3.83
5.70
2.00
2.45
3.51
5.13
1.93
2.34
3.29
4.73
1.87
2.25
3.12
4.44
1.83
2.18
2.99
4.21
1.79
2.12
2.89
4.02
50
.100
.050
.010
.001
2.81
4.03
7.17
12.22
2.41
3.18
5.06
7.96
2.20
2.79
4.20
6.34
2.06
2.56
3.72
5.46
1.97
2.40
3.41
4.90
1.90
2.29
3.19
4.51
1.84
2.20
3.02
4.22
1.80
2.13
2.89
4.00
1.76
2.07
2.78
3.82
60
.100
.050
.010
.001
2.79
4.00
7.08
11.97
2.39
3.15
4.98
7.77
2.18
2.76
4.13
6.17
2.04
2.53
3.65
5.31
1.95
2.37
3.34
4.76
1.87
2.25
3.12
4.37
1.82
2.17
2.95
4.09
1.77
2.10
2.82
3.86
1.74
2.04
2.72
3.69
100
.100
.050
.010
.001
2.76
3.94
6.90
11.50
2.36
3.09
4.82
7.41
2.14
2.70
3.98
5.86
2.00
2.46
3.51
5.02
1.91
2.31
3.21
4.48
1.83
2.19
2.99
4.11
1.78
2.10
2.82
3.83
1.73
2.03
2.69
3.61
1.69
1.97
2.59
3.44
200
.100
.050
.010
.001
2.73
3.89
6.76
11.15
2.33
3.04
4.71
7.15
2.11
2.65
3.88
5.63
1.97
2.42
3.41
4.81
1.88
2.26
3.11
4.29
1.80
2.14
2.89
3.92
1.75
2.06
2.73
3.65
1.70
1.98
2.60
3.43
1.66
1.93
2.50
3.26
1000
.100
.050
.010
.001
2.71
3.85
6.66
10.89
2.31
3.00
4.63
6.96
2.09
2.61
3.80
5.46
1.95
2.38
3.34
4.65
1.85
2.22
3.04
4.14
1.78
2.11
2.82
3.78
1.72
2.02
2.66
3.51
1.68
1.95
2.53
3.30
1.64
1.89
2.43
3.13
(continued )
38217_App_p662-690.qxd
Table A.9
12/20/06
09:48
Page 681
Appendix Tables
681
Critical Values for F Distributions (cont.)
1 numerator df
10
12
15
20
25
30
40
50
60
120
1000
1.87
2.24
3.13
4.56
1.82
2.16
2.99
4.31
1.77
2.09
2.85
4.06
1.72
2.01
2.70
3.79
1.68
1.96
2.60
3.63
1.66
1.92
2.54
3.52
1.63
1.87
2.45
3.37
1.61
1.84
2.40
3.28
1.59
1.82
2.36
3.22
1.56
1.77
2.27
3.06
1.52
1.72
2.18
2.91
1.86
2.22
3.09
4.48
1.81
2.15
2.96
4.24
1.76
2.07
2.81
3.99
1.71
1.99
2.66
3.72
1.67
1.94
2.57
3.56
1.65
1.90
2.50
3.44
1.61
1.85
2.42
3.30
1.59
1.82
2.36
3.21
1.58
1.80
2.33
3.15
1.54
1.75
2.23
2.99
1.51
1.70
2.14
2.84
1.85
2.20
3.06
4.41
1.80
2.13
2.93
4.17
1.75
2.06
2.78
3.92
1.70
1.97
2.63
3.66
1.66
1.92
2.54
3.49
1.64
1.88
2.47
3.38
1.60
1.84
2.38
3.23
1.58
1.81
2.33
3.14
1.57
1.79
2.29
3.08
1.53
1.73
2.20
2.92
1.50
1.68
2.11
2.78
1.84
2.19
3.03
4.35
1.79
2.12
2.90
4.11
1.74
2.04
2.75
3.86
1.69
1.96
2.60
3.60
1.65
1.91
2.51
3.43
1.63
1.87
2.44
3.32
1.59
1.82
2.35
3.18
1.57
1.79
2.30
3.09
1.56
1.77
2.26
3.02
1.52
1.71
2.17
2.86
1.48
1.66
2.08
2.72
1.83
2.18
3.00
4.29
1.78
2.10
2.87
4.05
1.73
2.03
2.73
3.80
1.68
1.94
2.57
3.54
1.64
1.89
2.48
3.38
1.62
1.85
2.41
3.27
1.58
1.81
2.33
3.12
1.56
1.77
2.27
3.03
1.55
1.75
2.23
2.97
1.51
1.70
2.14
2.81
1.47
1.65
2.05
2.66
1.82
2.16
2.98
4.24
1.77
2.09
2.84
4.00
1.72
2.01
2.70
3.75
1.67
1.93
2.55
3.49
1.63
1.88
2.45
3.33
1.61
1.84
2.39
3.22
1.57
1.79
2.30
3.07
1.55
1.76
2.25
2.98
1.54
1.74
2.21
2.92
1.50
1.68
2.11
2.76
1.46
1.63
2.02
2.61
1.76
2.08
2.80
3.87
1.71
2.00
2.66
3.64
1.66
1.92
2.52
3.40
1.61
1.84
2.37
3.14
1.57
1.78
2.27
2.98
1.54
1.74
2.20
2.87
1.51
1.69
2.11
2.73
1.48
1.66
2.06
2.64
1.47
1.64
2.02
2.57
1.42
1.58
1.92
2.41
1.38
1.52
1.82
2.25
1.73
2.03
2.70
3.67
1.68
1.95
2.56
3.44
1.63
1.87
2.42
3.20
1.57
1.78
2.27
2.95
1.53
1.73
2.17
2.79
1.50
1.69
2.10
2.68
1.46
1.63
2.01
2.53
1.44
1.60
1.95
2.44
1.42
1.58
1.91
2.38
1.38
1.51
1.80
2.21
1.33
1.45
1.70
2.05
1.71
1.99
2.63
3.54
1.66
1.92
2.50
3.32
1.60
1.84
2.35
3.08
1.54
1.75
2.20
2.83
1.50
1.69
2.10
2.67
1.48
1.65
2.03
2.55
1.44
1.59
1.94
2.41
1.41
1.56
1.88
2.32
1.40
1.53
1.84
2.25
1.35
1.47
1.73
2.08
1.30
1.40
1.62
1.92
1.66
1.93
2.50
3.30
1.61
1.85
2.37
3.07
1.56
1.77
2.22
2.84
1.49
1.68
2.07
2.59
1.45
1.62
1.97
2.43
1.42
1.57
1.89
2.32
1.38
1.52
1.80
2.17
1.35
1.48
1.74
2.08
1.34
1.45
1.69
2.01
1.28
1.38
1.57
1.83
1.22
1.30
1.45
1.64
1.63
1.88
2.41
3.12
1.58
1.80
2.27
2.90
1.52
1.72
2.13
2.67
1.46
1.62
1.97
2.42
1.41
1.56
1.87
2.26
1.38
1.52
1.79
2.15
1.34
1.46
1.69
2.00
1.31
1.41
1.63
1.90
1.29
1.39
1.58
1.83
1.23
1.30
1.45
1.64
1.16
1.21
1.30
1.43
1.61
1.84
2.34
2.99
1.55
1.76
2.20
2.77
1.49
1.68
2.06
2.54
1.43
1.58
1.90
2.30
1.38
1.52
1.79
2.14
1.35
1.47
1.72
2.02
1.30
1.41
1.61
1.87
1.27
1.36
1.54
1.77
1.25
1.33
1.50
1.69
1.18
1.24
1.35
1.49
1.08
1.11
1.16
1.22
38217_App_p662-690.qxd
682
12/20/06
09:48
Page 682
Appendix Tables
Table A.10
Critical Values for Studentized Range Distributions
m
2
3
4
5
6
7
8
9
10
11
12
5
.05
.01
3.64
5.70
4.60
6.98
5.22
7.80
5.67
8.42
6.03
8.91
6.33
9.32
6.58
9.67
6.80
9.97
6.99
10.24
7.17
10.48
7.32
10.70
6
.05
.01
3.46
5.24
4.34
6.33
4.90
7.03
5.30
7.56
5.63
7.97
5.90
8.32
6.12
8.61
6.32
8.87
6.49
9.10
6.65
9.30
6.79
9.48
7
.05
.01
3.34
4.95
4.16
5.92
4.68
6.54
5.06
7.01
5.36
7.37
5.61
7.68
5.82
7.94
6.00
8.17
6.16
8.37
6.30
8.55
6.43
8.71
8
.05
.01
3.26
4.75
4.04
5.64
4.53
6.20
4.89
6.62
5.17
6.96
5.40
7.24
5.60
7.47
5.77
7.68
5.92
7.86
6.05
8.03
6.18
8.18
9
.05
.01
3.20
4.60
3.95
5.43
4.41
5.96
4.76
6.35
5.02
6.66
5.24
6.91
5.43
7.13
5.59
7.33
5.74
7.49
5.87
7.65
5.98
7.78
10
.05
.01
3.15
4.48
3.88
5.27
4.33
5.77
4.65
6.14
4.91
6.43
5.12
6.67
5.30
6.87
5.46
7.05
5.60
7.21
5.72
7.36
5.83
7.49
11
.05
.01
3.11
4.39
3.82
5.15
4.26
5.62
4.57
5.97
4.82
6.25
5.03
6.48
5.20
6.67
5.35
6.84
5.49
6.99
5.61
7.13
5.71
7.25
12
.05
.01
3.08
4.32
3.77
5.05
4.20
5.50
4.51
5.84
4.75
6.10
4.95
6.32
5.12
6.51
5.27
6.67
5.39
6.81
5.51
6.94
5.61
7.06
13
.05
.01
3.06
4.26
3.73
4.96
4.15
5.40
4.45
5.73
4.69
5.98
4.88
6.19
5.05
6.37
5.19
6.53
5.32
6.67
5.43
6.79
5.53
6.90
14
.05
.01
3.03
4.21
3.70
4.89
4.11
5.32
4.41
5.63
4.64
5.88
4.83
6.08
4.99
6.26
5.13
6.41
5.25
6.54
5.36
6.66
5.46
6.77
15
.05
.01
3.01
4.17
3.67
4.84
4.08
5.25
4.37
5.56
4.59
5.80
4.78
5.99
4.94
6.16
5.08
6.31
5.20
6.44
5.31
6.55
5.40
6.66
16
.05
.01
3.00
4.13
3.65
4.79
4.05
5.19
4.33
5.49
4.56
5.72
4.74
5.92
4.90
6.08
5.03
6.22
5.15
6.35
5.26
6.46
5.35
6.56
17
.05
.01
2.98
4.10
3.63
4.74
4.02
5.14
4.30
5.43
4.52
5.66
4.70
5.85
4.86
6.01
4.99
6.15
5.11
6.27
5.21
6.38
5.31
6.48
18
.05
.01
2.97
4.07
3.61
4.70
4.00
5.09
4.28
5.38
4.49
5.60
4.67
5.79
4.82
5.94
4.96
6.08
5.07
6.20
5.17
6.31
5.27
6.41
19
.05
.01
2.96
4.05
3.59
4.67
3.98
5.05
4.25
5.33
4.47
5.55
4.65
5.73
4.79
5.89
4.92
6.02
5.04
6.14
5.14
6.25
5.23
6.34
20
.05
.01
2.95
4.02
3.58
4.64
3.96
5.02
4.23
5.29
4.45
5.51
4.62
5.69
4.77
5.84
4.90
5.97
5.01
6.09
5.11
6.19
5.20
6.28
24
.05
.01
2.92
3.96
3.53
4.55
3.90
4.91
4.17
5.17
4.37
5.37
4.54
5.54
4.68
5.69
4.81
5.81
4.92
5.92
5.01
6.02
5.10
6.11
30
.05
.01
2.89
3.89
3.49
4.45
3.85
4.80
4.10
5.05
4.30
5.24
4.46
5.40
4.60
5.54
4.72
5.65
4.82
5.76
4.92
5.85
5.00
5.93
40
.05
.01
2.86
3.82
3.44
4.37
3.79
4.70
4.04
4.93
4.23
5.11
4.39
5.26
4.52
5.39
4.63
5.50
4.73
5.60
4.82
5.69
4.90
5.76
60
.05
.01
2.83
3.76
3.40
4.28
3.74
4.59
3.98
4.82
4.16
4.99
4.31
5.13
4.44
5.25
4.55
5.36
4.65
5.45
4.73
5.53
4.81
5.60
120
.05
.01
2.80
3.70
3.36
4.20
3.68
4.50
3.92
4.71
4.10
4.87
4.24
5.01
4.36
5.12
4.47
5.21
4.56
5.30
4.64
5.37
4.71
5.44
∞
.05
.01
2.77
3.64
3.31
4.12
3.63
4.40
3.86
4.60
4.03
4.76
4.17
4.88
4.29
4.99
4.39
5.08
4.47
5.16
4.55
5.23
4.62
5.29
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Appendix Tables
Table A.11
683
Chi-Squared Curve Tail Areas
Upper-tail Area
1
2
3
4
5
.100
.100
.095
.090
.085
.080
.075
.070
.065
.060
.055
.050
.045
.040
.035
.030
.025
.020
.015
.010
.005
.001
.001
2.70
2.70
2.78
2.87
2.96
3.06
3.17
3.28
3.40
3.53
3.68
3.84
4.01
4.21
4.44
4.70
5.02
5.41
5.91
6.63
7.87
10.82
10.82
4.60
4.60
4.70
4.81
4.93
5.05
5.18
5.31
5.46
5.62
5.80
5.99
6.20
6.43
6.70
7.01
7.37
7.82
8.39
9.21
10.59
13.81
13.81
6.25
6.25
6.36
6.49
6.62
6.75
6.90
7.06
7.22
7.40
7.60
7.81
8.04
8.31
8.60
8.94
9.34
9.83
10.46
11.34
12.83
16.26
16.26
7.77
7.77
7.90
8.04
8.18
8.33
8.49
8.66
8.84
9.04
9.25
9.48
9.74
10.02
10.34
10.71
11.14
11.66
12.33
13.27
14.86
18.46
18.46
9.23
9.23
9.37
9.52
9.67
9.83
10.00
10.19
10.38
10.59
10.82
11.07
11.34
11.64
11.98
12.37
12.83
13.38
14.09
15.08
16.74
20.51
20.51
Upper-tail Area
6
7
8
9
10
.100
.100
.095
.090
.085
.080
.075
.070
.065
.060
.055
.050
.045
.040
.035
.030
.025
.020
.015
.010
.005
.001
.001
10.64
10.64
10.79
10.94
11.11
11.28
11.46
11.65
11.86
12.08
12.33
12.59
12.87
13.19
13.55
13.96
14.44
15.03
15.77
16.81
18.54
22.45
22.45
12.01
12.01
12.17
12.33
12.50
12.69
12.88
13.08
13.30
13.53
13.79
14.06
14.36
14.70
15.07
15.50
16.01
16.62
17.39
18.47
20.27
24.32
24.32
13.36
13.36
13.52
13.69
13.87
14.06
14.26
14.48
14.71
14.95
15.22
15.50
15.82
16.17
16.56
17.01
17.53
18.16
18.97
20.09
21.95
26.12
26.12
14.68
14.68
14.85
15.03
15.22
15.42
15.63
15.85
16.09
16.34
16.62
16.91
17.24
17.60
18.01
18.47
19.02
19.67
20.51
21.66
23.58
27.87
27.87
15.98
15.98
16.16
16.35
16.54
16.75
16.97
17.20
17.44
17.71
17.99
18.30
18.64
19.02
19.44
19.92
20.48
21.16
22.02
23.20
25.18
29.58
29.58
(continued )
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Appendix Tables
Table A.11
Chi-Squared Curve Tail Areas (cont.)
Upper-tail Area
.100
.100
.095
.090
.085
.080
.075
.070
.065
.060
.055
.050
.045
.040
.035
.030
.025
.020
.015
.010
.005
.001
.001
Upper-tail Area
.100
.100
.095
.090
.085
.080
.075
.070
.065
.060
.055
.050
.045
.040
.035
.030
.025
.020
.015
.010
.005
.001
.001
11
12
13
14
15
17.27
17.27
17.45
17.65
17.85
18.06
18.29
18.53
18.78
19.06
19.35
19.67
20.02
20.41
20.84
21.34
21.92
22.61
23.50
24.72
26.75
31.26
31.26
18.54
18.54
18.74
18.93
19.14
19.36
19.60
19.84
20.11
20.39
20.69
21.02
21.38
21.78
22.23
22.74
23.33
24.05
24.96
26.21
28.29
32.90
32.90
19.81
19.81
20.00
20.21
20.42
20.65
20.89
21.15
21.42
21.71
22.02
22.36
22.73
23.14
23.60
24.12
24.73
25.47
26.40
27.68
29.81
34.52
34.52
21.06
21.06
21.26
21.47
21.69
21.93
22.17
22.44
22.71
23.01
23.33
23.68
24.06
24.48
24.95
25.49
26.11
26.87
27.82
29.14
31.31
36.12
36.12
22.30
22.30
22.51
22.73
22.95
23.19
23.45
23.72
24.00
24.31
24.63
24.99
25.38
25.81
26.29
26.84
27.48
28.25
29.23
30.57
32.80
37.69
37.69
16
17
18
19
20
23.54
23.54
23.75
23.97
24.21
24.45
24.71
24.99
25.28
25.59
25.93
26.29
26.69
27.13
27.62
28.19
28.84
29.63
30.62
32.00
34.26
39.25
39.25
24.77
24.76
24.98
25.21
25.45
25.70
25.97
26.25
26.55
26.87
27.21
27.58
27.99
28.44
28.94
29.52
30.19
30.99
32.01
33.40
35.71
40.78
40.78
25.98
25.98
26.21
26.44
26.68
26.94
27.21
27.50
27.81
28.13
28.48
28.86
29.28
29.74
30.25
30.84
31.52
32.34
33.38
34.80
37.15
42.31
42.31
27.20
27.20
27.43
27.66
27.91
28.18
28.45
28.75
29.06
29.39
29.75
30.14
30.56
31.03
31.56
32.15
32.85
33.68
34.74
36.19
38.58
43.81
43.81
28.41
28.41
28.64
28.88
29.14
29.40
29.69
29.99
30.30
30.64
31.01
31.41
31.84
32.32
32.85
33.46
34.16
35.01
36.09
37.56
39.99
45.31
45.31
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Appendix Tables
Table A.12
Critical Values for the Ryan–Joiner Test of Normality
n
5
10
15
20
25
30
40
50
60
75
.10
.05
.01
.9033
.9347
.9506
.9600
.9662
.9707
.9767
.9807
.9835
.9865
.8804
.9180
.9383
.9503
.9582
.9639
.9715
.9764
.9799
.9835
.8320
.8804
.9110
.9290
.9408
.9490
.9597
.9664
.9710
.9757
685
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Appendix Tables
Table A.13
n
c1
P0(S c1)
3
4
6
9
10
13
14
15
17
19
20
21
22
24
26
28
28
30
32
34
35
36
34
37
39
42
44
41
44
47
50
52
48
52
55
59
61
56
60
61
64
68
71
64
65
69
70
74
.125
.125
.062
.094
.062
.031
.109
.047
.031
.016
.109
.055
.023
.008
.098
.055
.027
.012
.008
.004
.102
.049
.027
.010
.004
.097
.053
.024
.010
.005
.103
.051
.027
.009
.005
.102
.055
.046
.026
.010
.005
.108
.095
.055
.047
.024
5
6
7
8
9
10
11
12
13
P0(S c1) P(S c1 when H0 is true)
Critical Values for the Wilcoxon Signed-Rank Test
n
14
15
16
17
18
19
20
c1
P0(S c1)
78
79
81
73
74
79
84
89
92
83
84
89
90
95
100
101
104
93
94
100
106
112
113
116
104
105
112
118
125
129
116
124
131
138
143
128
136
137
144
152
157
140
150
158
167
172
.011
.009
.005
.108
.097
.052
.025
.010
.005
.104
.094
.053
.047
.024
.011
.009
.005
.106
.096
.052
.025
.011
.009
.005
.103
.095
.049
.025
.010
.005
.098
.049
.024
.010
.005
.098
.052
.048
.025
.010
.005
.101
.049
.024
.010
.005
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Appendix Tables
Table A.14
n
c
P0(W c)
3
3
4
15
17
18
20
21
22
23
24
24
26
27
27
28
29
30
24
25
26
27
28
29
30
30
32
33
34
33
35
36
37
36
38
40
41
36
37
39
.05
.057
.029
.036
.018
.048
.024
.012
.058
.017
.008
.042
.024
.012
.006
.057
.029
.014
.056
.032
.016
.008
.057
.019
.010
.005
.055
.021
.012
.006
.055
.024
.008
.004
.048
.028
.008
5
6
7
8
4
4
5
6
7
8
5
P0(W c) P(W c when H0 is true)
Critical Values for the Wilcoxon Rank-Sum Test
m
5
687
m
n
6
7
8
6
6
7
8
7
7
8
8
8
c
P0(W c)
40
40
41
43
44
43
45
47
48
47
49
51
52
50
52
54
55
54
56
58
60
58
61
63
65
66
68
71
72
71
73
76
78
84
87
90
92
.004
.041
.026
.009
.004
.053
.024
.009
.005
.047
.023
.009
.005
.047
.021
.008
.004
.051
.026
.011
.004
.054
.021
.01
.004
.049
.027
.009
.006
.047
.027
.01
.005
.052
.025
.01
.005
38217_App_p662-690.qxd
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5
6
7
8
9
10
11
12
09:48
Page 688
Appendix Tables
Table A.15
n
12/20/06
Critical Values for the Wilcoxon Signed-Rank Interval
Confidence
Level (%)
c
n
93.8
87.5
96.9
93.7
90.6
98.4
95.3
89.1
99.2
94.5
89.1
99.2
94.5
90.2
99.0
95.1
89.5
99.0
94.6
89.8
99.1
94.8
90.8
15
14
21
20
19
28
26
24
36
32
30
44
39
37
52
47
44
61
55
52
71
64
61
13
14
15
16
17
18
19
(x(n(n1)/2c1), x(c))
Confidence
Level (%)
c
n
99.0
95.2
90.6
99.1
95.1
89.6
99.0
95.2
90.5
99.1
94.9
89.5
99.1
94.9
90.2
99.0
95.2
90.1
99.1
95.1
90.4
81
74
70
93
84
79
104
95
90
117
106
100
130
118
112
143
131
124
158
144
137
20
21
22
23
24
25
Confidence
Level (%)
99.1
95.2
90.3
99.0
95.0
89.7
99.0
95.0
90.2
99.0
95.2
90.2
99.0
95.1
89.9
99.0
95.2
89.9
c
173
158
150
188
172
163
204
187
178
221
203
193
239
219
208
257
236
224
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Appendix Tables
Table A.16
Critical Values for the Wilcoxon Rank-Sum Interval
689
(dij(mnc1), dij(c))
Smaller Sample Size
5
6
7
8
Larger
Sample Size
Confidence
Level (%)
c
Confidence
Level (%)
c
Confidence
Level (%)
c
Confidence
Level (%)
c
5
99.2
94.4
90.5
99.1
94.8
91.8
99.0
95.2
89.4
98.9
95.5
90.7
98.8
95.8
88.8
99.2
94.5
90.1
99.1
94.8
91.0
99.1
95.2
89.6
25
22
21
29
26
25
33
30
28
37
34
32
41
38
35
46
41
39
50
45
43
54
49
46
99.1
95.9
90.7
99.2
94.9
89.9
99.2
95.7
89.2
99.2
95.0
91.2
98.9
94.4
90.7
99.0
95.2
90.2
99.0
94.7
89.8
34
31
29
39
35
33
44
40
37
49
44
42
53
48
46
58
53
50
63
57
54
98.9
94.7
90.3
99.1
94.6
90.6
99.2
94.5
90.9
99.0
94.5
89.1
98.9
95.6
89.6
99.0
95.5
90.0
44
40
38
50
45
43
56
50
48
61
55
52
66
61
57
72
66
62
99.0
95.0
89.5
98.9
95.4
90.7
99.1
94.5
89.9
99.1
94.9
90.9
99.0
95.3
90.2
56
51
48
62
57
54
69
62
59
75
68
65
81
74
70
6
7
8
9
10
11
12
Smaller Sample Size
9
10
11
12
Larger
Sample Size
Confidence
Level (%)
c
Confidence
Level (%)
c
Confidence
Level (%)
c
Confidence
Level (%)
c
9
98.9
95.0
90.6
99.0
94.7
90.5
99.0
95.4
90.5
99.1
95.1
90.5
69
63
60
76
69
66
83
76
72
90
82
78
99.1
94.8
89.5
99.0
94.9
90.1
99.1
95.0
90.7
84
76
72
91
83
79
99
90
86
98.9
95.3
89.9
99.1
94.9
89.6
99
91
86
108
98
93
99.0
94.8
89.9
116
106
101
10
11
12
0
.2
.4
.6
.8
1.0
0
.2
0.4
99
0.4
0.8
1.2
1.2
14
29 19
0.8
9
19 14 9 6
3
6
74
49
1.6
39
1.6
4
2.4
2.8
2.0
2.4
3
4
2.8
df 2
.01, one-tailed
2.0
df 2
3.2
3.2
d
d
0
.2
.4
.6
.8
1.0
0
.2
.4
.6
.8
74
74
49
0.4
99
0.4
99
0.8
0.8
19
1.2
1.2
14
14
1.6
39
29
19
1.6
9
9
2.4
3
2.8
2
2.0
6
2.4
4
2.8
3
d
3.2
df 2
.01, two-tailed
4
39
49
2.0
6
29
df 1
.05, two-tailed
d
09:48
.4
99
74
49
39
29
.05, one-tailed
1.0
12/20/06
.6
.8
1.0
Curves for t Tests
690
Table A.17
38217_App_p662-690.qxd
Page 690
Appendix Tables