Appendix C
Tables
Table A
Factorials
Table B
The Binomial Distribution
Table C
The Poisson Distribution
n
n!
Table D
Random Numbers
0
1
Table E
The Standard Normal Distribution
1
1
Table F
The t Distribution
2
2
Table G
The Chi-Square Distribution
3
6
Table H
The F Distribution
4
24
Table I
Critical Values for the PPMC
5
120
Table J
Critical Values for the Sign Test
Table K
Critical Values for the Wilcoxon Signed-Rank Test
Table L
Critical Values for the Rank Correlation Coefficient
Table M
Critical Values for the Number of Runs
Table N
Critical Values for the Tukey Test
Table A
Factorials
6
720
7
5,040
8
40,320
9
362,880
10
3,628,800
11
39,916,800
12
479,001,600
13
6,227,020,800
14
87,178,291,200
15
1,307,674,368,000
16
20,922,789,888,000
17
355,687,428,096,000
18
6,402,373,705,728,000
19
121,645,100,408,832,000
20
2,432,902,008,176,640,000
A–17
770
Appendix C Tables
Table B
The Binomial Distribution
p
n
x
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.95
2
0
1
2
0
1
2
3
0
1
2
3
4
0
1
2
3
4
5
0
1
2
3
4
5
6
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
8
0.902
0.095
0.002
0.857
0.135
0.007
0.810
0.180
0.010
0.729
0.243
0.027
0.001
0.656
0.292
0.049
0.004
0.640
0.320
0.040
0.512
0.384
0.096
0.008
0.410
0.410
0.154
0.026
0.002
0.328
0.410
0.205
0.051
0.006
0.490
0.420
0.090
0.343
0.441
0.189
0.027
0.240
0.412
0.265
0.076
0.008
0.168
0.360
0.309
0.132
0.028
0.002
0.118
0.303
0.324
0.185
0.060
0.010
0.001
0.082
0.247
0.318
0.227
0.097
0.025
0.004
0.360
0.480
0.160
0.216
0.432
0.288
0.064
0.130
0.346
0.346
0.154
0.026
0.078
0.259
0.346
0.230
0.077
0.010
0.047
0.187
0.311
0.276
0.138
0.037
0.004
0.028
0.131
0.261
0.290
0.194
0.077
0.017
0.002
0.017
0.090
0.209
0.279
0.232
0.124
0.041
0.008
0.001
0.250
0.500
0.250
0.125
0.375
0.375
0.125
0.062
0.250
0.375
0.250
0.062
0.031
0.156
0.312
0.312
0.156
0.031
0.016
0.094
0.234
0.312
0.234
0.094
0.016
0.008
0.055
0.164
0.273
0.273
0.164
0.055
0.008
0.004
0.031
0.109
0.219
0.273
0.219
0.109
0.031
0.004
0.160
0.480
0.360
0.064
0.288
0.432
0.216
0.026
0.154
0.346
0.346
0.130
0.010
0.077
0.230
0.346
0.259
0.078
0.004
0.037
0.138
0.276
0.311
0.187
0.047
0.002
0.017
0.077
0.194
0.290
0.261
0.131
0.028
0.001
0.008
0.041
0.124
0.232
0.279
0.209
0.090
0.017
0.090
0.420
0.490
0.027
0.189
0.441
0.343
0.008
0.076
0.265
0.412
0.240
0.002
0.028
0.132
0.309
0.360
0.168
0.001
0.010
0.060
0.185
0.324
0.303
0.118
0.040
0.320
0.640
0.008
0.096
0.384
0.512
0.002
0.026
0.154
0.410
0.410
0.010
0.180
0.810
0.001
0.027
0.243
0.729
0.002
0.095
0.902
3
4
5
6
7
8
A–18
0.815
0.171
0.014
0.774
0.204
0.021
0.001
0.590
0.328
0.073
0.008
0.735
0.232
0.031
0.002
0.531
0.354
0.098
0.015
0.001
0.262
0.393
0.246
0.082
0.015
0.002
0.698
0.257
0.041
0.004
0.478
0.372
0.124
0.023
0.003
0.210
0.367
0.275
0.115
0.029
0.004
0.430
0.383
0.149
0.033
0.005
0.168
0.336
0.294
0.147
0.046
0.009
0.001
0.663
0.279
0.051
0.005
0.058
0.198
0.296
0.254
0.136
0.047
0.010
0.001
0.007
0.135
0.857
0.004
0.049
0.292
0.656
0.014
0.171
0.815
0.006
0.051
0.205
0.410
0.328
0.008
0.073
0.328
0.590
0.001
0.021
0.204
0.774
0.002
0.015
0.082
0.246
0.393
0.262
0.001
0.015
0.098
0.354
0.531
0.002
0.031
0.232
0.735
0.004
0.025
0.097
0.227
0.318
0.247
0.082
0.004
0.029
0.115
0.275
0.367
0.210
0.003
0.023
0.124
0.372
0.478
0.004
0.041
0.257
0.698
0.001
0.010
0.047
0.136
0.254
0.296
0.198
0.058
0.001
0.009
0.046
0.147
0.294
0.336
0.168
0.005
0.033
0.149
0.383
0.430
0.005
0.051
0.279
0.663
Appendix C Tables
771
(continued)
Table B
p
n
x
0.05
0.1
0.2
0.3
0.4
0.5
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
12
0.630
0.299
0.063
0.008
0.001
0.387
0.387
0.172
0.045
0.007
0.001
0.134
0.302
0.302
0.176
0.066
0.017
0.003
0.040
0.156
0.267
0.267
0.172
0.074
0.021
0.004
0.010
0.060
0.161
0.251
0.251
0.167
0.074
0.021
0.004
0.349
0.387
0.194
0.057
0.011
0.001
0.107
0.268
0.302
0.201
0.088
0.026
0.006
0.001
0.028
0.121
0.233
0.267
0.200
0.103
0.037
0.009
0.001
0.006
0.040
0.121
0.215
0.251
0.201
0.111
0.042
0.011
0.002
0.002
0.018
0.070
0.164
0.246
0.246
0.164
0.070
0.018
0.002
0.001
0.010
0.044
0.117
0.205
0.246
0.205
0.117
0.044
0.010
0.001
0.086
0.236
0.295
0.221
0.111
0.039
0.010
0.002
0.020
0.093
0.200
0.257
0.220
0.132
0.057
0.017
0.004
0.001
0.004
0.027
0.089
0.177
0.236
0.221
0.147
0.070
0.023
0.005
0.001
0.069
0.206
0.283
0.236
0.133
0.053
0.016
0.003
0.001
0.014
0.071
0.168
0.240
0.231
0.158
0.079
0.029
0.008
0.001
0.002
0.017
0.064
0.142
0.213
0.227
0.177
0.101
0.042
0.012
0.002
10
11
12
0.599
0.315
0.075
0.010
0.001
0.569
0.329
0.087
0.014
0.001
0.540
0.341
0.099
0.017
0.002
0.314
0.384
0.213
0.071
0.016
0.002
0.282
0.377
0.230
0.085
0.021
0.004
0.005
0.027
0.081
0.161
0.226
0.226
0.161
0.081
0.027
0.005
0.003
0.016
0.054
0.121
0.193
0.226
0.193
0.121
0.054
0.016
0.003
0.6
0.7
0.8
0.9
0.95
0.004
0.021
0.074
0.167
0.251
0.251
0.161
0.060
0.010
0.004
0.021
0.074
0.172
0.267
0.267
0.156
0.040
0.003
0.017
0.066
0.176
0.302
0.302
0.134
0.001
0.007
0.045
0.172
0.387
0.387
0.001
0.008
0.063
0.299
0.630
0.002
0.011
0.042
0.111
0.201
0.251
0.215
0.121
0.040
0.006
0.001
0.009
0.037
0.103
0.200
0.267
0.233
0.121
0.028
0.001
0.006
0.026
0.088
0.201
0.302
0.268
0.107
0.001
0.011
0.057
0.194
0.387
0.349
0.001
0.010
0.075
0.315
0.599
0.001
0.005
0.023
0.070
0.147
0.221
0.236
0.177
0.089
0.027
0.004
0.001
0.004
0.017
0.057
0.132
0.220
0.257
0.200
0.093
0.020
0.002
0.010
0.039
0.111
0.221
0.295
0.236
0.086
0.002
0.016
0.071
0.213
0.384
0.314
0.001
0.014
0.087
0.329
0.569
0.002
0.012
0.042
0.101
0.177
0.227
0.213
0.142
0.064
0.017
0.002
0.001
0.008
0.029
0.079
0.158
0.231
0.240
0.168
0.071
0.014
0.001
0.003
0.016
0.053
0.133
0.236
0.283
0.206
0.069
0.004
0.021
0.085
0.230
0.377
0.282
0.002
0.017
0.099
0.341
0.540
A–19
772
Appendix C Tables
(continued)
Table B
p
n
x
0.05
0.1
0.2
0.3
0.4
13
0
1
2
3
4
5
6
7
8
9
10
11
12
13
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0.513
0.351
0.111
0.021
0.003
0.254
0.367
0.245
0.100
0.028
0.006
0.001
0.055
0.179
0.268
0.246
0.154
0.069
0.023
0.006
0.001
0.010
0.054
0.139
0.218
0.234
0.180
0.103
0.044
0.014
0.003
0.001
0.001
0.011
0.045
0.111
0.184
0.221
0.197
0.131
0.066
0.024
0.006
0.001
0.007
0.041
0.113
0.194
0.229
0.196
0.126
0.062
0.023
0.007
0.001
0.001
0.007
0.032
0.085
0.155
0.207
0.207
0.157
0.092
0.041
0.014
0.003
0.001
14
15
A–20
0.488
0.359
0.123
0.026
0.004
0.463
0.366
0.135
0.031
0.005
0.001
0.229
0.356
0.257
0.114
0.035
0.008
0.001
0.206
0.343
0.267
0.129
0.043
0.010
0.002
0.044
0.154
0.250
0.250
0.172
0.086
0.032
0.009
0.002
0.035
0.132
0.231
0.250
0.188
0.103
0.043
0.014
0.003
0.001
0.005
0.031
0.092
0.170
0.219
0.206
0.147
0.081
0.035
0.012
0.003
0.001
0.005
0.022
0.063
0.127
0.186
0.207
0.177
0.118
0.061
0.024
0.007
0.002
0.5
0.002
0.010
0.035
0.087
0.157
0.209
0.209
0.157
0.087
0.035
0.010
0.002
0.001
0.006
0.022
0.061
0.122
0.183
0.209
0.183
0.122
0.061
0.022
0.006
0.001
0.003
0.014
0.042
0.092
0.153
0.196
0.196
0.153
0.092
0.042
0.014
0.003
0.6
0.7
0.8
0.9
0.95
0.001
0.006
0.024
0.066
0.131
0.197
0.221
0.184
0.111
0.045
0.011
0.001
0.001
0.003
0.014
0.044
0.103
0.180
0.234
0.218
0.139
0.054
0.010
0.001
0.006
0.023
0.069
0.154
0.246
0.268
0.179
0.055
0.001
0.006
0.028
0.100
0.245
0.367
0.254
0.003
0.021
0.111
0.351
0.513
0.001
0.003
0.014
0.041
0.092
0.157
0.207
0.207
0.155
0.085
0.032
0.007
0.001
0.001
0.007
0.023
0.062
0.126
0.196
0.229
0.194
0.113
0.041
0.007
0.002
0.009
0.032
0.086
0.172
0.250
0.250
0.154
0.044
0.001
0.008
0.035
0.114
0.257
0.356
0.229
0.004
0.026
0.123
0.359
0.488
0.001
0.003
0.012
0.035
0.081
0.147
0.206
0.219
0.170
0.092
0.031
0.005
0.001
0.003
0.014
0.043
0.103
0.188
0.250
0.231
0.132
0.035
0.002
0.010
0.043
0.129
0.267
0.343
0.206
0.001
0.005
0.031
0.135
0.366
0.463
0.002
0.007
0.024
0.061
0.118
0.177
0.207
0.186
0.127
0.063
0.022
0.005
Appendix C Tables
773
(continued)
Table B
p
n
x
0.05
0.1
0.2
0.3
16
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
0.440
0.371
0.146
0.036
0.006
0.001
0.185
0.329
0.275
0.142
0.051
0.014
0.003
0.028
0.113
0.211
0.246
0.200
0.120
0.055
0.020
0.006
0.001
0.003
0.023
0.073
0.146
0.204
0.210
0.165
0.101
0.049
0.019
0.006
0.001
17
0.418
0.374
0.158
0.041
0.008
0.001
0.167
0.315
0.280
0.156
0.060
0.017
0.004
0.001
0.023
0.096
0.191
0.239
0.209
0.136
0.068
0.027
0.008
0.002
0.002
0.017
0.058
0.125
0.187
0.208
0.178
0.120
0.064
0.028
0.009
0.003
0.001
0.4
0.003
0.015
0.047
0.101
0.162
0.198
0.189
0.142
0.084
0.039
0.014
0.004
0.001
0.002
0.010
0.034
0.080
0.138
0.184
0.193
0.161
0.107
0.057
0.024
0.008
0.002
0.5
0.002
0.009
0.028
0.067
0.122
0.175
0.196
0.175
0.122
0.067
0.028
0.009
0.002
0.001
0.005
0.018
0.047
0.094
0.148
0.185
0.185
0.148
0.094
0.047
0.018
0.005
0.001
0.6
0.001
0.004
0.014
0.039
0.084
0.142
0.189
0.198
0.162
0.101
0.047
0.015
0.003
0.002
0.008
0.024
0.057
0.107
0.161
0.193
0.184
0.138
0.080
0.034
0.010
0.002
0.7
0.8
0.9
0.95
0.001
0.006
0.019
0.049
0.101
0.165
0.210
0.204
0.146
0.073
0.023
0.003
0.001
0.006
0.020
0.055
0.120
0.200
0.246
0.211
0.113
0.028
0.003
0.014
0.051
0.142
0.275
0.329
0.185
0.001
0.006
0.036
0.146
0.371
0.440
0.001
0.003
0.009
0.028
0.064
0.120
0.178
0.208
0.187
0.125
0.058
0.017
0.002
0.002
0.008
0.027
0.068
0.136
0.209
0.239
0.191
0.096
0.023
0.001
0.004
0.017
0.060
0.156
0.280
0.315
0.167
0.001
0.008
0.041
0.158
0.374
0.418
A–21
774
Appendix C Tables
(continued)
Table B
p
n
x
0.05
0.1
0.2
0.3
18
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0.397
0.376
0.168
0.047
0.009
0.001
0.150
0.300
0.284
0.168
0.070
0.022
0.005
0.001
0.018
0.081
0.172
0.230
0.215
0.151
0.082
0.035
0.012
0.003
0.001
0.002
0.013
0.046
0.105
0.168
0.202
0.187
0.138
0.081
0.039
0.015
0.005
0.001
19
A–22
0.377
0.377
0.179
0.053
0.011
0.002
0.135
0.285
0.285
0.180
0.080
0.027
0.007
0.001
0.014
0.068
0.154
0.218
0.218
0.164
0.095
0.044
0.017
0.005
0.001
0.001
0.009
0.036
0.087
0.149
0.192
0.192
0.153
0.098
0.051
0.022
0.008
0.002
0.001
0.4
0.001
0.007
0.025
0.061
0.115
0.166
0.189
0.173
0.128
0.077
0.037
0.015
0.004
0.001
0.001
0.005
0.017
0.047
0.093
0.145
0.180
0.180
0.146
0.098
0.053
0.024
0.008
0.002
0.001
0.5
0.001
0.003
0.012
0.033
0.071
0.121
0.167
0.185
0.167
0.121
0.071
0.033
0.012
0.003
0.001
0.002
0.007
0.022
0.052
0.096
0.144
0.176
0.176
0.144
0.096
0.052
0.022
0.007
0.002
0.6
0.001
0.004
0.015
0.037
0.077
0.128
0.173
0.189
0.166
0.115
0.061
0.025
0.007
0.001
0.001
0.002
0.008
0.024
0.053
0.098
0.146
0.180
0.180
0.145
0.093
0.047
0.017
0.005
0.001
0.7
0.8
0.9
0.95
0.001
0.005
0.015
0.039
0.081
0.138
0.187
0.202
0.168
0.105
0.046
0.013
0.002
0.001
0.003
0.012
0.035
0.082
0.151
0.215
0.230
0.172
0.081
0.018
0.001
0.005
0.022
0.070
0.168
0.284
0.300
0.150
0.001
0.009
0.047
0.168
0.376
0.397
0.001
0.002
0.008
0.022
0.051
0.098
0.153
0.192
0.192
0.149
0.087
0.036
0.009
0.001
0.001
0.005
0.071
0.044
0.095
0.164
0.218
0.218
0.154
0.068
0.014
0.001
0.007
0.027
0.080
0.180
0.285
0.285
0.135
0.002
0.011
0.053
0.179
0.377
0.377
775
Appendix C Tables
(concluded)
Table B
p
n
x
0.05
0.1
0.2
0.3
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.358
0.377
0.189
0.060
0.013
0.002
0.122
0.270
0.285
0.190
0.090
0.032
0.009
0.002
0.012
0.058
0.137
0.205
0.218
0.175
0.109
0.055
0.022
0.007
0.002
0.001
0.007
0.028
0.072
0.130
0.179
0.192
0.164
0.114
0.065
0.031
0.012
0.004
0.001
0.4
0.003
0.012
0.035
0.075
0.124
0.166
0.180
0.160
0.117
0.071
0.035
0.015
0.005
0.001
0.5
0.001
0.005
0.015
0.037
0.074
0.120
0.160
0.176
0.160
0.120
0.074
0.037
0.015
0.005
0.001
0.6
0.001
0.005
0.015
0.035
0.071
0.117
0.160
0.180
0.166
0.124
0.075
0.035
0.012
0.003
0.7
0.8
0.9
0.95
0.001
0.004
0.012
0.031
0.065
0.114
0.164
0.192
0.179
0.130
0.072
0.028
0.007
0.001
0.002
0.007
0.022
0.055
0.109
0.175
0.218
0.205
0.137
0.058
0.012
0.002
0.009
0.032
0.090
0.190
0.285
0.270
0.122
0.002
0.013
0.060
0.189
0.377
0.358
Note: All values of 0.0005 or less are omitted.
Source: J. Freund and G. Simon, Modern Elementary Statistics, Table “The Binomial Distribution,” © 1992 Prentice-Hall, Inc. Reproduced by permission of Pearson
Education, Inc.
A–23
768
Appendix B–3 Alternate Approach to the Standard Normal Distribution
Table B–1
The Standard Normal Distribution
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.0000
.0040
.0080
.0120
.0160
.0199
.0239
.0279
.0319
.0359
0.1
.0398
.0438
.0478
.0517
.0557
.0596
.0636
.0675
.0714
.0753
0.2
.0793
.0832
.0871
.0910
.0948
.0987
.1026
.1064
.1103
.1141
0.3
.1179
.1217
.1255
.1293
.1331
.1368
.1406
.1443
.1480
.1517
0.4
.1554
.1591
.1628
.1664
.1700
.1736
.1772
.1808
.1844
.1879
0.5
.1915
.1950
.1985
.2019
.2054
.2088
.2123
.2157
.2190
.2224
0.6
.2257
.2291
.2324
.2357
.2389
.2422
.2454
.2486
.2517
.2549
0.7
.2580
.2611
.2642
.2673
.2704
.2734
.2764
.2794
.2823
.2852
0.8
.2881
.2910
.2939
.2967
.2995
.3023
.3051
.3078
.3106
.3133
0.9
.3159
.3186
.3212
.3238
.3264
.3289
.3315
.3340
.3365
.3389
1.0
.3413
.3438
.3461
.3485
.3508
.3531
.3554
.3577
.3599
.3621
1.1
.3643
.3665
.3686
.3708
.3729
.3749
.3770
.3790
.3810
.3830
1.2
.3849
.3869
.3888
.3907
.3925
.3944
.3962
.3980
.3997
.4015
1.3
.4032
.4049
.4066
.4082
.4099
.4115
.4131
.4147
.4162
.4177
1.4
.4192
.4207
.4222
.4236
.4251
.4265
.4279
.4292
.4306
.4319
1.5
.4332
.4345
.4357
.4370
.4382
.4394
.4406
.4418
.4429
.4441
1.6
.4452
.4463
.4474
.4484
.4495
.4505
.4515
.4525
.4535
.4545
1.7
.4554
.4564
.4573
.4582
.4591
.4599
.4608
.4616
.4625
.4633
1.8
.4641
.4649
.4656
.4664
.4671
.4678
.4686
.4693
.4699
.4706
1.9
.4713
.4719
.4726
.4732
.4738
.4744
.4750
.4756
.4761
.4767
2.0
.4772
.4778
.4783
.4788
.4793
.4798
.4803
.4808
.4812
.4817
2.1
.4821
.4826
.4830
.4834
.4838
.4842
.4846
.4850
.4854
.4857
2.2
.4861
.4864
.4868
.4871
.4875
.4878
.4881
.4884
.4887
.4890
2.3
.4893
.4896
.4898
.4901
.4904
.4906
.4909
.4911
.4913
.4916
2.4
.4918
.4920
.4922
.4925
.4927
.4929
.4931
.4932
.4934
.4936
2.5
.4938
.4940
.4941
.4943
.4945
.4946
.4948
.4949
.4951
.4952
2.6
.4953
.4955
.4956
.4957
.4959
.4960
.4961
.4962
.4963
.4964
2.7
.4965
.4966
.4967
.4968
.4969
.4970
.4971
.4972
.4973
.4974
2.8
.4974
.4975
.4976
.4977
.4977
.4978
.4979
.4979
.4980
.4981
2.9
.4981
.4982
.4982
.4983
.4984
.4984
.4985
.4985
.4986
.4986
3.0
.4987
.4987
.4987
.4988
.4988
.4989
.4989
.4989
.4990
.4990
3.1
.4990
.4991
.4991
.4991
.4992
.4992
.4992
.4992
.4993
.4993
3.2
.4993
.4993
.4994
.4994
.4994
.4994
.4994
.4995
.4995
.4995
3.3
.4995
.4995
.4995
.4996
.4996
.4996
.4996
.4996
.4996
.4997
3.4
.4997
.4997
.4997
.4997
.4997
.4997
.4997
.4997
.4997
.4998
For z values greater than 3.49, use 0.4999.
Area given
in table
0
A–16
z
776
Table C
Appendix C Tables
The Poisson Distribution
L
x
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
1
2
3
4
5
6
.9048
.0905
.0045
.0002
.0000
.0000
.0000
.8187
.1637
.0164
.0011
.0001
.0000
.0000
.7408
.2222
.0333
.0033
.0003
.0000
.0000
.6703
.2681
.0536
.0072
.0007
.0001
.0000
.6065
.3033
.0758
.0126
.0016
.0002
.0000
.5488
.3293
.0988
.0198
.0030
.0004
.0000
.4966
.3476
.1217
.0284
.0050
.0007
.0001
.4493
.3595
.1438
.0383
.0077
.0012
.0002
.4066
.3659
.1647
.0494
.0111
.0020
.0003
.3679
.3679
.1839
.0613
.0153
.0031
.0005
7
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0001
L
x
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
0
1
2
3
4
5
6
7
8
.3329
.3662
.2014
.0738
.0203
.0045
.0008
.0001
.0000
.3012
.3614
.2169
.0867
.0260
.0062
.0012
.0002
.0000
.2725
.3543
.2303
.0998
.0324
.0084
.0018
.0003
.0001
.2466
.3452
.2417
.1128
.0395
.0111
.0026
.0005
.0001
.2231
.3347
.2510
.1255
.0471
.0141
.0035
.0008
.0001
.2019
.3230
.2584
.1378
.0551
.0176
.0047
.0011
.0002
.1827
.3106
.2640
.1496
.0636
.0216
.0061
.0015
.0003
.1653
.2975
.2678
.1607
.0723
.0260
.0078
.0020
.0005
.1496
.2842
.2700
.1710
.0812
.0309
.0098
.0027
.0006
.1353
.2707
.2707
.1804
.0902
.0361
.0120
.0034
.0009
9
.0000
.0000
.0000
.0000
.0000
.0000
.0001
.0001
.0001
.0002
L
x
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
0
1
2
3
4
5
6
7
8
9
10
11
.1225
.2572
.2700
.1890
.0992
.0417
.0146
.0044
.0011
.0003
.0001
.0000
.1108
.2438
.2681
.1966
.1082
.0476
.0174
.0055
.0015
.0004
.0001
.0000
.1003
.2306
.2652
.2033
.1169
.0538
.0206
.0068
.0019
.0005
.0001
.0000
.0907
.2177
.2613
.2090
.1254
.0602
.0241
.0083
.0025
.0007
.0002
.0000
.0821
.2052
.2565
.2138
.1336
.0668
.0278
.0099
.0031
.0009
.0002
.0000
.0743
.1931
.2510
.2176
.1414
.0735
.0319
.0118
.0038
.0011
.0003
.0001
.0672
.1815
.2450
.2205
.1488
.0804
.0362
.0139
.0047
.0014
.0004
.0001
.0608
.1703
.2384
.2225
.1557
.0872
.0407
.0163
.0057
.0018
.0005
.0001
.0550
.1596
.2314
.2237
.1622
.0940
.0455
.0188
.0068
.0022
.0006
.0002
.0498
.1494
.2240
.2240
.1680
.1008
.0504
.0216
.0081
.0027
.0008
.0002
12
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0001
L
x
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
0
1
2
3
4
.0450
.1397
.2165
.2237
.1734
.0408
.1304
.2087
.2226
.1781
.0369
.1217
.2008
.2209
.1823
.0334
.1135
.1929
.2186
.1858
.0302
.1057
.1850
.2158
.1888
.0273
.0984
.1771
.2125
.1912
.0247
.0915
.1692
.2087
.1931
.0224
.0850
.1615
.2046
.1944
.0202
.0789
.1539
.2001
.1951
.0183
.0733
.1465
.1954
.1954
A–24
Appendix C Tables
Table C
777
(continued)
L
x
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
5
6
7
8
9
10
11
12
13
.1075
.0555
.0246
.0095
.0033
.0010
.0003
.0001
.0000
.1140
.0608
.0278
.0111
.0040
.0013
.0004
.0001
.0000
.1203
.0662
.0312
.0129
.0047
.0016
.0005
.0001
.0000
.1264
.0716
.0348
.0148
.0056
.0019
.0006
.0002
.0000
.1322
.0771
.0385
.0169
.0066
.0023
.0007
.0002
.0001
.1377
.0826
.0425
.0191
.0076
.0028
.0009
.0003
.0001
.1429
.0881
.0466
.0215
.0089
.0033
.0011
.0003
.0001
.1477
.0936
.0508
.0241
.0102
.0039
.0013
.0004
.0001
.1522
.0989
.0551
.0269
.0116
.0045
.0016
.0005
.0002
.1563
.1042
.0595
.0298
.0132
.0053
.0019
.0006
.0002
14
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0001
L
x
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
.0166
.0679
.1393
.1904
.1951
.1600
.1093
.0640
.0328
.0150
.0061
.0023
.0008
.0002
.0001
.0150
.0630
.1323
.1852
.1944
.1633
.1143
.0686
.0360
.0168
.0071
.0027
.0009
.0003
.0001
.0136
.0583
.1254
.1798
.1933
.1662
.1191
.0732
.0393
.0188
.0081
.0032
.0011
.0004
.0001
.0123
.0540
.1188
.1743
.1917
.1687
.1237
.0778
.0428
.0209
.0092
.0037
.0014
.0005
.0001
.0111
.0500
.1125
.1687
.1898
.1708
.1281
.0824
.0463
.0232
.0104
.0043
.0016
.0006
.0002
.0101
.0462
.1063
.1631
.1875
.1725
.1323
.0869
.0500
.0255
.0118
.0049
.0019
.0007
.0002
.0091
.0427
.1005
.1574
.1849
.1738
.1362
.0914
.0537
.0280
.0132
.0056
.0022
.0008
.0003
.0082
.0395
.0948
.1517
.1820
.1747
.1398
.0959
.0575
.0307
.0147
.0064
.0026
.0009
.0003
.0074
.0365
.0894
.1460
.1789
.1753
.1432
.1002
.0614
.0334
.0164
.0073
.0030
.0011
.0004
.0067
.0337
.0842
.1404
.1755
.1755
.1462
.1044
.0653
.0363
.0181
.0082
.0034
.0013
.0005
15
.0000
.0000
.0000
.0000
.0001
.0001
.0001
.0001
.0001
.0002
L
x
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
0
1
2
3
4
.0061
.0311
.0793
.1348
.1719
.0055
.0287
.0746
.1293
.1681
.0050
.0265
.0701
.1239
.1641
.0045
.0244
.0659
.1185
.1600
.0041
.0225
.0618
.1133
.1558
.0037
.0207
.0580
.1082
.1515
.0033
.0191
.0544
.1033
.1472
.0030
.0176
.0509
.0985
.1428
.0027
.0162
.0477
.0938
.1383
.0025
.0149
.0446
.0892
.1339
A–25
778
Table C
Appendix C Tables
(continued)
L
x
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
5
6
7
8
9
10
11
12
13
14
15
16
.1753
.1490
.1086
.0692
.0392
.0200
.0093
.0039
.0015
.0006
.0002
.0001
.1748
.1515
.1125
.0731
.0423
.0220
.0104
.0045
.0018
.0007
.0002
.0001
.1740
.1537
.1163
.0771
.0454
.0241
.0116
.0051
.0021
.0008
.0003
.0001
.1728
.1555
.1200
.0810
.0486
.0262
.0129
.0058
.0024
.0009
.0003
.0001
.1714
.1571
.1234
.0849
.0519
.0285
.0143
.0065
.0028
.0011
.0004
.0001
.1697
.1584
.1267
.0887
.0552
.0309
.0157
.0073
.0032
.0013
.0005
.0002
.1678
.1594
.1298
.0925
.0586
.0334
.0173
.0082
.0036
.0015
.0006
.0002
.1656
.1601
.1326
.0962
.0620
.0359
.0190
.0092
.0041
.0017
.0007
.0002
.1632
.1605
.1353
.0998
.0654
.0386
.0207
.0102
.0046
.0019
.0008
.0003
.1606
.1606
.1377
.1033
.0688
.0413
.0225
.0113
.0052
.0022
.0009
.0003
17
.0000
.0000
.0000
.0000
.0000
.0000
.0001
.0001
.0001
.0001
L
x
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
.0022
.0137
.0417
.0848
.1294
.1579
.1605
.1399
.1066
.0723
.0441
.0245
.0124
.0058
.0025
.0010
.0004
.0001
.0000
.0000
.0020
.0126
.0390
.0806
.1249
.1549
.1601
.1418
.1099
.0757
.0469
.0265
.0137
.0065
.0029
.0012
.0005
.0002
.0001
.0000
.0018
.0116
.0364
.0765
.1205
.1519
.1595
.1435
.1130
.0791
.0498
.0285
.0150
.0073
.0033
.0014
.0005
.0002
.0001
.0000
.0017
.0106
.0340
.0726
.1162
.1487
.1586
.1450
.1160
.0825
.0528
.0307
.0164
.0081
.0037
.0016
.0006
.0002
.0001
.0000
.0015
.0098
.0318
.0688
.1118
.1454
.1575
.1462
.1188
.0858
.0558
.0330
.0179
.0089
.0041
.0018
.0007
.0003
.0001
.0000
.0014
.0090
.0296
.0652
.1076
.1420
.1562
.1472
.1215
.0891
.0588
.0353
.0194
.0098
.0046
.0020
.0008
.0003
.0001
.0000
.0012
.0082
.0276
.0617
.1034
.1385
.1546
.1480
.1240
.0923
.0618
.0377
.0210
.0108
.0052
.0023
.0010
.0004
.0001
.0000
.0011
.0076
.0258
.0584
.0992
.1349
.1529
.1486
.1263
.0954
.0649
.0401
.0227
.0119
.0058
.0026
.0011
.0004
.0002
.0001
.0010
.0070
.0240
.0552
.0952
.1314
.1511
.1489
.1284
.0985
.0679
.0426
.0245
.0130
.0064
.0029
.0013
.0005
.0002
.0001
.0009
.0064
.0223
.0521
.0912
.1277
.1490
.1490
.1304
.1014
.0710
.0452
.0264
.0142
.0071
.0033
.0014
.0006
.0002
.0001
A–26
Appendix C Tables
Table C
779
(continued)
L
x
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
.0008
.0059
.0208
.0492
.0874
.1241
.1468
.1489
.1321
.1042
.0740
.0478
.0283
.0154
.0078
.0037
.0016
.0007
.0003
.0001
.0000
.0007
.0054
.0194
.0464
.0836
.1204
.1445
.1486
.1337
.1070
.0770
.0504
.0303
.0168
.0086
.0041
.0019
.0008
.0003
.0001
.0000
.0007
.0049
.0180
.0438
.0799
.1167
.1420
.1481
.1351
.1096
.0800
.0531
.0323
.0181
.0095
.0046
.0021
.0009
.0004
.0001
.0001
.0006
.0045
.0167
.0413
.0764
.1130
.1394
.1474
.1363
.1121
.0829
.0558
.0344
.0196
.0104
.0051
.0024
.0010
.0004
.0002
.0001
.0006
.0041
.0156
.0389
.0729
.1094
.1367
.1465
.1373
.1144
.0858
.0585
.0366
.0211
.0113
.0057
.0026
.0012
.0005
.0002
.0001
.0005
.0038
.0145
.0366
.0696
.1057
.1339
.1454
.1382
.1167
.0887
.0613
.0388
.0227
.0123
.0062
.0030
.0013
.0006
.0002
.0001
.0005
.0035
.0134
.0345
.0663
.1021
.1311
.1442
.1388
.1187
.0914
.0640
.0411
.0243
.0134
.0069
.0033
.0015
.0006
.0003
.0001
.0004
.0032
.0125
.0324
.0632
.0986
.1282
.1428
.1392
.1207
.0941
.0667
.0434
.0260
.0145
.0075
.0037
.0017
.0007
.0003
.0001
.0004
.0029
.0116
.0305
.0602
.0951
.1252
.1413
.1395
.1224
.0967
.0695
.0457
.0278
.0157
.0083
.0041
.0019
.0008
.0003
.0001
.0003
.0027
.0107
.0286
.0573
.0916
.1221
.1396
.1396
.1241
.0993
.0722
.0481
.0296
.0169
.0090
.0045
.0021
.0009
.0004
.0002
21
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0001
.0001
x
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9.0
0
1
2
3
4
5
6
7
8
9
.0003
.0025
.0100
.0269
.0544
.0882
.1191
.1378
.1395
.1256
.0003
.0023
.0092
.0252
.0517
.0849
.1160
.1358
.1392
.1269
.0002
.0021
.0086
.0237
.0491
.0816
.1128
.1338
.1388
.1280
.0002
.0019
.0079
.0222
.0466
.0784
.1097
.1317
.1382
.1290
.0002
.0017
.0074
.0208
.0443
.0752
.1066
.1294
.1375
.1299
.0002
.0016
.0068
.0195
.0420
.0722
.1034
.1271
.1366
.1306
.0002
.0014
.0063
.0183
.0398
.0692
.1003
.1247
.1356
.1311
.0002
.0013
.0058
.0171
.0377
.0663
.0972
.1222
.1344
.1315
.0001
.0012
.0054
.0160
.0357
.0635
.0941
.1197
.1332
.1317
.0001
.0011
.0050
.0150
.0337
.0607
.0911
.1171
.1318
.1318
L
A–27
780
Table C
Appendix C Tables
(continued)
L
x
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9.0
10
11
12
13
14
15
16
17
18
19
20
21
.1017
.0749
.0505
.0315
.0182
.0098
.0050
.0024
.0011
.0005
.0002
.0001
.1040
.0776
.0530
.0334
.0196
.0107
.0055
.0026
.0012
.0005
.0002
.0001
.1063
.0802
.0555
.0354
.0210
.0116
.0060
.0029
.0014
.0006
.0002
.0001
.1084
.0828
.0579
.0374
.0225
.0126
.0066
.0033
.0015
.0007
.0003
.0001
.1104
.0853
.0604
.0395
.0240
.0136
.0072
.0036
.0017
.0008
.0003
.0001
.1123
.0878
.0629
.0416
.0256
.0147
.0079
.0040
.0019
.0009
.0004
.0002
.1140
.0902
.0654
.0438
.0272
.0158
.0086
.0044
.0021
.0010
.0004
.0002
.1157
.0925
.0679
.0459
.0289
.0169
.0093
.0048
.0024
.0011
.0005
.0002
.1172
.0948
.0703
.0481
.0306
.0182
.0101
.0053
.0026
.0012
.0005
.0002
.1186
.0970
.0728
.0504
.0324
.0194
.0109
.0058
.0029
.0014
.0006
.0003
22
.0000
.0000
.0000
.0000
.0001
.0001
.0001
.0001
.0001
.0001
L
x
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
.0001
.0010
.0046
.0140
.0319
.0581
.0881
.1145
.1302
.1317
.1198
.0991
.0752
.0526
.0342
.0208
.0118
.0063
.0032
.0015
.0001
.0009
.0043
.0131
.0302
.0555
.0851
.1118
.1286
.1315
.1210
.1012
.0776
.0549
.0361
.0221
.0127
.0069
.0035
.0017
.0001
.0009
.0040
.0123
.0285
.0530
.0822
.1091
.1269
.1311
.1219
.1031
.0799
.0572
.0380
.0235
.0137
.0075
.0039
.0019
.0001
.0008
.0037
.0115
.0269
.0506
.0793
.1064
.1251
.1306
.1228
.1049
.0822
.0594
.0399
.0250
.0147
.0081
.0042
.0021
.0001
.0007
.0034
.0107
.0254
.0483
.0764
.1037
.1232
.1300
.1235
.1067
.0844
.0617
.0419
.0265
.0157
.0088
.0046
.0023
.0001
.0007
.0031
.0100
.0240
.0460
.0736
.1010
.1212
.1293
.1241
.1083
.0866
.0640
.0439
.0281
.0168
.0095
.0051
.0026
.0001
.0006
.0029
.0093
.0226
.0439
.0709
.0982
.1191
.1284
.1245
.1098
.0888
.0662
.0459
.0297
.0180
.0103
.0055
.0028
.0001
.0005
.0027
.0087
.0213
.0418
.0682
.0955
.1170
.1274
.1249
.1112
.0908
.0685
.0479
.0313
.0192
.0111
.0060
.0031
.0001
.0005
.0025
.0081
.0201
.0398
.0656
.0928
.1148
.1263
.1250
.1125
.0928
.0707
.0500
.0330
.0204
.0119
.0065
.0034
.0000
.0005
.0023
.0076
.0189
.0378
.0631
.0901
.1126
.1251
.1251
.1137
.0948
.0729
.0521
.0347
.0217
.0128
.0071
.0037
A–28
Appendix C Tables
Table C
781
(continued)
L
x
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.0
20
21
22
23
.0007
.0003
.0001
.0000
.0008
.0003
.0001
.0001
.0009
.0004
.0002
.0001
.0010
.0004
.0002
.0001
.0011
.0005
.0002
.0001
.0012
.0006
.0002
.0001
.0014
.0006
.0003
.0001
.0015
.0007
.0003
.0001
.0017
.0008
.0004
.0002
.0019
.0009
.0004
.0002
24
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0001
.0001
.0001
L
x
11
12
13
14
15
16
17
18
19
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
.0000
.0002
.0010
.0037
.0102
.0224
.0411
.0646
.0888
.1085
.1194
.1194
.1094
.0926
.0728
.0534
.0367
.0237
.0145
.0084
.0046
.0024
.0012
.0006
.0003
.0001
.0000
.0000
.0000
.0000
.0000
.0001
.0004
.0018
.0053
.0127
.0255
.0437
.0655
.0874
.1048
.1144
.1144
.1056
.0905
.0724
.0543
.0383
.0256
.0161
.0097
.0055
.0030
.0016
.0008
.0004
.0002
.0001
.0000
.0000
.0000
.0000
.0002
.0008
.0027
.0070
.0152
.0281
.0457
.0661
.0859
.1015
.1099
.1099
.1021
.0885
.0719
.0550
.0397
.0272
.0177
.0109
.0065
.0037
.0020
.0010
.0005
.0002
.0001
.0001
.0000
.0000
.0001
.0004
.0013
.0037
.0087
.0174
.0304
.0473
.0663
.0844
.0984
.1060
.1060
.0989
.0866
.0713
.0554
.0409
.0286
.0191
.0121
.0074
.0043
.0024
.0013
.0007
.0003
.0002
.0000
.0000
.0000
.0002
.0006
.0019
.0048
.0104
.0194
.0324
.0486
.0663
.0829
.0956
.1024
.1024
.0960
.0847
.0706
.0557
.0418
.0299
.0204
.0133
.0083
.0050
.0029
.0016
.0009
.0004
.0000
.0000
.0000
.0001
.0003
.0010
.0026
.0060
.0120
.0213
.0341
.0496
.0661
.0814
.0930
.0992
.0992
.0934
.0830
.0699
.0559
.0426
.0310
.0216
.0144
.0092
.0057
.0034
.0019
.0011
.0000
.0000
.0000
.0000
.0001
.0005
.0014
.0034
.0072
.0135
.0230
.0355
.0504
.0658
.0800
.0906
.0963
.0963
.0909
.0814
.0692
.0560
.0433
.0320
.0226
.0154
.0101
.0063
.0038
.0023
.0000
.0000
.0000
.0000
.0001
.0002
.0007
.0018
.0042
.0083
.0150
.0245
.0368
.0509
.0655
.0786
.0884
.0936
.0936
.0887
.0798
.0684
.0560
.0438
.0328
.0237
.0164
.0109
.0070
.0044
.0000
.0000
.0000
.0000
.0000
.0001
.0004
.0010
.0024
.0050
.0095
.0164
.0259
.0378
.0514
.0650
.0772
.0863
.0911
.0911
.0866
.0783
.0676
.0559
.0442
.0336
.0246
.0173
.0117
.0077
.0000
.0000
.0000
.0000
.0000
.0001
.0002
.0005
.0013
.0029
.0058
.0106
.0176
.0271
.0387
.0516
.0646
.0760
.0844
.0888
.0888
.0846
.0769
.0669
.0557
.0446
.0343
.0254
.0181
.0125
A–29
782
Table C
Appendix C Tables
(concluded)
L
x
11
12
13
14
15
16
17
18
19
20
30
31
32
33
34
35
36
37
38
39
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0001
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0002
.0001
.0001
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0006
.0003
.0001
.0001
.0000
.0000
.0000
.0000
.0000
.0000
.0013
.0007
.0004
.0002
.0001
.0000
.0000
.0000
.0000
.0000
.0026
.0015
.0009
.0005
.0002
.0001
.0001
.0000
.0000
.0000
.0049
.0030
.0018
.0010
.0006
.0003
.0002
.0001
.0000
.0000
.0083
.0054
.0034
.0020
.0012
.0007
.0004
.0002
.0001
.0001
Reprinted with permission from W. H. Beyer, Handbook of Tables for Probability and Statistics, 2nd ed. Copyright CRC Press, Boca Raton, Fla., 1986.
A–30
Appendix C Tables
Table D
10480
22368
24130
42167
37570
77921
99562
96301
89579
85475
28918
63553
09429
10365
07119
51085
02368
01011
52162
07056
48663
54164
32639
29334
02488
81525
29676
00742
05366
91921
00582
00725
69011
25976
09763
91567
17955
46503
92157
14577
98427
34914
70060
53976
76072
90725
64364
08962
95012
15664
783
Random Numbers
15011
46573
48360
93093
39975
06907
72905
91977
14342
36857
69578
40961
93969
61129
97336
12765
21382
54092
53916
97628
91245
58492
32363
27001
33062
72295
20591
57392
04213
26418
04711
69884
65797
57948
83473
42595
56349
18584
89634
62765
07523
63976
28277
54914
29515
52210
67412
00358
68379
10493
01536
25595
22527
06243
81837
11008
56420
05463
63661
43342
88231
48235
52636
87529
71048
51821
52404
33362
46369
33787
85828
22421
05597
87637
28834
04839
68086
39064
25669
64117
87917
62797
95876
29888
73577
27958
90999
18845
94824
35605
33362
88720
39475
06990
40980
83974
33339
31662
93526
20492
02011
85393
97265
61680
16656
42751
69994
07972
10281
53988
33276
03427
92737
85689
08178
51259
60268
94904
58586
09998
14346
74103
24200
87308
07351
96423
26432
66432
26422
94305
77341
56170
55293
88604
12908
30134
49127
49618
78171
81263
64270
82765
46473
67245
07391
29992
31926
25388
70765
38391
81647
30995
76393
07856
06121
27756
98872
18876
17453
53060
70997
49626
88974
48237
77233
77452
89368
31273
23216
42698
09172
47070
13363
58731
19731
24878
46901
84673
44407
26766
42206
86324
18988
67917
30883
04024
20044
02304
84610
39667
01638
34476
23219
68350
58745
65831
14883
61642
10593
91132
91646
89198
64809
16376
91782
53498
31016
20922
18103
59533
79936
69445
33488
52267
13916
16308
19885
04146
14513
06691
30168
25306
38005
00256
92420
82651
20849
40027
44048
25940
35126
88072
27354
48708
18317
86385
59931
51038
82834
47358
92477
17032
53416
82948
25774
38857
24413
34072
04542
21999
67179
27982
15179
39440
60468
18602
71194
94595
57740
38867
56865
18663
36320
67689
47564
60756
55322
18594
83149
76988
90229
76468
94342
45834
60952
66566
89768
32832
37937
39972
74087
76222
26575
18912
28290
29880
06115
20655
09922
56873
66969
87589
94970
11398
22987
50490
59744
81249
76463
59516
14194
53402
24830
53537
81305
70659
18738
56869
84378
62300
05859
72695
17617
93394
81056
92144
44819
29852
98736
13602
04734
26384
28728
15398
61280
14778
81536
61362
63904
22209
99547
36086
08625
82271
35797
99730
20542
58727
25417
56307
98420
40836
25832
42878
80059
83765
92351
35648
54328
81652
62590
93965
49340
71341
49684
90655
44013
69014
25331
08158
90106
52180
30015
01511
97735
49442
01188
71585
23495
51851
59193
58151
35806
46557
50001
76797
86645
98947
45766
71500
81817
84637
40801
65424
05998
55536
18059
28168
44137
61607
04880
32427
69975
80287
39911
55657
97473
56891
02349
27195
36207
34095
32081
57004
60672
15053
48840
60045
12566
17983
31595
20847
08272
26358
85977
53900
65255
85030
64350
46104
22178
06646
06912
41135
67658
14780
12659
96067
66134
64568
42607
93161
59920
69774
41688
84855
02008
15475
48413
49518
45585
70002
94884
88267
96189
14361
89286
69352
17247
48223
20969
52666
30680
00849
14110
21916
63213
18425
58678
16439
01547
12234
84115
85104
29372
70960
64835
51132
94738
88916
30421
21524
17012
10367
32586
13300
92259
64760
75470
91402
43808
76038
29841
33611
34952
29080
73708
56942
25555
89656
46565
70663
19661
47363
41151
31720
35931
48373
28865
46751
99570
19174
19655
74917
06927
81825
21069
84903
44947
11458
85590
90511
27156
20285
74461
63990
44919
01915
17752
19509
61666
15227
64161
07684
86679
87074
57102
64584
66520
42416
76655
65855
80150
54262
37888
09250
83517
53389
21246
20103
04102
88863
72828
46634
14222
57375
04110
45578
14777
22923
91291
39615
63348
97758
01263
44394
10634
42508
05584
18593
91610
33703
30613
29975
28551
75601
05944
92747
35156
25625
99904
96909
18296
36188
50720
79666
80428
96096
34693
07844
62028
77919
12777
85963
38917
79656
36103
20562
35509
77490
46880
77775
00102
06541
60697
56228
23726
78547
62730
32261
90700
99505
58629
16379
54613
42880
12952
32307
56941
64952
78188
90322
74952
89868
90707
40719
55157
64951
35749
58104
32812
44592
22851
18510
94953
95725
25280
98253
90449
69618
76630
88006
48501
03547
88050
73211
42791
87338
20468
18062
45709
69348
66794
97809
59583
41546
51900
81788
92277
85653
Reprinted with permission from W. H. Beyer, Handbook of Tables for Probability and Statistics, 2nd ed. Copyright CRC Press, Boca Raton, Fla., 1986.
A–31
784
Table E
Appendix C Tables
The Standard Normal Distribution
Cumulative Standard Normal Distribution
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
3.4
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0002
3.3
.0005
.0005
.0005
.0004
.0004
.0004
.0004
.0004
.0004
.0003
3.2
.0007
.0007
.0006
.0006
.0006
.0006
.0006
.0005
.0005
.0005
3.1
.0010
.0009
.0009
.0009
.0008
.0008
.0008
.0008
.0007
.0007
3.0
.0013
.0013
.0013
.0012
.0012
.0011
.0011
.0011
.0010
.0010
2.9
.0019
.0018
.0018
.0017
.0016
.0016
.0015
.0015
.0014
.0014
2.8
.0026
.0025
.0024
.0023
.0023
.0022
.0021
.0021
.0020
.0019
2.7
.0035
.0034
.0033
.0032
.0031
.0030
.0029
.0028
.0027
.0026
2.6
.0047
.0045
.0044
.0043
.0041
.0040
.0039
.0038
.0037
.0036
2.5
.0062
.0060
.0059
.0057
.0055
.0054
.0052
.0051
.0049
.0048
2.4
.0082
.0080
.0078
.0075
.0073
.0071
.0069
.0068
.0066
.0064
2.3
.0107
.0104
.0102
.0099
.0096
.0094
.0091
.0089
.0087
.0084
2.2
.0139
.0136
.0132
.0129
.0125
.0122
.0119
.0116
.0113
.0110
2.1
.0179
.0174
.0170
.0166
.0162
.0158
.0154
.0150
.0146
.0143
2.0
.0228
.0222
.0217
.0212
.0207
.0202
.0197
.0192
.0188
.0183
1.9
.0287
.0281
.0274
.0268
.0262
.0256
.0250
.0244
.0239
.0233
1.8
.0359
.0351
.0344
.0336
.0329
.0322
.0314
.0307
.0301
.0294
1.7
.0446
.0436
.0427
.0418
.0409
.0401
.0392
.0384
.0375
.0367
1.6
.0548
.0537
.0526
.0516
.0505
.0495
.0485
.0475
.0465
.0455
1.5
.0668
.0655
.0643
.0630
.0618
.0606
.0594
.0582
.0571
.0559
1.4
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0694
.0681
1.3
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0838
.0823
1.2
.1151
.1131
.1112
.1093
.1075
.1056
.1038
.1020
.1003
.0985
1.1
.1357
.1335
.1314
.1292
.1271
.1251
.1230
.1210
.1190
.1170
1.0
.1587
.1562
.1539
.1515
.1492
.1469
.1446
.1423
.1401
.1379
0.9
.1841
.1814
.1788
.1762
.1736
.1711
.1685
.1660
.1635
.1611
0.8
.2119
.2090
.2061
.2033
.2005
.1977
.1949
.1922
.1894
.1867
0.7
.2420
.2389
.2358
.2327
.2296
.2266
.2236
.2206
.2177
.2148
0.6
.2743
.2709
.2676
.2643
.2611
.2578
.2546
.2514
.2483
.2451
0.5
.3085
.3050
.3015
.2981
.2946
.2912
.2877
.2843
.2810
.2776
0.4
.3446
.3409
.3372
.3336
.3300
.3264
.3228
.3192
.3156
.3121
0.3
.3821
.3783
.3745
.3707
.3669
.3632
.3594
.3557
.3520
.3483
0.2
.4207
.4168
.4129
.4090
.4052
.4013
.3974
.3936
.3897
.3859
0.1
.4602
.4562
.4522
.4483
.4443
.4404
.4364
.4325
.4286
.4247
0.0
.5000
.4960
.4920
.4880
.4840
.4801
.4761
.4721
.4681
.4641
For z values less than 3.49, use 0.0001.
Area
z
A–32
0
Appendix C Tables
Table E
785
(continued )
Cumulative Standard Normal Distribution
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.5000
.5040
.5080
.5120
.5160
.5199
.5239
.5279
.5319
.5359
0.1
.5398
.5438
.5478
.5517
.5557
.5596
.5636
.5675
.5714
.5753
0.2
.5793
.5832
.5871
.5910
.5948
.5987
.6026
.6064
.6103
.6141
0.3
.6179
.6217
.6255
.6293
.6331
.6368
.6406
.6443
.6480
.6517
0.4
.6554
.6591
.6628
.6664
.6700
.6736
.6772
.6808
.6844
.6879
0.5
.6915
.6950
.6985
.7019
.7054
.7088
.7123
.7157
.7190
.7224
0.6
.7257
.7291
.7324
.7357
.7389
.7422
.7454
.7486
.7517
.7549
0.7
.7580
.7611
.7642
.7673
.7704
.7734
.7764
.7794
.7823
.7852
0.8
.7881
.7910
.7939
.7967
.7995
.8023
.8051
.8078
.8106
.8133
0.9
.8159
.8186
.8212
.8238
.8264
.8289
.8315
.8340
.8365
.8389
1.0
.8413
.8438
.8461
.8485
.8508
.8531
.8554
.8577
.8599
.8621
1.1
.8643
.8665
.8686
.8708
.8729
.8749
.8770
.8790
.8810
.8830
1.2
.8849
.8869
.8888
.8907
.8925
.8944
.8962
.8980
.8997
.9015
1.3
.9032
.9049
.9066
.9082
.9099
.9115
.9131
.9147
.9162
.9177
1.4
.9192
.9207
.9222
.9236
.9251
.9265
.9279
.9292
.9306
.9319
1.5
.9332
.9345
.9357
.9370
.9382
.9394
.9406
.9418
.9429
.9441
1.6
.9452
.9463
.9474
.9484
.9495
.9505
.9515
.9525
.9535
.9545
1.7
.9554
.9564
.9573
.9582
.9591
.9599
.9608
.9616
.9625
.9633
1.8
.9641
.9649
.9656
.9664
.9671
.9678
.9686
.9693
.9699
.9706
1.9
.9713
.9719
.9726
.9732
.9738
.9744
.9750
.9756
.9761
.9767
2.0
.9772
.9778
.9783
.9788
.9793
.9798
.9803
.9808
.9812
.9817
2.1
.9821
.9826
.9830
.9834
.9838
.9842
.9846
.9850
.9854
.9857
2.2
.9861
.9864
.9868
.9871
.9875
.9878
.9881
.9884
.9887
.9890
2.3
.9893
.9896
.9898
.9901
.9904
.9906
.9909
.9911
.9913
.9916
2.4
.9918
.9920
.9922
.9925
.9927
.9929
.9931
.9932
.9934
.9936
2.5
.9938
.9940
.9941
.9943
.9945
.9946
.9948
.9949
.9951
.9952
2.6
.9953
.9955
.9956
.9957
.9959
.9960
.9961
.9962
.9963
.9964
2.7
.9965
.9966
.9967
.9968
.9969
.9970
.9971
.9972
.9973
.9974
2.8
.9974
.9975
.9976
.9977
.9977
.9978
.9979
.9979
.9980
.9981
2.9
.9981
.9982
.9982
.9983
.9984
.9984
.9985
.9985
.9986
.9986
3.0
.9987
.9987
.9987
.9988
.9988
.9989
.9989
.9989
.9990
.9990
3.1
.9990
.9991
.9991
.9991
.9992
.9992
.9992
.9992
.9993
.9993
3.2
.9993
.9993
.9994
.9994
.9994
.9994
.9994
.9995
.9995
.9995
3.3
.9995
.9995
.9995
.9996
.9996
.9996
.9996
.9996
.9996
.9997
3.4
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9998
For z values greater than 3.49, use 0.9999.
Area
0
z
A–33
786
Table F
d.f.
Appendix C Tables
The t Distribution
Confidence
intervals
80%
90%
95%
98%
99%
One tail, A
0.10
0.05
0.025
0.01
0.005
Two tails, A
0.20
0.10
0.05
0.02
0.01
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.309
1.307
1.306
1.304
1.303
1.301
1.299
1.297
1.296
1.295
1.294
1.293
1.292
1.291
1.290
1.283
1.282
1.282a
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.694
1.691
1.688
1.686
1.684
1.679
1.676
1.673
1.671
1.669
1.667
1.665
1.664
1.662
1.660
1.648
1.646
1.645b
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.037
2.032
2.028
2.024
2.021
2.014
2.009
2.004
2.000
1.997
1.994
1.992
1.990
1.987
1.984
1.965
1.962
1.960
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.449
2.441
2.434
2.429
2.423
2.412
2.403
2.396
2.390
2.385
2.381
2.377
2.374
2.368
2.364
2.334
2.330
2.326c
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.738
2.728
2.719
2.712
2.704
2.690
2.678
2.668
2.660
2.654
2.648
2.643
2.639
2.632
2.626
2.586
2.581
2.576d
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
32
34
36
38
40
45
50
55
60
65
70
75
80
90
100
500
1000
(z) a
This value has been rounded to 1.28 in the textbook.
This value has been rounded to 1.65 in the textbook.
c
This value has been rounded to 2.33 in the textbook.
d
This value has been rounded to 2.58 in the textbook.
One tail
Two tails
b
Source: Adapted from W. H. Beyer, Handbook of Tables for Probability and Statistics,
2nd ed., CRC Press, Boca Raton, Fla., 1986. Reprinted with permission.
A–34
Area
␣
t
Area
␣
2
t
Area
␣
2
t
787
Appendix C Tables
Table G
Degrees of
freedom
The Chi-Square Distribution
A
0.995
0.99
0.975
0.95
0.90
0.10
0.05
0.025
0.01
0.005
1
—
—
0.001
0.004
0.016
2.706
3.841
5.024
6.635
7.879
2
0.010
0.020
0.051
0.103
0.211
4.605
5.991
7.378
9.210
10.597
3
0.072
0.115
0.216
0.352
0.584
6.251
7.815
9.348
11.345
12.838
4
0.207
0.297
0.484
0.711
1.064
7.779
9.488
11.143
13.277
14.860
5
0.412
0.554
0.831
1.145
1.610
9.236
11.071
12.833
15.086
16.750
6
0.676
0.872
1.237
1.635
2.204
10.645
12.592
14.449
16.812
18.548
7
0.989
1.239
1.690
2.167
2.833
12.017
14.067
16.013
18.475
20.278
8
1.344
1.646
2.180
2.733
3.490
13.362
15.507
17.535
20.090
21.955
9
1.735
2.088
2.700
3.325
4.168
14.684
16.919
19.023
21.666
23.589
10
2.156
2.558
3.247
3.940
4.865
15.987
18.307
20.483
23.209
25.188
11
2.603
3.053
3.816
4.575
5.578
17.275
19.675
21.920
24.725
26.757
12
3.074
3.571
4.404
5.226
6.304
18.549
21.026
23.337
26.217
28.299
13
3.565
4.107
5.009
5.892
7.042
19.812
22.362
24.736
27.688
29.819
14
4.075
4.660
5.629
6.571
7.790
21.064
23.685
26.119
29.141
31.319
15
4.601
5.229
6.262
7.261
8.547
22.307
24.996
27.488
30.578
32.801
16
5.142
5.812
6.908
7.962
9.312
23.542
26.296
28.845
32.000
34.267
17
5.697
6.408
7.564
8.672
10.085
24.769
27.587
30.191
33.409
35.718
18
6.265
7.015
8.231
9.390
10.865
25.989
28.869
31.526
34.805
37.156
19
6.844
7.633
8.907
10.117
11.651
27.204
30.144
32.852
36.191
38.582
20
7.434
8.260
9.591
10.851
12.443
28.412
31.410
34.170
37.566
39.997
21
8.034
8.897
10.283
11.591
13.240
29.615
32.671
35.479
38.932
41.401
22
8.643
9.542
10.982
12.338
14.042
30.813
33.924
36.781
40.289
42.796
23
9.262
10.196
11.689
13.091
14.848
32.007
35.172
38.076
41.638
44.181
24
9.886
10.856
12.401
13.848
15.659
33.196
36.415
39.364
42.980
45.559
25
10.520
11.524
13.120
14.611
16.473
34.382
37.652
40.646
44.314
46.928
26
11.160
12.198
13.844
15.379
17.292
35.563
38.885
41.923
45.642
48.290
27
11.808
12.879
14.573
16.151
18.114
36.741
40.113
43.194
46.963
49.645
28
12.461
13.565
15.308
16.928
18.939
37.916
41.337
44.461
48.278
50.993
29
13.121
14.257
16.047
17.708
19.768
39.087
42.557
45.722
49.588
52.336
30
13.787
14.954
16.791
18.493
20.599
40.256
43.773
46.979
50.892
53.672
40
20.707
22.164
24.433
26.509
29.051
51.805
55.758
59.342
63.691
66.766
50
27.991
29.707
32.357
34.764
37.689
63.167
67.505
71.420
76.154
79.490
60
35.534
37.485
40.482
43.188
46.459
74.397
79.082
83.298
88.379
91.952
70
43.275
45.442
48.758
51.739
55.329
85.527
90.531
95.023
100.425
104.215
80
51.172
53.540
57.153
60.391
64.278
96.578
101.879
106.629
112.329
116.321
90
59.196
61.754
65.647
69.126
73.291
107.565
113.145
118.136
124.116
128.299
100
67.328
70.065
74.222
77.929
82.358
118.498
124.342
129.561
135.807
140.169
Source: Owen, Handbook of Statistical Tables, Table A–4 “Chi-Square Distribution Table,” © 1962 by Addison-Wesley
Publishing Company, Inc. Copyright renewal © 1990. Reproduced by permission of Pearson Education, Inc.
Area ␣
␹2
A–35
788
A–36
Appendix C Tables
Table H
The F Distribution
A 0.005
d.f.D.:
degrees of
freedom,
denominator
1
2
d.f.N.: degrees of freedom, numerator
1
16,211
198.5
2
20,000
199.0
3
21,615
199.2
4
22,500
199.2
5
23,056
199.3
6
23,437
199.3
7
23,715
199.4
8
23,925
199.4
9
24,091
199.4
10
12
15
20
24
30
40
60
120
24,224
24,426
24,630
24,836
24,940
25,044
25,148
25,253
25,359
25,465
199.4
199.4
199.4
199.4
199.5
199.5
199.5
199.5
199.5
199.5
3
55.55
49.80
47.47
46.19
45.39
44.84
44.43
44.13
43.88
43.69
43.39
43.08
42.78
42.62
42.47
42.31
42.15
41.99
41.83
4
31.33
26.28
24.26
23.15
22.46
21.97
21.62
21.35
21.14
20.97
20.70
20.44
20.17
20.03
19.89
19.75
19.61
19.47
19.32
5
22.78
18.31
16.53
15.56
14.94
14.51
14.20
13.96
13.77
13.62
13.38
13.15
12.90
12.78
12.66
12.53
12.40
12.27
12.14
6
18.63
14.54
12.92
12.03
11.46
11.07
10.79
10.57
10.39
10.25
10.03
9.81
9.59
9.47
9.36
9.24
9.12
9.00
8.88
7
16.24
12.40
10.88
10.05
9.52
9.16
8.89
8.68
8.51
8.38
8.18
7.97
7.75
7.65
7.53
7.42
7.31
7.19
7.08
8
14.69
11.04
9.60
8.81
8.30
7.95
7.69
7.50
7.34
7.21
7.01
6.81
6.61
6.50
6.40
6.29
6.18
6.06
5.95
9
13.61
10.11
8.72
7.96
7.47
7.13
6.88
6.69
6.54
6.42
6.23
6.03
5.83
5.73
5.62
5.52
5.41
5.30
5.19
10
12.83
9.43
8.08
7.34
6.87
6.54
6.30
6.12
5.97
5.85
5.66
5.47
5.27
5.17
5.07
4.97
4.86
4.75
4.64
11
12.23
8.91
7.60
6.88
6.42
6.10
5.86
5.68
5.54
5.42
5.24
5.05
4.86
4.76
4.65
4.55
4.44
4.34
4.23
12
11.75
8.51
7.23
6.52
6.07
5.76
5.52
5.35
5.20
5.09
4.91
4.72
4.53
4.43
4.33
4.23
4.12
4.01
3.90
13
11.37
8.19
6.93
6.23
5.79
5.48
5.25
5.08
4.94
4.82
4.64
4.46
4.27
4.17
4.07
3.97
3.87
3.76
3.65
14
11.06
7.92
6.68
6.00
5.56
5.26
5.03
4.86
4.72
4.60
4.43
4.25
4.06
3.96
3.86
3.76
3.66
3.55
3.44
15
10.80
7.70
6.48
5.80
5.37
5.07
4.85
4.67
4.54
4.42
4.25
4.07
3.88
3.79
3.69
3.58
3.48
3.37
3.26
16
10.58
7.51
6.30
5.64
5.21
4.91
4.69
4.52
4.38
4.27
4.10
3.92
3.73
3.64
3.54
3.44
3.33
3.22
3.11
17
10.38
7.35
6.16
5.50
5.07
4.78
4.56
4.39
4.25
4.14
3.97
3.79
3.61
3.51
3.41
3.31
3.21
3.10
2.98
18
10.22
7.21
6.03
5.37
4.96
4.66
4.44
4.28
4.14
4.03
3.86
3.68
3.50
3.40
3.30
3.20
3.10
2.99
2.87
19
10.07
7.09
5.92
5.27
4.85
4.56
4.34
4.18
4.04
3.93
3.76
3.59
3.40
3.31
3.21
3.11
3.00
2.89
2.78
20
9.94
6.99
5.82
5.17
4.76
4.47
4.26
4.09
3.96
3.85
3.68
3.50
3.32
3.22
3.12
3.02
2.92
2.81
2.69
21
9.83
6.89
5.73
5.09
4.68
4.39
4.18
4.01
3.88
3.77
3.60
3.43
3.24
3.15
3.05
2.95
2.84
2.73
2.61
22
9.73
6.81
5.65
5.02
4.61
4.32
4.11
3.94
3.81
3.70
3.54
3.36
3.18
3.08
2.98
2.88
2.77
2.66
2.55
23
9.63
6.73
5.58
4.95
4.54
4.26
4.05
3.88
3.75
3.64
3.47
3.30
3.12
3.02
2.92
2.82
2.71
2.60
2.48
24
9.55
6.66
5.52
4.89
4.49
4.20
3.99
3.83
3.69
3.59
3.42
3.25
3.06
2.97
2.87
2.77
2.66
2.55
2.43
25
9.48
6.60
5.46
4.84
4.43
4.15
3.94
3.78
3.64
3.54
3.37
3.20
3.01
2.92
2.82
2.72
2.61
2.50
2.38
26
9.41
6.54
5.41
4.79
4.38
4.10
3.89
3.73
3.60
3.49
3.33
3.15
2.97
2.87
2.77
2.67
2.56
2.45
2.33
27
9.34
6.49
5.36
4.74
4.34
4.06
3.85
3.69
3.56
3.45
3.28
3.11
2.93
2.83
2.73
2.63
2.52
2.41
2.25
28
9.28
6.44
5.32
4.70
4.30
4.02
3.81
3.65
3.52
3.41
3.25
3.07
2.89
2.79
2.69
2.59
2.48
2.37
2.29
29
9.23
6.40
5.28
4.66
4.26
3.98
3.77
3.61
3.48
3.38
3.21
3.04
2.86
2.76
2.66
2.56
2.45
2.33
2.24
30
9.18
6.35
5.24
4.62
4.23
3.95
3.74
3.58
3.45
3.34
3.18
3.01
2.82
2.73
2.63
2.52
2.42
2.30
2.18
40
8.83
6.07
4.98
4.37
3.99
3.71
3.51
3.35
3.22
3.12
2.95
2.78
2.60
2.50
2.40
2.30
2.18
2.06
1.93
60
8.49
5.79
4.73
4.14
3.76
3.49
3.29
3.13
3.01
2.90
2.74
2.57
2.39
2.29
2.19
2.08
1.96
1.83
1.69
120
8.18
5.54
4.50
3.92
3.55
3.28
3.09
2.93
2.81
2.71
2.54
2.37
2.19
2.09
1.98
1.87
1.75
1.61
1.43
7.88
5.30
4.28
3.72
3.35
3.09
2.90
2.74
2.62
2.52
2.36
2.19
2.00
1.90
1.79
1.67
1.53
1.36
1.00
Table H
(continued)
A 0.01
d.f.D.:
degrees of
freedom,
denominator
1
d.f.N.: degrees of freedom, numerator
1
4052
2
4999.5
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
5403
5625
5764
5859
5928
5982
6022
6056
6106
6157
6209
6235
6261
6287
6313
120
6339
6366
98.50
99.00
99.17
99.25
99.30
99.33
99.36
99.37
99.39
99.40
99.42
99.43
99.45
99.46
99.47
99.47
99.48
99.49
99.50
3
34.12
30.82
29.46
28.71
28.24
27.91
27.67
27.49
27.35
27.23
27.05
26.87
26.69
26.60
26.50
26.41
26.32
26.22
26.13
4
21.20
18.00
16.69
15.98
15.52
15.21
14.98
14.80
14.66
14.55
14.37
14.20
14.02
13.93
13.84
13.75
13.65
13.56
13.46
5
16.26
13.27
12.06
11.39
10.97
10.67
10.46
10.29
10.16
10.05
9.89
9.72
9.55
9.47
9.38
9.29
9.20
9.11
9.02
6
13.75
10.92
9.78
9.15
8.75
8.47
8.26
8.10
7.98
7.87
7.72
7.56
7.40
7.31
7.23
7.14
7.06
6.97
6.88
7
12.25
9.55
8.45
7.85
7.46
7.19
6.99
6.84
6.72
6.62
6.47
6.31
6.16
6.07
5.99
5.91
5.82
5.74
5.65
8
11.26
8.65
7.59
7.01
6.63
6.37
6.18
6.03
5.91
5.81
5.67
5.52
5.36
5.28
5.20
5.12
5.03
4.95
4.86
9
10.56
8.02
6.99
6.42
6.06
5.80
5.61
5.47
5.35
5.26
5.11
4.96
4.81
4.73
4.65
4.57
4.48
4.40
4.31
10
10.04
7.56
6.55
5.99
5.64
5.39
5.20
5.06
4.94
4.85
4.71
4.56
4.41
4.33
4.25
4.17
4.08
4.00
3.91
11
9.65
7.21
6.22
5.67
5.32
5.07
4.89
4.74
4.63
4.54
4.40
4.25
4.10
4.02
3.94
3.86
3.78
3.69
3.60
12
9.33
6.93
5.95
5.41
5.06
4.82
4.64
4.50
4.39
4.30
4.16
4.01
3.86
3.78
3.70
3.62
3.54
3.45
3.36
13
9.07
6.70
5.74
5.21
4.86
4.62
4.44
4.30
4.19
4.10
3.96
3.82
3.66
3.59
3.51
3.43
3.34
3.25
3.17
14
8.86
6.51
5.56
5.04
4.69
4.46
4.28
4.14
4.03
3.94
3.80
3.66
3.51
3.43
3.35
3.27
3.18
3.09
3.00
15
8.68
6.36
5.42
4.89
4.56
4.32
4.14
4.00
3.89
3.80
3.67
3.52
3.37
3.29
3.21
3.13
3.05
2.96
2.87
16
8.53
6.23
5.29
4.77
4.44
4.20
4.03
3.89
3.78
3.69
3.55
3.41
3.26
3.18
3.10
3.02
2.93
2.84
2.75
17
8.40
6.11
5.18
4.67
4.34
4.10
3.93
3.79
3.68
3.59
3.46
3.31
3.16
3.08
3.00
2.92
2.83
2.75
2.65
18
8.29
6.01
5.09
4.58
4.25
4.01
3.84
3.71
3.60
3.51
3.37
3.23
3.08
3.00
2.92
2.84
2.75
2.66
2.57
19
8.18
5.93
5.01
4.50
4.17
3.94
3.77
3.63
3.52
3.43
3.30
3.15
3.00
2.92
2.84
2.76
2.67
2.58
2.49
20
8.10
5.85
4.94
4.43
4.10
3.87
3.70
3.56
3.46
3.37
3.23
3.09
2.94
2.86
2.78
2.69
2.61
2.52
2.42
21
8.02
5.78
4.87
4.37
4.04
3.81
3.64
3.51
3.40
3.31
3.17
3.03
2.88
2.80
2.72
2.64
2.55
2.46
2.36
22
7.95
5.72
4.82
4.31
3.99
3.76
3.59
3.45
3.35
3.26
3.12
2.98
2.83
2.75
2.67
2.58
2.50
2.40
2.31
23
7.88
5.66
4.76
4.26
3.94
3.71
3.54
3.41
3.30
3.21
3.07
2.93
2.78
2.70
2.62
2.54
2.45
2.35
2.26
24
7.82
5.61
4.72
4.22
3.90
3.67
3.50
3.36
3.26
3.17
3.03
2.89
2.74
2.66
2.58
2.49
2.40
2.31
2.21
25
7.77
5.57
4.68
4.18
3.85
3.63
3.46
3.32
3.22
3.13
2.99
2.85
2.70
2.62
2.54
2.45
2.36
2.27
2.17
26
7.72
5.53
4.64
4.14
3.82
3.59
3.42
3.29
3.18
3.09
2.96
2.81
2.66
2.58
2.50
2.42
2.33
2.23
2.13
27
7.68
5.49
4.60
4.11
3.78
3.56
3.39
3.26
3.15
3.06
2.93
2.78
2.63
2.55
2.47
2.38
2.29
2.20
2.10
28
7.64
5.45
4.57
4.07
3.75
3.53
3.36
3.23
3.12
3.03
2.90
2.75
2.60
2.52
2.44
2.35
2.26
2.17
2.06
29
7.60
5.42
4.54
4.04
3.73
3.50
3.33
3.20
3.09
3.00
2.87
2.73
2.57
2.49
2.41
2.33
2.23
2.14
2.03
30
7.56
5.39
4.51
4.02
3.70
3.47
3.30
3.17
3.07
2.98
2.84
2.70
2.55
2.47
2.39
2.30
2.21
2.11
2.01
40
7.31
5.18
4.31
3.83
3.51
3.29
3.12
2.99
2.89
2.80
2.66
2.52
2.37
2.29
2.20
2.11
2.02
1.92
1.80
60
7.08
4.98
4.13
3.65
3.34
3.12
2.95
2.82
2.72
2.63
2.50
2.35
2.20
2.12
2.03
1.94
1.84
1.73
1.60
120
6.85
4.79
3.95
3.48
3.17
2.96
2.79
2.66
2.56
2.47
2.34
2.19
2.03
1.95
1.86
1.76
1.66
1.53
1.38
6.63
4.61
3.78
3.32
3.02
2.80
2.64
2.51
2.41
2.32
2.18
2.04
1.88
1.79
1.70
1.59
1.47
1.32
1.00
Appendix C Tables
2
789
A–37
790
A–38
Appendix C Tables
Table H
(continued)
A 0.025
d.f.D.:
degrees of
freedom,
denominator
1
d.f.N.: degrees of freedom, numerator
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
647.8
799.5
864.2
899.6
921.8
937.1
948.2
956.7
963.3
968.6
976.7
984.9
993.1
997.2
1001
1006
1010
120
1014
1018
2
38.51
39.00
39.17
39.25
39.30
39.33
39.36
39.37
39.39
39.40
39.41
39.43
39.45
39.46
39.46
39.47
39.48
39.49
39.50
3
17.44
16.04
15.44
15.10
14.88
14.73
14.62
14.54
14.47
14.42
14.34
14.25
14.17
14.12
14.08
14.04
13.99
13.95
13.90
4
12.22
10.65
9.98
9.60
9.36
9.20
9.07
8.98
8.90
8.84
8.75
8.66
8.56
8.51
8.46
8.41
8.36
8.31
8.26
5
10.01
8.43
7.76
7.39
7.15
6.98
6.85
6.76
6.68
6.62
6.52
6.43
6.33
6.28
6.23
6.18
6.12
6.07
6.02
6
8.81
7.26
6.60
6.23
5.99
5.82
5.70
5.60
5.52
5.46
5.37
5.27
5.17
5.12
5.07
5.01
4.96
4.90
4.85
7
8.07
6.54
5.89
5.52
5.29
5.12
4.99
4.90
4.82
4.76
4.67
4.57
4.47
4.42
4.36
4.31
4.25
4.20
4.14
8
7.57
6.06
5.42
5.05
4.82
4.65
4.53
4.43
4.36
4.30
4.20
4.10
4.00
3.95
3.89
3.84
3.78
3.73
3.67
9
7.21
5.71
5.08
4.72
4.48
4.32
4.20
4.10
4.03
3.96
3.87
3.77
3.67
3.61
3.56
3.51
3.45
3.39
3.33
10
6.94
5.46
4.83
4.47
4.24
4.07
3.95
3.85
3.78
3.72
3.62
3.52
3.42
3.37
3.31
3.26
3.20
3.14
3.08
11
6.72
5.26
4.63
4.28
4.04
3.88
3.76
3.66
3.59
3.53
3.43
3.33
3.23
3.17
3.12
3.06
3.00
2.94
2.88
12
6.55
5.10
4.47
4.12
3.89
3.73
3.61
3.51
3.44
3.37
3.28
3.18
3.07
3.02
2.96
2.91
2.85
2.79
2.72
13
6.41
4.97
4.35
4.00
3.77
3.60
3.48
3.39
3.31
3.25
3.15
3.05
2.95
2.89
2.84
2.78
2.72
2.66
2.60
14
6.30
4.86
4.24
3.89
3.66
3.50
3.38
3.29
3.21
3.15
3.05
2.95
2.84
2.79
2.73
2.67
2.61
2.55
2.49
15
6.20
4.77
4.15
3.80
3.58
3.41
3.29
3.20
3.12
3.06
2.96
2.86
2.76
2.70
2.64
2.59
2.52
2.46
2.40
16
6.12
4.69
4.08
3.73
3.50
3.34
3.22
3.12
3.05
2.99
2.89
2.79
2.68
2.63
2.57
2.51
2.45
2.38
2.32
17
6.04
4.62
4.01
3.66
3.44
3.28
3.16
3.06
2.98
2.92
2.82
2.72
2.62
2.56
2.50
2.44
2.38
2.32
2.25
18
5.98
4.56
3.95
3.61
3.38
3.22
3.10
3.01
2.93
2.87
2.77
2.67
2.56
2.50
2.44
2.38
2.32
2.26
2.19
19
5.92
4.51
3.90
3.56
3.33
3.17
3.05
2.96
2.88
2.82
2.72
2.62
2.51
2.45
2.39
2.33
2.27
2.20
2.13
20
5.87
4.46
3.86
3.51
3.29
3.13
3.01
2.91
2.84
2.77
2.68
2.57
2.46
2.41
2.35
2.29
2.22
2.16
2.09
21
5.83
4.42
3.82
3.48
3.25
3.09
2.97
2.87
2.80
2.73
2.64
2.53
2.42
2.37
2.31
2.25
2.18
2.11
2.04
22
5.79
4.38
3.78
3.44
3.22
3.05
2.93
2.84
2.76
2.70
2.60
2.50
2.39
2.33
2.27
2.21
2.14
2.08
2.00
23
5.75
4.35
3.75
3.41
3.18
3.02
2.90
2.81
2.73
2.67
2.57
2.47
2.36
2.30
2.24
2.18
2.11
2.04
1.97
24
5.72
4.32
3.72
3.38
3.15
2.99
2.87
2.78
2.70
2.64
2.54
2.44
2.33
2.27
2.21
2.15
2.08
2.01
1.94
25
5.69
4.29
3.69
3.35
3.13
2.97
2.85
2.75
2.68
2.61
2.51
2.41
2.30
2.24
2.18
2.12
2.05
1.98
1.91
26
5.66
4.27
3.67
3.33
3.10
2.94
2.82
2.73
2.65
2.59
2.49
2.39
2.28
2.22
2.16
2.09
2.03
1.95
1.88
27
5.63
4.24
3.65
3.31
3.08
2.92
2.80
2.71
2.63
2.57
2.47
2.36
2.25
2.19
2.13
2.07
2.00
1.93
1.85
28
5.61
4.22
3.63
3.29
3.06
2.90
2.78
2.69
2.61
2.55
2.45
2.34
2.23
2.17
2.11
2.05
1.98
1.91
1.83
29
5.59
4.20
3.61
3.27
3.04
2.88
2.76
2.67
2.59
2.53
2.43
2.32
2.21
2.15
2.09
2.03
1.96
1.89
1.81
30
5.57
4.18
3.59
3.25
3.03
2.87
2.75
2.65
2.57
2.51
2.41
2.31
2.20
2.14
2.07
2.01
1.94
1.87
1.79
40
5.42
4.05
3.46
3.13
2.90
2.74
2.62
2.53
2.45
2.39
2.29
2.18
2.07
2.01
1.94
1.88
1.80
1.72
1.64
60
5.29
3.93
3.34
3.01
2.79
2.63
2.51
2.41
2.33
2.27
2.17
2.06
1.94
1.88
1.82
1.74
1.67
1.58
1.48
120
5.15
3.80
3.23
2.89
2.67
2.52
2.39
2.30
2.22
2.16
2.05
1.94
1.82
1.76
1.69
1.61
1.53
1.43
1.31
5.02
3.69
3.12
2.79
2.57
2.41
2.29
2.19
2.11
2.05
1.94
1.83
1.71
1.64
1.57
1.48
1.39
1.27
1.00
Table H
(continued)
A 0.05
d.f.D.:
degrees of
freedom,
denominator
1
d.f.N.: degrees of freedom, numerator
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
120
161.4
199.5
215.7
224.6
230.2
234.0
236.8
238.9
240.5
241.9
243.9
245.9
248.0
249.1
250.1
251.1
252.2
253.3
254.3
18.51
19.00
19.16
19.25
19.30
19.33
19.35
19.37
19.38
19.40
19.41
19.43
19.45
19.45
19.46
19.47
19.48
19.49
19.50
3
10.13
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
8.79
8.74
8.70
8.66
8.64
8.62
8.59
8.57
8.55
8.53
4
7.71
6.94
6.59
6.39
6.26
6.16
6.09
6.04
6.00
5.96
5.91
5.86
5.80
5.77
5.75
5.72
5.69
5.66
5.63
5
6.61
5.79
5.41
5.19
5.05
4.95
4.88
4.82
4.77
4.74
4.68
4.62
4.56
4.53
4.50
4.46
4.43
4.40
4.36
6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
4.06
4.00
3.94
3.87
3.84
3.81
3.77
3.74
3.70
3.67
7
5.59
4.74
4.35
4.12
3.97
3.87
3.79
3.73
3.68
3.64
3.57
3.51
3.44
3.41
3.38
3.34
3.30
3.27
3.23
8
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
3.35
3.28
3.22
3.15
3.12
3.08
3.04
3.01
2.97
2.93
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
3.23
3.18
3.14
3.07
3.01
2.94
2.90
2.86
2.83
2.79
2.75
2.71
10
4.96
4.10
3.71
3.48
3.33
3.22
3.14
3.07
3.02
2.98
2.91
2.85
2.77
2.74
2.70
2.66
2.62
2.58
2.54
11
4.84
3.98
3.59
3.36
3.20
3.09
3.01
2.95
2.90
2.85
2.79
2.72
2.65
2.61
2.57
2.53
2.49
2.45
2.40
12
4.75
3.89
3.49
3.26
3.11
3.00
2.91
2.85
2.80
2.75
2.69
2.62
2.54
2.51
2.47
2.43
2.38
2.34
2.30
13
4.67
3.81
3.41
3.18
3.03
2.92
2.83
2.77
2.71
2.67
2.60
2.53
2.46
2.42
2.38
2.34
2.30
2.25
2.21
14
4.60
3.74
3.34
3.11
2.96
2.85
2.76
2.70
2.65
2.60
2.53
2.46
2.39
2.35
2.31
2.27
2.22
2.18
2.13
15
4.54
3.68
3.29
3.06
2.90
2.79
2.71
2.64
2.59
2.54
2.48
2.40
2.33
2.29
2.25
2.20
2.16
2.11
2.07
16
4.49
3.63
3.24
3.01
2.85
2.74
2.66
2.59
2.54
2.49
2.42
2.35
2.28
2.24
2.19
2.15
2.11
2.06
2.01
17
4.45
3.59
3.20
2.96
2.81
2.70
2.61
2.55
2.49
2.45
2.38
2.31
2.23
2.19
2.15
2.10
2.06
2.01
1.96
18
4.41
3.55
3.16
2.93
2.77
2.66
2.58
2.51
2.46
2.41
2.34
2.27
2.19
2.15
2.11
2.06
2.02
1.97
1.92
19
4.38
3.52
3.13
2.90
2.74
2.63
2.54
2.48
2.42
2.38
2.31
2.23
2.16
2.11
2.07
2.03
1.98
1.93
1.88
20
4.35
3.49
3.10
2.87
2.71
2.60
2.51
2.45
2.39
2.35
2.28
2.20
2.12
2.08
2.04
1.99
1.95
1.90
1.84
21
4.32
3.47
3.07
2.84
2.68
2.57
2.49
2.42
2.37
2.32
2.25
2.18
2.10
2.05
2.01
1.96
1.92
1.87
1.81
22
4.30
3.44
3.05
2.82
2.66
2.55
2.46
2.40
2.34
2.30
2.23
2.15
2.07
2.03
1.98
1.94
1.89
1.84
1.78
23
4.28
3.42
3.03
2.80
2.64
2.53
2.44
2.37
2.32
2.27
2.20
2.13
2.05
2.01
1.96
1.91
1.86
1.81
1.76
24
4.26
3.40
3.01
2.78
2.62
2.51
2.42
2.36
2.30
2.25
2.18
2.11
2.03
1.98
1.94
1.89
1.84
1.79
1.73
25
4.24
3.39
2.99
2.76
2.60
2.49
2.40
2.34
2.28
2.24
2.16
2.09
2.01
1.96
1.92
1.87
1.82
1.77
1.71
26
4.23
3.37
2.98
2.74
2.59
2.47
2.39
2.32
2.27
2.22
2.15
2.07
1.99
1.95
1.90
1.85
1.80
1.75
1.69
27
4.21
3.35
2.96
2.73
2.57
2.46
2.37
2.31
2.25
2.20
2.13
2.06
1.97
1.93
1.88
1.84
1.79
1.73
1.67
28
4.20
3.34
2.95
2.71
2.56
2.45
2.36
2.29
2.24
2.19
2.12
2.04
1.96
1.91
1.87
1.82
1.77
1.71
1.65
29
4.18
3.33
2.93
2.70
2.55
2.43
2.35
2.28
2.22
2.18
2.10
2.03
1.94
1.90
1.85
1.81
1.75
1.70
1.64
30
4.17
3.32
2.92
2.69
2.53
2.42
2.33
2.27
2.21
2.16
2.09
2.01
1.93
1.89
1.84
1.79
1.74
1.68
1.62
40
4.08
3.23
2.84
2.61
2.45
2.34
2.25
2.18
2.12
2.08
2.00
1.92
1.84
1.79
1.74
1.69
1.64
1.58
1.51
60
4.00
3.15
2.76
2.53
2.37
2.25
2.17
2.10
2.04
1.99
1.92
1.84
1.75
1.70
1.65
1.59
1.53
1.47
1.39
120
3.92
3.07
2.68
2.45
2.29
2.17
2.09
2.02
1.96
1.91
1.83
1.75
1.66
1.61
1.55
1.50
1.43
1.35
1.25
3.84
3.00
2.60
2.37
2.21
2.10
2.01
1.94
1.88
1.83
1.75
1.67
1.57
1.52
1.46
1.39
1.32
1.22
1.00
Appendix C Tables
2
791
A–39
792
A–40
Appendix C Tables
Table H
(concluded)
A 0.10
d.f.D.:
degrees of
freedom,
denominator
d.f.N.: degrees of freedom, numerator
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
120
1
39.86
49.50
53.59
55.83
57.24
58.20
58.91
59.44
59.86
60.19
60.71
61.22
61.74
62.00
62.26
62.53
62.79
63.06
63.33
2
8.53
9.00
9.16
9.24
9.29
9.33
9.35
9.37
9.38
9.39
9.41
9.42
9.44
9.45
9.46
9.47
9.47
9.48
9.49
3
5.54
5.46
5.39
5.34
5.31
5.28
5.27
5.25
5.24
5.23
5.22
5.20
5.18
5.18
5.17
5.16
5.15
5.14
5.13
4
4.54
4.32
4.19
4.11
4.05
4.01
3.98
3.95
3.94
3.92
3.90
3.87
3.84
3.83
3.82
3.80
3.79
3.78
3.76
5
4.06
3.78
3.62
3.52
3.45
3.40
3.37
3.34
3.32
3.30
3.27
3.24
3.21
3.19
3.17
3.16
3.14
3.12
3.10
6
3.78
3.46
3.29
3.18
3.11
3.05
3.01
2.98
2.96
2.94
2.90
2.87
2.84
2.82
2.80
2.78
2.76
2.74
2.72
7
3.59
3.26
3.07
2.96
2.88
2.83
2.78
2.75
2.72
2.70
2.67
2.63
2.59
2.58
2.56
2.54
2.51
2.49
2.47
8
3.46
3.11
2.92
2.81
2.73
2.67
2.62
2.59
2.56
2.54
2.50
2.46
2.42
2.40
2.38
2.36
2.34
2.32
2.29
9
3.36
3.01
2.81
2.69
2.61
2.55
2.51
2.47
2.44
2.42
2.38
2.34
2.30
2.28
2.25
2.23
2.21
2.18
2.16
10
3.29
2.92
2.73
2.61
2.52
2.46
2.41
2.38
2.35
2.32
2.28
2.24
2.20
2.18
2.16
2.13
2.11
2.08
2.06
11
3.23
2.86
2.66
2.54
2.45
2.39
2.34
2.30
2.27
2.25
2.21
2.17
2.12
2.10
2.08
2.05
2.03
2.00
1.97
12
3.18
2.81
2.61
2.48
2.39
2.33
2.28
2.24
2.21
2.19
2.15
2.10
2.06
2.04
2.01
1.99
1.96
1.93
1.90
13
3.14
2.76
2.56
2.43
2.35
2.28
2.23
2.20
2.16
2.14
2.10
2.05
2.01
1.98
1.96
1.93
1.90
1.88
1.85
14
3.10
2.73
2.52
2.39
2.31
2.24
2.19
2.15
2.12
2.10
2.05
2.01
1.96
1.94
1.91
1.89
1.86
1.83
1.80
15
3.07
2.70
2.49
2.36
2.27
2.21
2.16
2.12
2.09
2.06
2.02
1.97
1.92
1.90
1.87
1.85
1.82
1.79
1.76
16
3.05
2.67
2.46
2.33
2.24
2.18
2.13
2.09
2.06
2.03
1.99
1.94
1.89
1.87
1.84
1.81
1.78
1.75
1.72
17
3.03
2.64
2.44
2.31
2.22
2.15
2.10
2.06
2.03
2.00
1.96
1.91
1.86
1.84
1.81
1.78
1.75
1.72
1.69
18
3.01
2.62
2.42
2.29
2.20
2.13
2.08
2.04
2.00
1.98
1.93
1.89
1.84
1.81
1.78
1.75
1.72
1.69
1.66
19
2.99
2.61
2.40
2.27
2.18
2.11
2.06
2.02
1.98
1.96
1.91
1.86
1.81
1.79
1.76
1.73
1.70
1.67
1.63
20
2.97
2.59
2.38
2.25
2.16
2.09
2.04
2.00
1.96
1.94
1.89
1.84
1.79
1.77
1.74
1.71
1.68
1.64
1.61
21
2.96
2.57
2.36
2.23
2.14
2.08
2.02
1.98
1.95
1.92
1.87
1.83
1.78
1.75
1.72
1.69
1.66
1.62
1.59
22
2.95
2.56
2.35
2.22
2.13
2.06
2.01
1.97
1.93
1.90
1.86
1.81
1.76
1.73
1.70
1.67
1.64
1.60
1.57
23
2.94
2.55
2.34
2.21
2.11
2.05
1.99
1.95
1.92
1.89
1.84
1.80
1.74
1.72
1.69
1.66
1.62
1.59
1.55
24
2.93
2.54
2.33
2.19
2.10
2.04
1.98
1.94
1.91
1.88
1.83
1.78
1.73
1.70
1.67
1.64
1.61
1.57
1.53
25
2.92
2.53
2.32
2.18
2.09
2.02
1.97
1.93
1.89
1.87
1.82
1.77
1.72
1.69
1.66
1.63
1.59
1.56
1.52
26
2.91
2.52
2.31
2.17
2.08
2.01
1.96
1.92
1.88
1.86
1.81
1.76
1.71
1.68
1.65
1.61
1.58
1.54
1.50
27
2.90
2.51
2.30
2.17
2.07
2.00
1.95
1.91
1.87
1.85
1.80
1.75
1.70
1.67
1.64
1.60
1.57
1.53
1.49
28
2.89
2.50
2.29
2.16
2.06
2.00
1.94
1.90
1.87
1.84
1.79
1.74
1.69
1.66
1.63
1.59
1.56
1.52
1.48
29
2.89
2.50
2.28
2.15
2.06
1.99
1.93
1.89
1.86
1.83
1.78
1.73
1.68
1.65
1.62
1.58
1.55
1.51
1.47
30
2.88
2.49
2.28
2.14
2.05
1.98
1.93
1.88
1.85
1.82
1.77
1.72
1.67
1.64
1.61
1.57
1.54
1.50
1.46
40
2.84
2.44
2.23
2.09
2.00
1.93
1.87
1.83
1.79
1.76
1.71
1.66
1.61
1.57
1.54
1.51
1.47
1.42
1.38
60
2.79
2.39
2.18
2.04
1.95
1.87
1.82
1.77
1.74
1.71
1.66
1.60
1.54
1.51
1.48
1.44
1.40
1.35
1.29
120
2.75
2.35
2.13
1.99
1.90
1.82
1.77
1.72
1.68
1.65
1.60
1.55
1.48
1.45
1.41
1.37
1.32
1.26
1.19
2.71
2.30
2.08
1.94
1.85
1.77
1.72
1.67
1.63
1.60
1.55
1.49
1.42
1.38
1.34
1.30
1.24
1.17
1.00
From M. Merrington and C. M. Thompson (1943). Table of Percentage Points of the Inverted Beta (F) Distribution. Biometrika 33, pp. 74–87. Reprinted with permission from Biometrika.
793
Appendix C Tables
Table I
Critical Values for the PPMC
Table J
Reject H0: r 0 if the absolute value of r is greater than
the value given in the table. The values are for a two-tailed
test; d.f. n 2.
A 0.05
A 0.01
1
0.999
0.999
2
0.950
0.999
3
0.878
0.959
4
0.811
0.917
5
0.754
0.875
d.f.
Critical Values for the Sign Test
Reject the null hypothesis if the smaller number of positive
or negative signs is less than or equal to the value in
the table.
One-tailed,
A 0.005
A 0.01
A 0.025
A 0.05
n
Two-tailed,
A 0.01
A 0.02
A 0.05
A 0.10
8
0
0
0
1
9
0
0
1
1
0
0
1
1
6
0.707
0.834
10
7
0.666
0.798
11
0
1
1
2
1
1
2
2
8
0.632
0.765
12
9
0.602
0.735
13
1
1
2
3
1
2
3
3
10
0.576
0.708
14
11
0.553
0.684
15
2
2
3
3
2
2
3
4
12
0.532
0.661
16
13
0.514
0.641
17
2
3
4
4
3
3
4
5
14
0.497
0.623
18
15
0.482
0.606
19
3
4
4
5
3
4
5
5
16
0.468
0.590
20
17
0.456
0.575
21
4
4
5
6
4
5
5
6
18
0.444
0.561
22
19
0.433
0.549
23
4
5
6
7
5
5
6
7
5
6
6
7
20
0.423
0.537
24
25
0.381
0.487
25
30
0.349
0.449
35
0.325
0.418
40
0.304
0.393
45
0.288
0.372
50
0.273
0.354
60
0.250
0.325
70
0.232
0.302
80
0.217
0.283
90
0.205
0.267
100
0.195
0.254
Note: Table J is for one-tailed or two-tailed tests. The term n represents the total
number of positive and negative signs. The test value is the number of less
frequent signs.
Source: Table 1, p. 560, from “The Statistical Sign Test” by W. J. Dixon and
A. M. Mood, vol. 41. no. 236 (Dec. 1946), pp. 557–566.
Source: From Biometrika Tables for Statisticians, vol. 1 (1962), p. 138.
Reprinted with permission.
A–41
794
Appendix C Tables
Table K
Critical Values for the Wilcoxon
Signed-Rank Test
Table L
Reject the null hypothesis if the test value is less than or
equal to the value given in the table.
One-tailed,
A 0.05
n
Two-tailed,
A 0.10
A 0.025
A 0.05
A 0.01
A 0.02
A 0.005
A 0.01
5
1
6
2
1
7
4
2
0
8
6
4
2
0
9
8
6
3
2
10
11
8
5
3
11
14
11
7
5
12
17
14
10
7
13
21
17
13
10
14
26
21
16
13
15
30
25
20
16
16
36
30
24
19
17
41
35
28
23
18
47
40
33
28
19
54
46
38
32
20
60
52
43
37
21
68
59
49
43
22
75
66
56
49
23
83
73
62
55
24
92
81
69
61
25
101
90
77
68
26
110
98
85
76
27
120
107
93
84
28
130
117
102
92
29
141
127
111
100
30
152
137
120
109
Source: From Some Rapid Approximate Statistical Procedures, Copyright 1949,
1964 Lerderle Laboratories, American Cyanamid Co., Wayne, N.J. Reprinted
with permission.
A–42
Critical Values for the Rank Correlation
Coefficient
Reject H0: r 0 if the absolute value of rS is greater than
the value given in the table.
n
A 0.10
5
0.900
6
0.829
7
0.714
8
0.643
A 0.05
A 0.02
A 0.01
—
—
—
0.886
0.943
—
0.786
0.893
0.929
0.738
0.833
0.881
9
0.600
0.700
0.783
0.833
10
0.564
0.648
0.745
0.794
11
0.536
0.618
0.709
0.818
12
0.497
0.591
0.703
0.780
13
0.475
0.566
0.673
0.745
14
0.457
0.545
0.646
0.716
15
0.441
0.525
0.623
0.689
16
0.425
0.507
0.601
0.666
17
0.412
0.490
0.582
0.645
18
0.399
0.476
0.564
0.625
19
0.388
0.462
0.549
0.608
20
0.377
0.450
0.534
0.591
21
0.368
0.438
0.521
0.576
22
0.359
0.428
0.508
0.562
23
0.351
0.418
0.496
0.549
24
0.343
0.409
0.485
0.537
25
0.336
0.400
0.475
0.526
26
0.329
0.392
0.465
0.515
27
0.323
0.385
0.456
0.505
28
0.317
0.377
0.488
0.496
29
0.311
0.370
0.440
0.487
30
0.305
0.364
0.432
0.478
Source: From N. L. Johnson and F. C. Leone, Statistical and Experimental
Design, vol. I (1964), p. 412. Reprinted with permission from the Institute of
Mathematical Statistics.
Appendix C Tables
Table M
795
Critical Values for the Number of Runs
This table gives the critical values at a 0.05 for a two-tailed test. Reject the null hypothesis if the number of runs is less than
or equal to the smaller value or greater than or equal to the larger value.
Value of n2
Value
of n1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
1
6
1
8
1
8
1
8
2
8
2
8
2
8
2
8
2
8
2
8
2
8
2
8
2
8
3
8
3
8
3
8
3
8
3
8
3
8
1
6
1
8
1
9
2
9
2
9
2
10
3
10
3
10
3
10
3
10
3
10
3
10
3
10
3
10
4
10
4
10
4
10
4
10
4
10
1
6
1
8
2
9
2
10
3
10
3
11
3
11
3
12
3
12
4
12
4
12
4
12
4
12
4
12
4
12
4
12
5
12
5
12
5
12
1
6
2
8
2
9
3
10
3
11
3
12
3
12
4
13
4
13
4
13
4
13
5
14
5
14
5
14
5
14
5
14
5
14
6
14
6
14
1
6
2
8
2
10
3
11
3
12
3
13
4
13
4
14
5
14
5
14
5
14
5
15
5
15
6
15
6
16
6
16
6
16
6
16
6
16
1
6
2
8
3
10
3
11
3
12
4
13
4
14
5
14
5
15
5
15
6
16
6
16
6
16
6
16
6
17
7
17
7
17
7
17
7
17
1
6
2
8
3
10
3
12
4
13
4
14
5
14
5
15
5
16
6
16
6
16
6
17
7
17
7
18
7
18
7
18
8
18
8
18
8
18
1
6
2
8
3
10
3
12
4
13
5
14
5
15
5
16
6
16
6
17
7
17
7
18
7
18
7
18
8
19
8
19
8
19
8
20
9
20
1
6
2
8
3
10
4
12
4
13
5
14
5
15
6
16
6
17
7
17
7
18
7
19
8
19
8
19
8
20
9
20
9
20
9
21
9
21
2
6
2
8
3
10
4
12
4
13
5
14
6
16
6
16
7
17
7
18
7
19
8
19
8
20
8
20
9
21
9
21
9
21
10
22
10
22
2
6
2
8
3
10
4
12
5
14
5
15
6
16
6
17
7
18
7
19
8
19
8
20
9
20
9
21
9
21
10
22
10
22
10
23
10
23
2
6
2
8
3
10
4
12
5
14
5
15
6
16
7
17
7
18
8
19
8
20
9
20
9
21
9
22
10
22
10
23
10
23
11
23
11
24
2
6
3
8
3
10
4
12
5
14
6
15
6
16
7
18
7
18
8
19
8
20
9
21
9
22
10
22
10
23
11
23
11
24
11
24
12
25
2
6
3
8
4
10
4
12
5
14
6
16
6
17
7
18
8
19
8
20
9
21
9
21
10
22
10
23
11
23
11
24
11
25
12
25
12
25
2
6
3
8
4
10
4
12
5
14
6
16
7
17
7
18
8
19
9
20
9
21
10
22
10
23
11
23
11
24
11
25
12
25
12
26
13
26
2
6
3
8
4
10
5
12
5
14
6
16
7
17
8
18
8
19
9
20
9
21
10
22
10
23
11
24
11
25
12
25
12
26
13
26
13
27
2
6
3
8
4
10
5
12
6
14
6
16
7
17
8
18
8
20
9
21
10
22
10
23
11
23
11
24
12
25
12
26
13
26
13
27
13
27
2
6
3
8
4
10
5
12
6
14
6
16
7
17
8
18
9
20
9
21
10
22
10
23
11
24
12
25
12
25
13
26
13
27
13
27
14
28
Source: Adapted from C. Eisenhardt and F. Swed, “Tables for Testing Randomness of Grouping in a Sequence of Alternatives,” The Annals of Statistics, vol. 14 (1943),
pp. 83–86. Reprinted with permission of the Institute of Mathematical Statistics and of the Benjamin/Cummings Publishing Company, in whose publication, Elementary
Statistics, 3rd ed. (1989), by Mario F. Triola, this table appears.
A–43
796
A–44
Appendix C Tables
Table N
Critical Values for the Tukey Test
A 0.01
k
v
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1 90.03 135.0 164.3 185.6 202.2 215.8 227.2 237.0 245.6 253.2 260.0 266.2 271.8 277.0 281.8 286.3 290.4 294.3 298.0
2 14.04 19.02 22.29 24.72 26.63 28.20 29.53 30.68 31.69 32.59 33.40 34.13 34.81 35.43 36.00 36.53 37.03 37.50 37.95
3 8.26 10.62 12.17 13.33 14.24 15.00 15.64 16.20 16.69 17.13 17.53 17.89 18.22 18.52 18.81 19.07 19.32 19.55 19.77
4 6.51
8.12
9.17
9.96 10.58 11.10 11.55 11.93 12.27 12.57 12.84 13.09 13.32 13.53 13.73 13.91 14.08 14.24 14.40
5 5.70
6.98
7.80
8.42
8.91
9.32
9.67
9.97 10.24 10.48 10.70 10.89 11.08 11.24 11.40 11.55 11.68 11.81 11.93
6 5.24
6.33
7.03
7.56
7.97
8.32
8.61
8.87
9.10
9.30
9.48
9.65
9.81
9.95 10.08 10.21 10.32 10.43 10.54
7 4.95
5.92
6.54
7.01
7.37
7.68
7.94
8.17
8.37
8.55
8.71
8.86
9.00
9.12
9.24
9.35
9.46
9.55
9.65
8 4.75
5.64
6.20
6.62
6.96
7.24
7.47
7.68
7.86
8.03
8.18
8.31
8.44
8.55
8.66
8.76
8.85
8.94
9.03
9 4.60
5.43
5.96
6.35
6.66
6.91
7.13
7.33
7.49
7.65
7.78
7.91
8.03
8.13
8.23
8.33
8.41
8.49
8.57
10 4.48
5.27
5.77
6.14
6.43
6.67
6.87
7.05
7.21
7.36
7.49
7.60
7.71
7.81
7.91
7.99
8.08
8.15
8.23
11 4.39
5.15
5.62
5.97
6.25
6.48
6.67
6.84
6.99
7.13
7.25
7.36
7.46
7.56
7.65
7.73
7.81
7.88
7.95
12 4.32
5.05
5.50
5.84
6.10
6.32
6.51
6.67
6.81
6.94
7.06
7.17
7.26
7.36
7.44
7.52
7.59
7.66
7.73
13 4.26
4.96
5.40
5.73
5.98
6.19
6.37
6.53
6.67
6.79
6.90
7.01
7.10
7.19
7.27
7.35
7.42
7.48
7.55
14 4.21
4.89
5.32
5.63
5.88
6.08
6.26
6.41
6.54
6.66
6.77
6.87
6.96
7.05
7.13
7.20
7.27
7.33
7.39
15 4.17
4.84
5.25
5.56
5.80
5.99
6.16
6.31
6.44
6.55
6.66
6.76
6.84
6.93
7.00
7.07
7.14
7.20
7.26
16 4.13
4.79
5.19
5.49
5.72
5.92
6.08
6.22
6.35
6.46
6.56
6.66
6.74
6.82
6.90
6.97
7.03
7.09
7.15
17 4.10
4.74
5.14
5.43
5.66
5.85
6.01
6.15
6.27
6.38
6.48
6.57
6.66
6.73
6.81
6.87
6.94
7.00
7.05
18 4.07
4.70
5.09
5.38
5.60
5.79
5.94
6.08
6.20
6.31
6.41
6.50
6.58
6.65
6.73
6.79
6.85
6.91
6.97
19 4.05
4.67
5.05
5.33
5.55
5.73
5.89
6.02
6.14
6.25
6.34
6.43
6.51
6.58
6.65
6.72
6.78
6.84
6.89
20 4.02
4.64
5.02
5.29
5.51
5.69
5.84
5.97
6.09
6.19
6.28
6.37
6.45
6.52
6.59
6.65
6.71
6.77
6.82
24 3.96
4.55
4.91
5.17
5.37
5.54
5.69
5.81
5.92
6.02
6.11
6.19
6.26
6.33
6.39
6.45
6.51
6.56
6.61
30 3.89
4.45
4.80
5.05
5.24
5.40
5.54
5.65
5.76
5.85
5.93
6.01
6.08
6.14
6.20
6.26
6.31
6.36
6.41
40 3.82
4.37
4.70
4.93
5.11
5.26
5.39
5.50
5.60
5.69
5.76
5.83
5.90
5.96
6.02
6.07
6.12
6.16
6.21
60 3.76
4.28
4.59
4.82
4.99
5.13
5.25
5.36
5.45
5.53
5.60
5.67
5.73
5.78
5.84
5.89
5.93
5.97
6.01
120 3.70
4.20
4.50
4.71
4.87
5.01
5.12
5.21
5.30
5.37
5.44
5.50
5.56
5.61
5.66
5.71
5.75
5.79
5.83
3.64
4.12
4.40
4.60
4.76
4.88
4.99
5.08
5.16
5.23
5.29
5.35
5.40
5.45
5.49
5.54
5.57
5.61
5.65
(continued)
Table N
A 0.05
k
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
24
30
40
60
120
17.97
6.08
4.50
3.93
3.64
3.46
3.34
3.26
3.20
3.15
3.11
3.08
3.06
3.03
3.01
3.00
2.98
2.97
2.96
2.95
2.92
2.89
2.86
2.83
2.80
2.77
26.98
8.33
5.91
5.04
4.60
4.34
4.16
4.04
3.95
3.88
3.82
3.77
3.73
3.70
3.67
3.65
3.63
3.61
3.59
3.58
3.53
3.49
3.44
3.40
3.36
3.31
32.82
9.80
6.82
5.76
5.22
4.90
4.68
4.53
4.41
4.33
4.26
4.20
4.15
4.11
4.08
4.05
4.02
4.00
3.98
3.96
3.90
3.85
3.79
3.74
3.68
3.63
37.08
10.88
7.50
6.29
5.67
5.30
5.06
4.89
4.76
4.65
4.57
4.51
4.45
4.41
4.37
4.33
4.30
4.28
4.25
4.23
4.17
4.10
4.04
3.98
3.92
3.86
40.41
11.74
8.04
6.71
6.03
5.63
5.36
5.17
5.02
4.91
4.82
4.75
4.69
4.64
4.59
4.56
4.52
4.49
4.47
4.45
4.37
4.30
4.23
4.16
4.10
4.03
43.12
12.44
8.48
7.05
6.33
5.90
5.61
5.40
5.24
5.12
5.03
4.95
4.88
4.83
4.78
4.74
4.70
4.67
4.65
4.62
4.54
4.46
4.39
4.31
4.24
4.17
45.40
13.03
8.85
7.35
6.58
6.12
5.82
5.60
5.43
5.30
5.20
5.12
5.05
4.99
4.94
4.90
4.86
4.82
4.79
4.77
4.68
4.60
4.52
4.44
4.36
4.29
47.36
13.54
9.18
7.60
6.80
6.32
6.00
5.77
5.59
5.46
5.35
5.27
5.19
5.13
5.08
5.03
4.99
4.96
4.92
4.90
4.81
4.72
4.63
4.55
4.47
4.39
49.07
13.99
9.46
7.83
6.99
6.49
6.16
5.92
5.74
5.60
5.49
5.39
5.32
5.25
5.20
5.15
5.11
5.07
5.04
5.01
4.92
4.82
4.73
4.65
4.56
4.47
50.59
14.39
9.72
8.03
7.17
6.65
6.30
6.05
5.87
5.72
5.61
5.51
5.43
5.36
5.31
5.26
5.21
5.17
5.14
5.11
5.01
4.92
4.82
4.73
4.64
4.55
51.96
14.75
9.95
8.21
7.32
6.79
6.43
6.18
5.98
5.83
5.71
5.61
5.53
5.46
5.40
5.35
5.31
5.27
5.23
5.20
5.10
5.00
4.90
4.81
4.71
4.62
53.20
15.08
10.15
8.37
7.47
6.92
6.55
6.29
6.09
5.93
5.81
5.71
5.63
5.55
5.49
5.44
5.39
5.35
5.31
5.28
5.18
5.08
4.98
4.88
4.78
4.68
54.33
15.38
10.35
8.52
7.60
7.03
6.66
6.39
6.19
6.03
5.90
5.80
5.71
5.64
5.57
5.52
5.47
5.43
5.39
5.36
5.25
5.15
5.04
4.94
4.84
4.74
55.36
15.65
10.53
8.66
7.72
7.14
6.76
6.48
6.28
6.11
5.98
5.88
5.79
5.71
5.65
5.59
5.54
5.50
5.46
5.43
5.32
5.21
5.11
5.00
4.90
4.80
56.32
15.91
10.69
8.79
7.83
7.24
6.85
6.57
6.36
6.19
6.06
5.95
5.86
5.79
5.72
5.66
5.61
5.57
5.53
5.49
5.38
5.27
5.16
5.06
4.95
4.85
57.22
16.14
10.84
8.91
7.93
7.34
6.94
6.65
6.44
6.27
6.13
6.02
5.93
5.85
5.78
5.73
5.67
5.63
5.59
5.55
5.44
5.33
5.22
5.11
5.00
4.89
58.04
16.37
10.98
9.03
8.03
7.43
7.02
6.73
6.51
6.34
6.20
6.09
5.99
5.91
5.85
5.79
5.73
5.69
5.65
5.61
5.49
5.38
5.27
5.15
5.04
4.93
58.83
16.57
11.11
9.13
8.12
7.51
7.10
6.80
6.58
6.40
6.27
6.15
6.05
5.97
5.90
5.84
5.79
5.74
5.70
5.66
5.55
5.43
5.31
5.20
5.09
4.97
59.56
16.77
11.24
9.23
8.21
7.59
7.17
6.87
6.64
6.47
6.33
6.21
6.11
6.03
5.96
5.90
5.84
5.79
5.75
5.71
5.59
5.47
5.36
5.24
5.13
5.01
Appendix C Tables
v
797
A–45
798
A–46
Appendix C Tables
(concluded)
Table N
A 0.10
k
v
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
24
30
40
60
120
8.93
4.13
3.33
3.01
2.85
2.75
2.68
2.63
2.59
2.56
2.54
2.52
2.50
2.49
2.48
2.47
2.46
2.45
2.45
2.44
2.42
2.40
2.38
2.36
2.34
2.33
13.44
5.73
4.47
3.98
3.72
3.56
3.45
3.37
3.32
3.27
3.23
3.20
3.18
3.16
3.14
3.12
3.11
3.10
3.09
3.08
3.05
3.02
2.99
2.96
2.93
2.90
16.36
6.77
5.20
4.59
4.26
4.07
3.93
3.83
3.76
3.70
3.66
3.62
3.59
3.56
3.54
3.52
3.50
3.49
3.47
3.46
3.42
3.39
3.35
3.31
3.28
3.24
18.49
7.54
5.74
5.03
4.66
4.44
4.28
4.17
4.08
4.02
3.96
3.92
3.88
3.85
3.83
3.80
3.78
3.77
3.75
3.74
3.69
3.65
3.60
3.56
3.52
3.48
20.15
8.14
6.16
5.39
4.98
4.73
4.55
4.43
4.34
4.26
4.20
4.16
4.12
4.08
4.05
4.03
4.00
3.98
3.97
3.95
3.90
3.85
3.80
3.75
3.71
3.66
21.51
8.63
6.51
5.68
5.24
4.97
4.78
4.65
4.54
4.47
4.40
4.35
4.30
4.27
4.23
4.21
4.18
4.16
4.14
4.12
4.07
4.02
3.96
3.91
3.86
3.81
22.64
9.05
6.81
5.93
5.46
5.17
4.97
4.83
4.72
4.64
4.57
4.51
4.46
4.42
4.39
4.36
4.33
4.31
4.29
4.27
4.21
4.16
4.10
4.04
3.99
3.93
23.62
9.41
7.06
6.14
5.65
5.34
5.14
4.99
4.87
4.78
4.71
4.65
4.60
4.56
4.52
4.49
4.46
4.44
4.42
4.40
4.34
4.28
4.21
4.16
4.10
4.04
24.48
9.72
7.29
6.33
5.82
5.50
5.28
5.13
5.01
4.91
4.84
4.78
4.72
4.68
4.64
4.61
4.58
4.55
4.53
4.51
4.44
4.38
4.32
4.25
4.19
4.13
25.24
10.01
7.49
6.49
5.97
5.64
5.41
5.25
5.13
5.03
4.95
4.89
4.83
4.79
4.75
4.71
4.68
4.65
4.63
4.61
4.54
4.47
4.41
4.34
4.28
4.21
25.92
10.26
7.67
6.65
6.10
5.76
5.53
5.36
5.23
5.13
5.05
4.99
4.93
4.88
4.84
4.81
4.77
4.75
4.72
4.70
4.63
4.56
4.49
4.42
4.35
4.28
26.54
10.49
7.83
6.78
6.22
5.87
5.64
5.46
5.33
5.23
5.15
5.08
5.02
4.97
4.93
4.89
4.86
4.83
4.80
4.78
4.71
4.64
4.56
4.49
4.42
4.35
27.10
10.70
7.98
6.91
6.34
5.98
5.74
5.56
5.42
5.32
5.23
5.16
5.10
5.05
5.01
4.97
4.93
4.90
4.88
4.85
4.78
4.71
4.63
4.56
4.48
4.41
27.62
10.89
8.12
7.02
6.44
6.07
5.83
5.64
5.51
5.40
5.31
5.24
5.18
5.12
5.08
5.04
5.01
4.98
4.95
4.92
4.85
4.77
4.69
4.62
4.54
4.47
28.10
11.07
8.25
7.13
6.54
6.16
5.91
5.72
5.58
5.47
5.38
5.31
5.25
5.19
5.15
5.11
5.07
5.04
5.01
4.99
4.91
4.83
4.75
4.67
4.60
4.52
28.54
11.24
8.37
7.23
6.63
6.25
5.99
5.80
5.66
5.54
5.45
5.37
5.31
5.26
5.21
5.17
5.13
5.10
5.07
5.05
4.97
4.89
4.81
4.73
4.65
4.57
28.96
11.39
8.48
7.33
6.71
6.32
6.06
5.87
5.72
5.61
5.51
5.44
5.37
5.32
5.27
5.23
5.19
5.16
5.13
5.10
5.02
4.94
4.86
4.78
4.69
4.61
29.35
11.54
8.58
7.41
6.79
6.40
6.13
5.93
5.79
5.67
5.57
5.49
5.43
5.37
5.32
5.28
5.24
5.21
5.18
5.16
5.07
4.99
4.90
4.82
4.74
4.65
29.71
11.68
8.68
7.50
6.86
6.47
6.19
6.00
5.85
5.73
5.63
5.55
5.48
5.43
5.38
5.33
5.30
5.26
5.23
5.20
5.12
5.03
4.95
4.86
4.78
4.69
Source: “Tables of Range and Studentized Range,” Annals of Mathematical Statistics, vol. 31, no. 4. Reprinted with permission of the Institute of Mathematical Sciences.