Statistical Tables
Critical Values
\(r\)
|
|
One-tailed Test
|
Two-tailed Test
|
|
df
|
0.1
|
0.05
|
0.01
|
0.1
|
0.05
|
0.01
|
|
2
|
0.90
|
0.95
|
0.99
|
0.95
|
0.98
|
0.99
|
|
3
|
0.81
|
0.88
|
0.96
|
0.88
|
0.92
|
0.96
|
|
4
|
0.73
|
0.81
|
0.92
|
0.81
|
0.87
|
0.92
|
|
5
|
0.67
|
0.75
|
0.87
|
0.75
|
0.82
|
0.87
|
|
6
|
0.62
|
0.71
|
0.83
|
0.71
|
0.77
|
0.83
|
|
7
|
0.58
|
0.67
|
0.80
|
0.67
|
0.73
|
0.80
|
|
8
|
0.55
|
0.63
|
0.76
|
0.63
|
0.70
|
0.76
|
|
9
|
0.52
|
0.60
|
0.73
|
0.60
|
0.67
|
0.73
|
|
10
|
0.50
|
0.58
|
0.71
|
0.58
|
0.64
|
0.71
|
|
11
|
0.48
|
0.55
|
0.68
|
0.55
|
0.62
|
0.68
|
|
12
|
0.46
|
0.53
|
0.66
|
0.53
|
0.59
|
0.66
|
|
13
|
0.44
|
0.51
|
0.64
|
0.51
|
0.57
|
0.64
|
|
14
|
0.43
|
0.50
|
0.62
|
0.50
|
0.56
|
0.62
|
|
15
|
0.41
|
0.48
|
0.61
|
0.48
|
0.54
|
0.61
|
|
16
|
0.40
|
0.47
|
0.59
|
0.47
|
0.53
|
0.59
|
|
17
|
0.39
|
0.46
|
0.58
|
0.46
|
0.51
|
0.58
|
|
18
|
0.38
|
0.44
|
0.56
|
0.44
|
0.50
|
0.56
|
|
19
|
0.37
|
0.43
|
0.55
|
0.43
|
0.49
|
0.55
|
|
20
|
0.36
|
0.42
|
0.54
|
0.42
|
0.48
|
0.54
|
|
21
|
0.35
|
0.41
|
0.53
|
0.41
|
0.47
|
0.53
|
|
22
|
0.34
|
0.40
|
0.52
|
0.40
|
0.46
|
0.52
|
|
23
|
0.34
|
0.40
|
0.51
|
0.40
|
0.45
|
0.51
|
|
24
|
0.33
|
0.39
|
0.50
|
0.39
|
0.44
|
0.50
|
|
25
|
0.32
|
0.38
|
0.49
|
0.38
|
0.43
|
0.49
|
|
26
|
0.32
|
0.37
|
0.48
|
0.37
|
0.42
|
0.48
|
|
27
|
0.31
|
0.37
|
0.47
|
0.37
|
0.42
|
0.47
|
|
28
|
0.31
|
0.36
|
0.46
|
0.36
|
0.41
|
0.46
|
|
29
|
0.30
|
0.36
|
0.46
|
0.36
|
0.40
|
0.46
|
|
30
|
0.30
|
0.35
|
0.45
|
0.35
|
0.40
|
0.45
|
|
31
|
0.29
|
0.34
|
0.44
|
0.34
|
0.39
|
0.44
|
|
32
|
0.29
|
0.34
|
0.44
|
0.34
|
0.38
|
0.44
|
|
33
|
0.28
|
0.33
|
0.43
|
0.33
|
0.38
|
0.43
|
|
34
|
0.28
|
0.33
|
0.42
|
0.33
|
0.37
|
0.42
|
|
35
|
0.27
|
0.32
|
0.42
|
0.32
|
0.37
|
0.42
|
|
36
|
0.27
|
0.32
|
0.41
|
0.32
|
0.36
|
0.41
|
|
37
|
0.27
|
0.32
|
0.41
|
0.32
|
0.36
|
0.41
|
|
38
|
0.26
|
0.31
|
0.40
|
0.31
|
0.35
|
0.40
|
|
39
|
0.26
|
0.31
|
0.40
|
0.31
|
0.35
|
0.40
|
|
40
|
0.26
|
0.30
|
0.39
|
0.30
|
0.35
|
0.39
|
|
41
|
0.25
|
0.30
|
0.39
|
0.30
|
0.34
|
0.39
|
|
42
|
0.25
|
0.30
|
0.38
|
0.30
|
0.34
|
0.38
|
|
43
|
0.25
|
0.29
|
0.38
|
0.29
|
0.33
|
0.38
|
|
44
|
0.25
|
0.29
|
0.38
|
0.29
|
0.33
|
0.38
|
|
45
|
0.24
|
0.29
|
0.37
|
0.29
|
0.33
|
0.37
|
|
46
|
0.24
|
0.28
|
0.37
|
0.28
|
0.32
|
0.37
|
|
47
|
0.24
|
0.28
|
0.36
|
0.28
|
0.32
|
0.36
|
|
48
|
0.24
|
0.28
|
0.36
|
0.28
|
0.32
|
0.36
|
|
49
|
0.23
|
0.28
|
0.36
|
0.28
|
0.31
|
0.36
|
|
50
|
0.23
|
0.27
|
0.35
|
0.27
|
0.31
|
0.35
|
|
51
|
0.23
|
0.27
|
0.35
|
0.27
|
0.31
|
0.35
|
|
52
|
0.23
|
0.27
|
0.35
|
0.27
|
0.30
|
0.35
|
|
53
|
0.22
|
0.27
|
0.34
|
0.27
|
0.30
|
0.34
|
|
54
|
0.22
|
0.26
|
0.34
|
0.26
|
0.30
|
0.34
|
|
55
|
0.22
|
0.26
|
0.34
|
0.26
|
0.30
|
0.34
|
|
56
|
0.22
|
0.26
|
0.34
|
0.26
|
0.29
|
0.34
|
|
57
|
0.22
|
0.26
|
0.33
|
0.26
|
0.29
|
0.33
|
|
58
|
0.21
|
0.25
|
0.33
|
0.25
|
0.29
|
0.33
|
|
59
|
0.21
|
0.25
|
0.33
|
0.25
|
0.29
|
0.33
|
|
60
|
0.21
|
0.25
|
0.32
|
0.25
|
0.28
|
0.32
|
|
61
|
0.21
|
0.25
|
0.32
|
0.25
|
0.28
|
0.32
|
|
62
|
0.21
|
0.25
|
0.32
|
0.25
|
0.28
|
0.32
|
|
63
|
0.21
|
0.24
|
0.32
|
0.24
|
0.28
|
0.32
|
|
64
|
0.20
|
0.24
|
0.31
|
0.24
|
0.28
|
0.31
|
|
65
|
0.20
|
0.24
|
0.31
|
0.24
|
0.27
|
0.31
|
|
66
|
0.20
|
0.24
|
0.31
|
0.24
|
0.27
|
0.31
|
|
67
|
0.20
|
0.24
|
0.31
|
0.24
|
0.27
|
0.31
|
|
68
|
0.20
|
0.24
|
0.31
|
0.24
|
0.27
|
0.31
|
|
69
|
0.20
|
0.23
|
0.30
|
0.23
|
0.27
|
0.30
|
|
70
|
0.20
|
0.23
|
0.30
|
0.23
|
0.26
|
0.30
|
|
71
|
0.19
|
0.23
|
0.30
|
0.23
|
0.26
|
0.30
|
|
72
|
0.19
|
0.23
|
0.30
|
0.23
|
0.26
|
0.30
|
|
73
|
0.19
|
0.23
|
0.30
|
0.23
|
0.26
|
0.30
|
|
74
|
0.19
|
0.23
|
0.29
|
0.23
|
0.26
|
0.29
|
|
75
|
0.19
|
0.22
|
0.29
|
0.22
|
0.26
|
0.29
|
|
76
|
0.19
|
0.22
|
0.29
|
0.22
|
0.25
|
0.29
|
|
77
|
0.19
|
0.22
|
0.29
|
0.22
|
0.25
|
0.29
|
|
78
|
0.19
|
0.22
|
0.29
|
0.22
|
0.25
|
0.29
|
|
79
|
0.18
|
0.22
|
0.28
|
0.22
|
0.25
|
0.28
|
|
80
|
0.18
|
0.22
|
0.28
|
0.22
|
0.25
|
0.28
|
|
81
|
0.18
|
0.22
|
0.28
|
0.22
|
0.25
|
0.28
|
|
82
|
0.18
|
0.21
|
0.28
|
0.21
|
0.24
|
0.28
|
|
83
|
0.18
|
0.21
|
0.28
|
0.21
|
0.24
|
0.28
|
|
84
|
0.18
|
0.21
|
0.28
|
0.21
|
0.24
|
0.28
|
|
85
|
0.18
|
0.21
|
0.27
|
0.21
|
0.24
|
0.27
|
|
86
|
0.18
|
0.21
|
0.27
|
0.21
|
0.24
|
0.27
|
|
87
|
0.18
|
0.21
|
0.27
|
0.21
|
0.24
|
0.27
|
|
88
|
0.17
|
0.21
|
0.27
|
0.21
|
0.24
|
0.27
|
|
89
|
0.17
|
0.21
|
0.27
|
0.21
|
0.23
|
0.27
|
|
90
|
0.17
|
0.20
|
0.27
|
0.20
|
0.23
|
0.27
|
|
91
|
0.17
|
0.20
|
0.27
|
0.20
|
0.23
|
0.27
|
|
92
|
0.17
|
0.20
|
0.26
|
0.20
|
0.23
|
0.26
|
|
93
|
0.17
|
0.20
|
0.26
|
0.20
|
0.23
|
0.26
|
|
94
|
0.17
|
0.20
|
0.26
|
0.20
|
0.23
|
0.26
|
|
95
|
0.17
|
0.20
|
0.26
|
0.20
|
0.23
|
0.26
|
|
96
|
0.17
|
0.20
|
0.26
|
0.20
|
0.23
|
0.26
|
|
97
|
0.17
|
0.20
|
0.26
|
0.20
|
0.23
|
0.26
|
|
98
|
0.17
|
0.20
|
0.26
|
0.20
|
0.22
|
0.26
|
|
99
|
0.16
|
0.20
|
0.26
|
0.20
|
0.22
|
0.26
|
|
100
|
0.16
|
0.19
|
0.25
|
0.19
|
0.22
|
0.25
|
\(t\)
|
One-tailed Test
|
Two-tailed Test
|
|
df
|
0.05
|
0.025
|
0.01
|
0.005
|
0.0025
|
df
|
0.1
|
0.05
|
0.02
|
0.01
|
0.005
|
|
1
|
6.314
|
12.706
|
31.821
|
63.657
|
127.321
|
1
|
6.314
|
12.706
|
31.821
|
63.657
|
127.321
|
|
2
|
2.920
|
4.303
|
6.965
|
9.925
|
14.089
|
2
|
2.920
|
4.303
|
6.965
|
9.925
|
14.089
|
|
3
|
2.353
|
3.182
|
4.541
|
5.841
|
7.453
|
3
|
2.353
|
3.182
|
4.541
|
5.841
|
7.453
|
|
4
|
2.132
|
2.776
|
3.747
|
4.604
|
5.598
|
4
|
2.132
|
2.776
|
3.747
|
4.604
|
5.598
|
|
5
|
2.015
|
2.571
|
3.365
|
4.032
|
4.773
|
5
|
2.015
|
2.571
|
3.365
|
4.032
|
4.773
|
|
6
|
1.943
|
2.447
|
3.143
|
3.707
|
4.317
|
6
|
1.943
|
2.447
|
3.143
|
3.707
|
4.317
|
|
7
|
1.895
|
2.365
|
2.998
|
3.499
|
4.029
|
7
|
1.895
|
2.365
|
2.998
|
3.499
|
4.029
|
|
8
|
1.860
|
2.306
|
2.896
|
3.355
|
3.833
|
8
|
1.860
|
2.306
|
2.896
|
3.355
|
3.833
|
|
9
|
1.833
|
2.262
|
2.821
|
3.250
|
3.690
|
9
|
1.833
|
2.262
|
2.821
|
3.250
|
3.690
|
|
10
|
1.812
|
2.228
|
2.764
|
3.169
|
3.581
|
10
|
1.812
|
2.228
|
2.764
|
3.169
|
3.581
|
|
11
|
1.796
|
2.201
|
2.718
|
3.106
|
3.497
|
11
|
1.796
|
2.201
|
2.718
|
3.106
|
3.497
|
|
12
|
1.782
|
2.179
|
2.681
|
3.055
|
3.428
|
12
|
1.782
|
2.179
|
2.681
|
3.055
|
3.428
|
|
13
|
1.771
|
2.160
|
2.650
|
3.012
|
3.372
|
13
|
1.771
|
2.160
|
2.650
|
3.012
|
3.372
|
|
14
|
1.761
|
2.145
|
2.624
|
2.977
|
3.326
|
14
|
1.761
|
2.145
|
2.624
|
2.977
|
3.326
|
|
15
|
1.753
|
2.131
|
2.602
|
2.947
|
3.286
|
15
|
1.753
|
2.131
|
2.602
|
2.947
|
3.286
|
|
16
|
1.746
|
2.120
|
2.583
|
2.921
|
3.252
|
16
|
1.746
|
2.120
|
2.583
|
2.921
|
3.252
|
|
17
|
1.740
|
2.110
|
2.567
|
2.898
|
3.222
|
17
|
1.740
|
2.110
|
2.567
|
2.898
|
3.222
|
|
18
|
1.734
|
2.101
|
2.552
|
2.878
|
3.197
|
18
|
1.734
|
2.101
|
2.552
|
2.878
|
3.197
|
|
19
|
1.729
|
2.093
|
2.539
|
2.861
|
3.174
|
19
|
1.729
|
2.093
|
2.539
|
2.861
|
3.174
|
|
20
|
1.725
|
2.086
|
2.528
|
2.845
|
3.153
|
20
|
1.725
|
2.086
|
2.528
|
2.845
|
3.153
|
|
21
|
1.721
|
2.080
|
2.518
|
2.831
|
3.135
|
21
|
1.721
|
2.080
|
2.518
|
2.831
|
3.135
|
|
22
|
1.717
|
2.074
|
2.508
|
2.819
|
3.119
|
22
|
1.717
|
2.074
|
2.508
|
2.819
|
3.119
|
|
23
|
1.714
|
2.069
|
2.500
|
2.807
|
3.104
|
23
|
1.714
|
2.069
|
2.500
|
2.807
|
3.104
|
|
24
|
1.711
|
2.064
|
2.492
|
2.797
|
3.091
|
24
|
1.711
|
2.064
|
2.492
|
2.797
|
3.091
|
|
25
|
1.708
|
2.060
|
2.485
|
2.787
|
3.078
|
25
|
1.708
|
2.060
|
2.485
|
2.787
|
3.078
|
|
26
|
1.706
|
2.056
|
2.479
|
2.779
|
3.067
|
26
|
1.706
|
2.056
|
2.479
|
2.779
|
3.067
|
|
27
|
1.703
|
2.052
|
2.473
|
2.771
|
3.057
|
27
|
1.703
|
2.052
|
2.473
|
2.771
|
3.057
|
|
28
|
1.701
|
2.048
|
2.467
|
2.763
|
3.047
|
28
|
1.701
|
2.048
|
2.467
|
2.763
|
3.047
|
|
29
|
1.699
|
2.045
|
2.462
|
2.756
|
3.038
|
29
|
1.699
|
2.045
|
2.462
|
2.756
|
3.038
|
|
30
|
1.697
|
2.042
|
2.457
|
2.750
|
3.030
|
30
|
1.697
|
2.042
|
2.457
|
2.750
|
3.030
|
|
31
|
1.696
|
2.040
|
2.453
|
2.744
|
3.022
|
31
|
1.696
|
2.040
|
2.453
|
2.744
|
3.022
|
|
32
|
1.694
|
2.037
|
2.449
|
2.738
|
3.015
|
32
|
1.694
|
2.037
|
2.449
|
2.738
|
3.015
|
|
33
|
1.692
|
2.035
|
2.445
|
2.733
|
3.008
|
33
|
1.692
|
2.035
|
2.445
|
2.733
|
3.008
|
|
34
|
1.691
|
2.032
|
2.441
|
2.728
|
3.002
|
34
|
1.691
|
2.032
|
2.441
|
2.728
|
3.002
|
|
35
|
1.690
|
2.030
|
2.438
|
2.724
|
2.996
|
35
|
1.690
|
2.030
|
2.438
|
2.724
|
2.996
|
|
36
|
1.688
|
2.028
|
2.434
|
2.719
|
2.990
|
36
|
1.688
|
2.028
|
2.434
|
2.719
|
2.990
|
|
37
|
1.687
|
2.026
|
2.431
|
2.715
|
2.985
|
37
|
1.687
|
2.026
|
2.431
|
2.715
|
2.985
|
|
38
|
1.686
|
2.024
|
2.429
|
2.712
|
2.980
|
38
|
1.686
|
2.024
|
2.429
|
2.712
|
2.980
|
|
39
|
1.685
|
2.023
|
2.426
|
2.708
|
2.976
|
39
|
1.685
|
2.023
|
2.426
|
2.708
|
2.976
|
|
40
|
1.684
|
2.021
|
2.423
|
2.704
|
2.971
|
40
|
1.684
|
2.021
|
2.423
|
2.704
|
2.971
|
|
41
|
1.683
|
2.020
|
2.421
|
2.701
|
2.967
|
41
|
1.683
|
2.020
|
2.421
|
2.701
|
2.967
|
|
42
|
1.682
|
2.018
|
2.418
|
2.698
|
2.963
|
42
|
1.682
|
2.018
|
2.418
|
2.698
|
2.963
|
|
43
|
1.681
|
2.017
|
2.416
|
2.695
|
2.959
|
43
|
1.681
|
2.017
|
2.416
|
2.695
|
2.959
|
|
44
|
1.680
|
2.015
|
2.414
|
2.692
|
2.956
|
44
|
1.680
|
2.015
|
2.414
|
2.692
|
2.956
|
|
45
|
1.679
|
2.014
|
2.412
|
2.690
|
2.952
|
45
|
1.679
|
2.014
|
2.412
|
2.690
|
2.952
|
|
46
|
1.679
|
2.013
|
2.410
|
2.687
|
2.949
|
46
|
1.679
|
2.013
|
2.410
|
2.687
|
2.949
|
|
47
|
1.678
|
2.012
|
2.408
|
2.685
|
2.946
|
47
|
1.678
|
2.012
|
2.408
|
2.685
|
2.946
|
|
48
|
1.677
|
2.011
|
2.407
|
2.682
|
2.943
|
48
|
1.677
|
2.011
|
2.407
|
2.682
|
2.943
|
|
49
|
1.677
|
2.010
|
2.405
|
2.680
|
2.940
|
49
|
1.677
|
2.010
|
2.405
|
2.680
|
2.940
|
|
50
|
1.676
|
2.009
|
2.403
|
2.678
|
2.937
|
50
|
1.676
|
2.009
|
2.403
|
2.678
|
2.937
|
|
51
|
1.675
|
2.008
|
2.402
|
2.676
|
2.934
|
51
|
1.675
|
2.008
|
2.402
|
2.676
|
2.934
|
|
52
|
1.675
|
2.007
|
2.400
|
2.674
|
2.932
|
52
|
1.675
|
2.007
|
2.400
|
2.674
|
2.932
|
|
53
|
1.674
|
2.006
|
2.399
|
2.672
|
2.929
|
53
|
1.674
|
2.006
|
2.399
|
2.672
|
2.929
|
|
54
|
1.674
|
2.005
|
2.397
|
2.670
|
2.927
|
54
|
1.674
|
2.005
|
2.397
|
2.670
|
2.927
|
|
55
|
1.673
|
2.004
|
2.396
|
2.668
|
2.925
|
55
|
1.673
|
2.004
|
2.396
|
2.668
|
2.925
|
|
56
|
1.673
|
2.003
|
2.395
|
2.667
|
2.923
|
56
|
1.673
|
2.003
|
2.395
|
2.667
|
2.923
|
|
57
|
1.672
|
2.002
|
2.394
|
2.665
|
2.920
|
57
|
1.672
|
2.002
|
2.394
|
2.665
|
2.920
|
|
58
|
1.672
|
2.002
|
2.392
|
2.663
|
2.918
|
58
|
1.672
|
2.002
|
2.392
|
2.663
|
2.918
|
|
59
|
1.671
|
2.001
|
2.391
|
2.662
|
2.916
|
59
|
1.671
|
2.001
|
2.391
|
2.662
|
2.916
|
|
60
|
1.671
|
2.000
|
2.390
|
2.660
|
2.915
|
60
|
1.671
|
2.000
|
2.390
|
2.660
|
2.915
|
|
61
|
1.670
|
2.000
|
2.389
|
2.659
|
2.913
|
61
|
1.670
|
2.000
|
2.389
|
2.659
|
2.913
|
|
62
|
1.670
|
1.999
|
2.388
|
2.657
|
2.911
|
62
|
1.670
|
1.999
|
2.388
|
2.657
|
2.911
|
|
63
|
1.669
|
1.998
|
2.387
|
2.656
|
2.909
|
63
|
1.669
|
1.998
|
2.387
|
2.656
|
2.909
|
|
64
|
1.669
|
1.998
|
2.386
|
2.655
|
2.908
|
64
|
1.669
|
1.998
|
2.386
|
2.655
|
2.908
|
|
65
|
1.669
|
1.997
|
2.385
|
2.654
|
2.906
|
65
|
1.669
|
1.997
|
2.385
|
2.654
|
2.906
|
|
66
|
1.668
|
1.997
|
2.384
|
2.652
|
2.904
|
66
|
1.668
|
1.997
|
2.384
|
2.652
|
2.904
|
|
67
|
1.668
|
1.996
|
2.383
|
2.651
|
2.903
|
67
|
1.668
|
1.996
|
2.383
|
2.651
|
2.903
|
|
68
|
1.668
|
1.995
|
2.382
|
2.650
|
2.902
|
68
|
1.668
|
1.995
|
2.382
|
2.650
|
2.902
|
|
69
|
1.667
|
1.995
|
2.382
|
2.649
|
2.900
|
69
|
1.667
|
1.995
|
2.382
|
2.649
|
2.900
|
|
70
|
1.667
|
1.994
|
2.381
|
2.648
|
2.899
|
70
|
1.667
|
1.994
|
2.381
|
2.648
|
2.899
|
|
71
|
1.667
|
1.994
|
2.380
|
2.647
|
2.897
|
71
|
1.667
|
1.994
|
2.380
|
2.647
|
2.897
|
|
72
|
1.666
|
1.993
|
2.379
|
2.646
|
2.896
|
72
|
1.666
|
1.993
|
2.379
|
2.646
|
2.896
|
|
73
|
1.666
|
1.993
|
2.379
|
2.645
|
2.895
|
73
|
1.666
|
1.993
|
2.379
|
2.645
|
2.895
|
|
74
|
1.666
|
1.993
|
2.378
|
2.644
|
2.894
|
74
|
1.666
|
1.993
|
2.378
|
2.644
|
2.894
|
|
75
|
1.665
|
1.992
|
2.377
|
2.643
|
2.892
|
75
|
1.665
|
1.992
|
2.377
|
2.643
|
2.892
|
|
76
|
1.665
|
1.992
|
2.376
|
2.642
|
2.891
|
76
|
1.665
|
1.992
|
2.376
|
2.642
|
2.891
|
|
77
|
1.665
|
1.991
|
2.376
|
2.641
|
2.890
|
77
|
1.665
|
1.991
|
2.376
|
2.641
|
2.890
|
|
78
|
1.665
|
1.991
|
2.375
|
2.640
|
2.889
|
78
|
1.665
|
1.991
|
2.375
|
2.640
|
2.889
|
|
79
|
1.664
|
1.990
|
2.374
|
2.640
|
2.888
|
79
|
1.664
|
1.990
|
2.374
|
2.640
|
2.888
|
|
80
|
1.664
|
1.990
|
2.374
|
2.639
|
2.887
|
80
|
1.664
|
1.990
|
2.374
|
2.639
|
2.887
|
|
81
|
1.664
|
1.990
|
2.373
|
2.638
|
2.886
|
81
|
1.664
|
1.990
|
2.373
|
2.638
|
2.886
|
|
82
|
1.664
|
1.989
|
2.373
|
2.637
|
2.885
|
82
|
1.664
|
1.989
|
2.373
|
2.637
|
2.885
|
|
83
|
1.663
|
1.989
|
2.372
|
2.636
|
2.884
|
83
|
1.663
|
1.989
|
2.372
|
2.636
|
2.884
|
|
84
|
1.663
|
1.989
|
2.372
|
2.636
|
2.883
|
84
|
1.663
|
1.989
|
2.372
|
2.636
|
2.883
|
|
85
|
1.663
|
1.988
|
2.371
|
2.635
|
2.882
|
85
|
1.663
|
1.988
|
2.371
|
2.635
|
2.882
|
|
86
|
1.663
|
1.988
|
2.370
|
2.634
|
2.881
|
86
|
1.663
|
1.988
|
2.370
|
2.634
|
2.881
|
|
87
|
1.663
|
1.988
|
2.370
|
2.634
|
2.880
|
87
|
1.663
|
1.988
|
2.370
|
2.634
|
2.880
|
|
88
|
1.662
|
1.987
|
2.369
|
2.633
|
2.880
|
88
|
1.662
|
1.987
|
2.369
|
2.633
|
2.880
|
|
89
|
1.662
|
1.987
|
2.369
|
2.632
|
2.879
|
89
|
1.662
|
1.987
|
2.369
|
2.632
|
2.879
|
|
90
|
1.662
|
1.987
|
2.368
|
2.632
|
2.878
|
90
|
1.662
|
1.987
|
2.368
|
2.632
|
2.878
|
|
91
|
1.662
|
1.986
|
2.368
|
2.631
|
2.877
|
91
|
1.662
|
1.986
|
2.368
|
2.631
|
2.877
|
|
92
|
1.662
|
1.986
|
2.368
|
2.630
|
2.876
|
92
|
1.662
|
1.986
|
2.368
|
2.630
|
2.876
|
|
93
|
1.661
|
1.986
|
2.367
|
2.630
|
2.876
|
93
|
1.661
|
1.986
|
2.367
|
2.630
|
2.876
|
|
94
|
1.661
|
1.986
|
2.367
|
2.629
|
2.875
|
94
|
1.661
|
1.986
|
2.367
|
2.629
|
2.875
|
|
95
|
1.661
|
1.985
|
2.366
|
2.629
|
2.874
|
95
|
1.661
|
1.985
|
2.366
|
2.629
|
2.874
|
|
96
|
1.661
|
1.985
|
2.366
|
2.628
|
2.873
|
96
|
1.661
|
1.985
|
2.366
|
2.628
|
2.873
|
|
97
|
1.661
|
1.985
|
2.365
|
2.627
|
2.873
|
97
|
1.661
|
1.985
|
2.365
|
2.627
|
2.873
|
|
98
|
1.661
|
1.984
|
2.365
|
2.627
|
2.872
|
98
|
1.661
|
1.984
|
2.365
|
2.627
|
2.872
|
|
99
|
1.660
|
1.984
|
2.365
|
2.626
|
2.871
|
99
|
1.660
|
1.984
|
2.365
|
2.626
|
2.871
|
|
100
|
1.660
|
1.984
|
2.364
|
2.626
|
2.871
|
100
|
1.660
|
1.984
|
2.364
|
2.626
|
2.871
|
|
101
|
1.660
|
1.984
|
2.364
|
2.625
|
2.870
|
101
|
1.660
|
1.984
|
2.364
|
2.625
|
2.870
|
|
102
|
1.660
|
1.983
|
2.363
|
2.625
|
2.869
|
102
|
1.660
|
1.983
|
2.363
|
2.625
|
2.869
|
|
103
|
1.660
|
1.983
|
2.363
|
2.624
|
2.869
|
103
|
1.660
|
1.983
|
2.363
|
2.624
|
2.869
|
|
104
|
1.660
|
1.983
|
2.363
|
2.624
|
2.868
|
104
|
1.660
|
1.983
|
2.363
|
2.624
|
2.868
|
|
105
|
1.659
|
1.983
|
2.362
|
2.623
|
2.868
|
105
|
1.659
|
1.983
|
2.362
|
2.623
|
2.868
|
|
106
|
1.659
|
1.983
|
2.362
|
2.623
|
2.867
|
106
|
1.659
|
1.983
|
2.362
|
2.623
|
2.867
|
|
107
|
1.659
|
1.982
|
2.362
|
2.623
|
2.866
|
107
|
1.659
|
1.982
|
2.362
|
2.623
|
2.866
|
|
108
|
1.659
|
1.982
|
2.361
|
2.622
|
2.866
|
108
|
1.659
|
1.982
|
2.361
|
2.622
|
2.866
|
|
109
|
1.659
|
1.982
|
2.361
|
2.622
|
2.865
|
109
|
1.659
|
1.982
|
2.361
|
2.622
|
2.865
|
|
110
|
1.659
|
1.982
|
2.361
|
2.621
|
2.865
|
110
|
1.659
|
1.982
|
2.361
|
2.621
|
2.865
|
|
111
|
1.659
|
1.982
|
2.360
|
2.621
|
2.864
|
111
|
1.659
|
1.982
|
2.360
|
2.621
|
2.864
|
|
112
|
1.659
|
1.981
|
2.360
|
2.620
|
2.864
|
112
|
1.659
|
1.981
|
2.360
|
2.620
|
2.864
|
|
113
|
1.658
|
1.981
|
2.360
|
2.620
|
2.863
|
113
|
1.658
|
1.981
|
2.360
|
2.620
|
2.863
|
|
114
|
1.658
|
1.981
|
2.360
|
2.620
|
2.863
|
114
|
1.658
|
1.981
|
2.360
|
2.620
|
2.863
|
|
115
|
1.658
|
1.981
|
2.359
|
2.619
|
2.862
|
115
|
1.658
|
1.981
|
2.359
|
2.619
|
2.862
|
|
116
|
1.658
|
1.981
|
2.359
|
2.619
|
2.862
|
116
|
1.658
|
1.981
|
2.359
|
2.619
|
2.862
|
|
117
|
1.658
|
1.980
|
2.359
|
2.619
|
2.861
|
117
|
1.658
|
1.980
|
2.359
|
2.619
|
2.861
|
|
118
|
1.658
|
1.980
|
2.358
|
2.618
|
2.861
|
118
|
1.658
|
1.980
|
2.358
|
2.618
|
2.861
|
|
119
|
1.658
|
1.980
|
2.358
|
2.618
|
2.860
|
119
|
1.658
|
1.980
|
2.358
|
2.618
|
2.860
|
|
120
|
1.658
|
1.980
|
2.358
|
2.617
|
2.860
|
120
|
1.658
|
1.980
|
2.358
|
2.617
|
2.860
|
\(F\)
\(\alpha = 0.05\)
|
|
\(df_{numerator}\)
|
|
\(df_{denominator}\)
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
1
|
161.45
|
199.50
|
215.71
|
224.58
|
230.16
|
233.99
|
236.77
|
238.88
|
240.54
|
241.88
|
|
2
|
18.51
|
19.00
|
19.16
|
19.25
|
19.30
|
19.33
|
19.35
|
19.37
|
19.38
|
19.40
|
|
3
|
10.13
|
9.55
|
9.28
|
9.12
|
9.01
|
8.94
|
8.89
|
8.85
|
8.81
|
8.79
|
|
4
|
7.71
|
6.94
|
6.59
|
6.39
|
6.26
|
6.16
|
6.09
|
6.04
|
6.00
|
5.96
|
|
5
|
6.61
|
5.79
|
5.41
|
5.19
|
5.05
|
4.95
|
4.88
|
4.82
|
4.77
|
4.74
|
|
6
|
5.99
|
5.14
|
4.76
|
4.53
|
4.39
|
4.28
|
4.21
|
4.15
|
4.10
|
4.06
|
|
7
|
5.59
|
4.74
|
4.35
|
4.12
|
3.97
|
3.87
|
3.79
|
3.73
|
3.68
|
3.64
|
|
8
|
5.32
|
4.46
|
4.07
|
3.84
|
3.69
|
3.58
|
3.50
|
3.44
|
3.39
|
3.35
|
|
9
|
5.12
|
4.26
|
3.86
|
3.63
|
3.48
|
3.37
|
3.29
|
3.23
|
3.18
|
3.14
|
|
10
|
4.96
|
4.10
|
3.71
|
3.48
|
3.33
|
3.22
|
3.14
|
3.07
|
3.02
|
2.98
|
|
11
|
4.84
|
3.98
|
3.59
|
3.36
|
3.20
|
3.09
|
3.01
|
2.95
|
2.90
|
2.85
|
|
12
|
4.75
|
3.89
|
3.49
|
3.26
|
3.11
|
3.00
|
2.91
|
2.85
|
2.80
|
2.75
|
|
13
|
4.67
|
3.81
|
3.41
|
3.18
|
3.03
|
2.92
|
2.83
|
2.77
|
2.71
|
2.67
|
|
14
|
4.60
|
3.74
|
3.34
|
3.11
|
2.96
|
2.85
|
2.76
|
2.70
|
2.65
|
2.60
|
|
15
|
4.54
|
3.68
|
3.29
|
3.06
|
2.90
|
2.79
|
2.71
|
2.64
|
2.59
|
2.54
|
|
16
|
4.49
|
3.63
|
3.24
|
3.01
|
2.85
|
2.74
|
2.66
|
2.59
|
2.54
|
2.49
|
|
17
|
4.45
|
3.59
|
3.20
|
2.96
|
2.81
|
2.70
|
2.61
|
2.55
|
2.49
|
2.45
|
|
18
|
4.41
|
3.55
|
3.16
|
2.93
|
2.77
|
2.66
|
2.58
|
2.51
|
2.46
|
2.41
|
|
19
|
4.38
|
3.52
|
3.13
|
2.90
|
2.74
|
2.63
|
2.54
|
2.48
|
2.42
|
2.38
|
|
20
|
4.35
|
3.49
|
3.10
|
2.87
|
2.71
|
2.60
|
2.51
|
2.45
|
2.39
|
2.35
|
|
21
|
4.32
|
3.47
|
3.07
|
2.84
|
2.68
|
2.57
|
2.49
|
2.42
|
2.37
|
2.32
|
|
22
|
4.30
|
3.44
|
3.05
|
2.82
|
2.66
|
2.55
|
2.46
|
2.40
|
2.34
|
2.30
|
|
23
|
4.28
|
3.42
|
3.03
|
2.80
|
2.64
|
2.53
|
2.44
|
2.37
|
2.32
|
2.27
|
|
24
|
4.26
|
3.40
|
3.01
|
2.78
|
2.62
|
2.51
|
2.42
|
2.36
|
2.30
|
2.25
|
|
25
|
4.24
|
3.39
|
2.99
|
2.76
|
2.60
|
2.49
|
2.40
|
2.34
|
2.28
|
2.24
|
|
26
|
4.23
|
3.37
|
2.98
|
2.74
|
2.59
|
2.47
|
2.39
|
2.32
|
2.27
|
2.22
|
|
27
|
4.21
|
3.35
|
2.96
|
2.73
|
2.57
|
2.46
|
2.37
|
2.31
|
2.25
|
2.20
|
|
28
|
4.20
|
3.34
|
2.95
|
2.71
|
2.56
|
2.45
|
2.36
|
2.29
|
2.24
|
2.19
|
|
29
|
4.18
|
3.33
|
2.93
|
2.70
|
2.55
|
2.43
|
2.35
|
2.28
|
2.22
|
2.18
|
|
30
|
4.17
|
3.32
|
2.92
|
2.69
|
2.53
|
2.42
|
2.33
|
2.27
|
2.21
|
2.16
|
|
31
|
4.16
|
3.30
|
2.91
|
2.68
|
2.52
|
2.41
|
2.32
|
2.25
|
2.20
|
2.15
|
|
32
|
4.15
|
3.29
|
2.90
|
2.67
|
2.51
|
2.40
|
2.31
|
2.24
|
2.19
|
2.14
|
|
33
|
4.14
|
3.28
|
2.89
|
2.66
|
2.50
|
2.39
|
2.30
|
2.23
|
2.18
|
2.13
|
|
34
|
4.13
|
3.28
|
2.88
|
2.65
|
2.49
|
2.38
|
2.29
|
2.23
|
2.17
|
2.12
|
|
35
|
4.12
|
3.27
|
2.87
|
2.64
|
2.49
|
2.37
|
2.29
|
2.22
|
2.16
|
2.11
|
|
36
|
4.11
|
3.26
|
2.87
|
2.63
|
2.48
|
2.36
|
2.28
|
2.21
|
2.15
|
2.11
|
|
37
|
4.11
|
3.25
|
2.86
|
2.63
|
2.47
|
2.36
|
2.27
|
2.20
|
2.14
|
2.10
|
|
38
|
4.10
|
3.24
|
2.85
|
2.62
|
2.46
|
2.35
|
2.26
|
2.19
|
2.14
|
2.09
|
|
39
|
4.09
|
3.24
|
2.85
|
2.61
|
2.46
|
2.34
|
2.26
|
2.19
|
2.13
|
2.08
|
|
40
|
4.08
|
3.23
|
2.84
|
2.61
|
2.45
|
2.34
|
2.25
|
2.18
|
2.12
|
2.08
|
|
41
|
4.08
|
3.23
|
2.83
|
2.60
|
2.44
|
2.33
|
2.24
|
2.17
|
2.12
|
2.07
|
|
42
|
4.07
|
3.22
|
2.83
|
2.59
|
2.44
|
2.32
|
2.24
|
2.17
|
2.11
|
2.06
|
|
43
|
4.07
|
3.21
|
2.82
|
2.59
|
2.43
|
2.32
|
2.23
|
2.16
|
2.11
|
2.06
|
|
44
|
4.06
|
3.21
|
2.82
|
2.58
|
2.43
|
2.31
|
2.23
|
2.16
|
2.10
|
2.05
|
|
45
|
4.06
|
3.20
|
2.81
|
2.58
|
2.42
|
2.31
|
2.22
|
2.15
|
2.10
|
2.05
|
|
46
|
4.05
|
3.20
|
2.81
|
2.57
|
2.42
|
2.30
|
2.22
|
2.15
|
2.09
|
2.04
|
|
47
|
4.05
|
3.20
|
2.80
|
2.57
|
2.41
|
2.30
|
2.21
|
2.14
|
2.09
|
2.04
|
|
48
|
4.04
|
3.19
|
2.80
|
2.57
|
2.41
|
2.29
|
2.21
|
2.14
|
2.08
|
2.03
|
|
49
|
4.04
|
3.19
|
2.79
|
2.56
|
2.40
|
2.29
|
2.20
|
2.13
|
2.08
|
2.03
|
|
50
|
4.03
|
3.18
|
2.79
|
2.56
|
2.40
|
2.29
|
2.20
|
2.13
|
2.07
|
2.03
|
|
51
|
4.03
|
3.18
|
2.79
|
2.55
|
2.40
|
2.28
|
2.20
|
2.13
|
2.07
|
2.02
|
|
52
|
4.03
|
3.18
|
2.78
|
2.55
|
2.39
|
2.28
|
2.19
|
2.12
|
2.07
|
2.02
|
|
53
|
4.02
|
3.17
|
2.78
|
2.55
|
2.39
|
2.28
|
2.19
|
2.12
|
2.06
|
2.01
|
|
54
|
4.02
|
3.17
|
2.78
|
2.54
|
2.39
|
2.27
|
2.18
|
2.12
|
2.06
|
2.01
|
|
55
|
4.02
|
3.16
|
2.77
|
2.54
|
2.38
|
2.27
|
2.18
|
2.11
|
2.06
|
2.01
|
|
56
|
4.01
|
3.16
|
2.77
|
2.54
|
2.38
|
2.27
|
2.18
|
2.11
|
2.05
|
2.00
|
|
57
|
4.01
|
3.16
|
2.77
|
2.53
|
2.38
|
2.26
|
2.18
|
2.11
|
2.05
|
2.00
|
|
58
|
4.01
|
3.16
|
2.76
|
2.53
|
2.37
|
2.26
|
2.17
|
2.10
|
2.05
|
2.00
|
|
59
|
4.00
|
3.15
|
2.76
|
2.53
|
2.37
|
2.26
|
2.17
|
2.10
|
2.04
|
2.00
|
|
60
|
4.00
|
3.15
|
2.76
|
2.53
|
2.37
|
2.25
|
2.17
|
2.10
|
2.04
|
1.99
|
|
61
|
4.00
|
3.15
|
2.76
|
2.52
|
2.37
|
2.25
|
2.16
|
2.09
|
2.04
|
1.99
|
|
62
|
4.00
|
3.15
|
2.75
|
2.52
|
2.36
|
2.25
|
2.16
|
2.09
|
2.03
|
1.99
|
|
63
|
3.99
|
3.14
|
2.75
|
2.52
|
2.36
|
2.25
|
2.16
|
2.09
|
2.03
|
1.98
|
|
64
|
3.99
|
3.14
|
2.75
|
2.52
|
2.36
|
2.24
|
2.16
|
2.09
|
2.03
|
1.98
|
|
65
|
3.99
|
3.14
|
2.75
|
2.51
|
2.36
|
2.24
|
2.15
|
2.08
|
2.03
|
1.98
|
|
66
|
3.99
|
3.14
|
2.74
|
2.51
|
2.35
|
2.24
|
2.15
|
2.08
|
2.03
|
1.98
|
|
67
|
3.98
|
3.13
|
2.74
|
2.51
|
2.35
|
2.24
|
2.15
|
2.08
|
2.02
|
1.98
|
|
68
|
3.98
|
3.13
|
2.74
|
2.51
|
2.35
|
2.24
|
2.15
|
2.08
|
2.02
|
1.97
|
|
69
|
3.98
|
3.13
|
2.74
|
2.50
|
2.35
|
2.23
|
2.15
|
2.08
|
2.02
|
1.97
|
|
70
|
3.98
|
3.13
|
2.74
|
2.50
|
2.35
|
2.23
|
2.14
|
2.07
|
2.02
|
1.97
|
|
71
|
3.98
|
3.13
|
2.73
|
2.50
|
2.34
|
2.23
|
2.14
|
2.07
|
2.01
|
1.97
|
|
72
|
3.97
|
3.12
|
2.73
|
2.50
|
2.34
|
2.23
|
2.14
|
2.07
|
2.01
|
1.96
|
|
73
|
3.97
|
3.12
|
2.73
|
2.50
|
2.34
|
2.23
|
2.14
|
2.07
|
2.01
|
1.96
|
|
74
|
3.97
|
3.12
|
2.73
|
2.50
|
2.34
|
2.22
|
2.14
|
2.07
|
2.01
|
1.96
|
|
75
|
3.97
|
3.12
|
2.73
|
2.49
|
2.34
|
2.22
|
2.13
|
2.06
|
2.01
|
1.96
|
|
76
|
3.97
|
3.12
|
2.72
|
2.49
|
2.33
|
2.22
|
2.13
|
2.06
|
2.01
|
1.96
|
|
77
|
3.97
|
3.12
|
2.72
|
2.49
|
2.33
|
2.22
|
2.13
|
2.06
|
2.00
|
1.96
|
|
78
|
3.96
|
3.11
|
2.72
|
2.49
|
2.33
|
2.22
|
2.13
|
2.06
|
2.00
|
1.95
|
|
79
|
3.96
|
3.11
|
2.72
|
2.49
|
2.33
|
2.22
|
2.13
|
2.06
|
2.00
|
1.95
|
|
80
|
3.96
|
3.11
|
2.72
|
2.49
|
2.33
|
2.21
|
2.13
|
2.06
|
2.00
|
1.95
|
|
81
|
3.96
|
3.11
|
2.72
|
2.48
|
2.33
|
2.21
|
2.12
|
2.05
|
2.00
|
1.95
|
|
82
|
3.96
|
3.11
|
2.72
|
2.48
|
2.33
|
2.21
|
2.12
|
2.05
|
2.00
|
1.95
|
|
83
|
3.96
|
3.11
|
2.71
|
2.48
|
2.32
|
2.21
|
2.12
|
2.05
|
1.99
|
1.95
|
|
84
|
3.95
|
3.11
|
2.71
|
2.48
|
2.32
|
2.21
|
2.12
|
2.05
|
1.99
|
1.95
|
|
85
|
3.95
|
3.10
|
2.71
|
2.48
|
2.32
|
2.21
|
2.12
|
2.05
|
1.99
|
1.94
|
|
86
|
3.95
|
3.10
|
2.71
|
2.48
|
2.32
|
2.21
|
2.12
|
2.05
|
1.99
|
1.94
|
|
87
|
3.95
|
3.10
|
2.71
|
2.48
|
2.32
|
2.20
|
2.12
|
2.05
|
1.99
|
1.94
|
|
88
|
3.95
|
3.10
|
2.71
|
2.48
|
2.32
|
2.20
|
2.12
|
2.05
|
1.99
|
1.94
|
|
89
|
3.95
|
3.10
|
2.71
|
2.47
|
2.32
|
2.20
|
2.11
|
2.04
|
1.99
|
1.94
|
|
90
|
3.95
|
3.10
|
2.71
|
2.47
|
2.32
|
2.20
|
2.11
|
2.04
|
1.99
|
1.94
|
|
91
|
3.95
|
3.10
|
2.70
|
2.47
|
2.31
|
2.20
|
2.11
|
2.04
|
1.98
|
1.94
|
|
92
|
3.94
|
3.10
|
2.70
|
2.47
|
2.31
|
2.20
|
2.11
|
2.04
|
1.98
|
1.94
|
|
93
|
3.94
|
3.09
|
2.70
|
2.47
|
2.31
|
2.20
|
2.11
|
2.04
|
1.98
|
1.93
|
|
94
|
3.94
|
3.09
|
2.70
|
2.47
|
2.31
|
2.20
|
2.11
|
2.04
|
1.98
|
1.93
|
|
95
|
3.94
|
3.09
|
2.70
|
2.47
|
2.31
|
2.20
|
2.11
|
2.04
|
1.98
|
1.93
|
|
96
|
3.94
|
3.09
|
2.70
|
2.47
|
2.31
|
2.19
|
2.11
|
2.04
|
1.98
|
1.93
|
|
97
|
3.94
|
3.09
|
2.70
|
2.47
|
2.31
|
2.19
|
2.11
|
2.04
|
1.98
|
1.93
|
|
98
|
3.94
|
3.09
|
2.70
|
2.46
|
2.31
|
2.19
|
2.10
|
2.03
|
1.98
|
1.93
|
|
99
|
3.94
|
3.09
|
2.70
|
2.46
|
2.31
|
2.19
|
2.10
|
2.03
|
1.98
|
1.93
|
|
100
|
3.94
|
3.09
|
2.70
|
2.46
|
2.31
|
2.19
|
2.10
|
2.03
|
1.97
|
1.93
|
\(\alpha = 0.01\)
|
|
\(df_{numerator}\)
|
|
\(df_{denominator}\)
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
1
|
4052.18
|
4999.50
|
5403.35
|
5624.58
|
5763.65
|
5858.99
|
5928.36
|
5981.07
|
6022.47
|
6055.85
|
|
2
|
98.50
|
99.00
|
99.17
|
99.25
|
99.30
|
99.33
|
99.36
|
99.37
|
99.39
|
99.40
|
|
3
|
34.12
|
30.82
|
29.46
|
28.71
|
28.24
|
27.91
|
27.67
|
27.49
|
27.35
|
27.23
|
|
4
|
21.20
|
18.00
|
16.69
|
15.98
|
15.52
|
15.21
|
14.98
|
14.80
|
14.66
|
14.55
|
|
5
|
16.26
|
13.27
|
12.06
|
11.39
|
10.97
|
10.67
|
10.46
|
10.29
|
10.16
|
10.05
|
|
6
|
13.75
|
10.92
|
9.78
|
9.15
|
8.75
|
8.47
|
8.26
|
8.10
|
7.98
|
7.87
|
|
7
|
12.25
|
9.55
|
8.45
|
7.85
|
7.46
|
7.19
|
6.99
|
6.84
|
6.72
|
6.62
|
|
8
|
11.26
|
8.65
|
7.59
|
7.01
|
6.63
|
6.37
|
6.18
|
6.03
|
5.91
|
5.81
|
|
9
|
10.56
|
8.02
|
6.99
|
6.42
|
6.06
|
5.80
|
5.61
|
5.47
|
5.35
|
5.26
|
|
10
|
10.04
|
7.56
|
6.55
|
5.99
|
5.64
|
5.39
|
5.20
|
5.06
|
4.94
|
4.85
|
|
11
|
9.65
|
7.21
|
6.22
|
5.67
|
5.32
|
5.07
|
4.89
|
4.74
|
4.63
|
4.54
|
|
12
|
9.33
|
6.93
|
5.95
|
5.41
|
5.06
|
4.82
|
4.64
|
4.50
|
4.39
|
4.30
|
|
13
|
9.07
|
6.70
|
5.74
|
5.21
|
4.86
|
4.62
|
4.44
|
4.30
|
4.19
|
4.10
|
|
14
|
8.86
|
6.51
|
5.56
|
5.04
|
4.69
|
4.46
|
4.28
|
4.14
|
4.03
|
3.94
|
|
15
|
8.68
|
6.36
|
5.42
|
4.89
|
4.56
|
4.32
|
4.14
|
4.00
|
3.89
|
3.80
|
|
16
|
8.53
|
6.23
|
5.29
|
4.77
|
4.44
|
4.20
|
4.03
|
3.89
|
3.78
|
3.69
|
|
17
|
8.40
|
6.11
|
5.18
|
4.67
|
4.34
|
4.10
|
3.93
|
3.79
|
3.68
|
3.59
|
|
18
|
8.29
|
6.01
|
5.09
|
4.58
|
4.25
|
4.01
|
3.84
|
3.71
|
3.60
|
3.51
|
|
19
|
8.18
|
5.93
|
5.01
|
4.50
|
4.17
|
3.94
|
3.77
|
3.63
|
3.52
|
3.43
|
|
20
|
8.10
|
5.85
|
4.94
|
4.43
|
4.10
|
3.87
|
3.70
|
3.56
|
3.46
|
3.37
|
|
21
|
8.02
|
5.78
|
4.87
|
4.37
|
4.04
|
3.81
|
3.64
|
3.51
|
3.40
|
3.31
|
|
22
|
7.95
|
5.72
|
4.82
|
4.31
|
3.99
|
3.76
|
3.59
|
3.45
|
3.35
|
3.26
|
|
23
|
7.88
|
5.66
|
4.76
|
4.26
|
3.94
|
3.71
|
3.54
|
3.41
|
3.30
|
3.21
|
|
24
|
7.82
|
5.61
|
4.72
|
4.22
|
3.90
|
3.67
|
3.50
|
3.36
|
3.26
|
3.17
|
|
25
|
7.77
|
5.57
|
4.68
|
4.18
|
3.85
|
3.63
|
3.46
|
3.32
|
3.22
|
3.13
|
|
26
|
7.72
|
5.53
|
4.64
|
4.14
|
3.82
|
3.59
|
3.42
|
3.29
|
3.18
|
3.09
|
|
27
|
7.68
|
5.49
|
4.60
|
4.11
|
3.78
|
3.56
|
3.39
|
3.26
|
3.15
|
3.06
|
|
28
|
7.64
|
5.45
|
4.57
|
4.07
|
3.75
|
3.53
|
3.36
|
3.23
|
3.12
|
3.03
|
|
29
|
7.60
|
5.42
|
4.54
|
4.04
|
3.73
|
3.50
|
3.33
|
3.20
|
3.09
|
3.00
|
|
30
|
7.56
|
5.39
|
4.51
|
4.02
|
3.70
|
3.47
|
3.30
|
3.17
|
3.07
|
2.98
|
|
31
|
7.53
|
5.36
|
4.48
|
3.99
|
3.67
|
3.45
|
3.28
|
3.15
|
3.04
|
2.96
|
|
32
|
7.50
|
5.34
|
4.46
|
3.97
|
3.65
|
3.43
|
3.26
|
3.13
|
3.02
|
2.93
|
|
33
|
7.47
|
5.31
|
4.44
|
3.95
|
3.63
|
3.41
|
3.24
|
3.11
|
3.00
|
2.91
|
|
34
|
7.44
|
5.29
|
4.42
|
3.93
|
3.61
|
3.39
|
3.22
|
3.09
|
2.98
|
2.89
|
|
35
|
7.42
|
5.27
|
4.40
|
3.91
|
3.59
|
3.37
|
3.20
|
3.07
|
2.96
|
2.88
|
|
36
|
7.40
|
5.25
|
4.38
|
3.89
|
3.57
|
3.35
|
3.18
|
3.05
|
2.95
|
2.86
|
|
37
|
7.37
|
5.23
|
4.36
|
3.87
|
3.56
|
3.33
|
3.17
|
3.04
|
2.93
|
2.84
|
|
38
|
7.35
|
5.21
|
4.34
|
3.86
|
3.54
|
3.32
|
3.15
|
3.02
|
2.92
|
2.83
|
|
39
|
7.33
|
5.19
|
4.33
|
3.84
|
3.53
|
3.30
|
3.14
|
3.01
|
2.90
|
2.81
|
|
40
|
7.31
|
5.18
|
4.31
|
3.83
|
3.51
|
3.29
|
3.12
|
2.99
|
2.89
|
2.80
|
|
41
|
7.30
|
5.16
|
4.30
|
3.81
|
3.50
|
3.28
|
3.11
|
2.98
|
2.87
|
2.79
|
|
42
|
7.28
|
5.15
|
4.29
|
3.80
|
3.49
|
3.27
|
3.10
|
2.97
|
2.86
|
2.78
|
|
43
|
7.26
|
5.14
|
4.27
|
3.79
|
3.48
|
3.25
|
3.09
|
2.96
|
2.85
|
2.76
|
|
44
|
7.25
|
5.12
|
4.26
|
3.78
|
3.47
|
3.24
|
3.08
|
2.95
|
2.84
|
2.75
|
|
45
|
7.23
|
5.11
|
4.25
|
3.77
|
3.45
|
3.23
|
3.07
|
2.94
|
2.83
|
2.74
|
|
46
|
7.22
|
5.10
|
4.24
|
3.76
|
3.44
|
3.22
|
3.06
|
2.93
|
2.82
|
2.73
|
|
47
|
7.21
|
5.09
|
4.23
|
3.75
|
3.43
|
3.21
|
3.05
|
2.92
|
2.81
|
2.72
|
|
48
|
7.19
|
5.08
|
4.22
|
3.74
|
3.43
|
3.20
|
3.04
|
2.91
|
2.80
|
2.71
|
|
49
|
7.18
|
5.07
|
4.21
|
3.73
|
3.42
|
3.19
|
3.03
|
2.90
|
2.79
|
2.71
|
|
50
|
7.17
|
5.06
|
4.20
|
3.72
|
3.41
|
3.19
|
3.02
|
2.89
|
2.78
|
2.70
|
|
51
|
7.16
|
5.05
|
4.19
|
3.71
|
3.40
|
3.18
|
3.01
|
2.88
|
2.78
|
2.69
|
|
52
|
7.15
|
5.04
|
4.18
|
3.70
|
3.39
|
3.17
|
3.00
|
2.87
|
2.77
|
2.68
|
|
53
|
7.14
|
5.03
|
4.17
|
3.70
|
3.38
|
3.16
|
3.00
|
2.87
|
2.76
|
2.68
|
|
54
|
7.13
|
5.02
|
4.17
|
3.69
|
3.38
|
3.16
|
2.99
|
2.86
|
2.76
|
2.67
|
|
55
|
7.12
|
5.01
|
4.16
|
3.68
|
3.37
|
3.15
|
2.98
|
2.85
|
2.75
|
2.66
|
|
56
|
7.11
|
5.01
|
4.15
|
3.67
|
3.36
|
3.14
|
2.98
|
2.85
|
2.74
|
2.66
|
|
57
|
7.10
|
5.00
|
4.15
|
3.67
|
3.36
|
3.14
|
2.97
|
2.84
|
2.74
|
2.65
|
|
58
|
7.09
|
4.99
|
4.14
|
3.66
|
3.35
|
3.13
|
2.96
|
2.83
|
2.73
|
2.64
|
|
59
|
7.08
|
4.98
|
4.13
|
3.65
|
3.34
|
3.12
|
2.96
|
2.83
|
2.72
|
2.64
|
|
60
|
7.08
|
4.98
|
4.13
|
3.65
|
3.34
|
3.12
|
2.95
|
2.82
|
2.72
|
2.63
|
|
61
|
7.07
|
4.97
|
4.12
|
3.64
|
3.33
|
3.11
|
2.95
|
2.82
|
2.71
|
2.63
|
|
62
|
7.06
|
4.96
|
4.11
|
3.64
|
3.33
|
3.11
|
2.94
|
2.81
|
2.71
|
2.62
|
|
63
|
7.06
|
4.96
|
4.11
|
3.63
|
3.32
|
3.10
|
2.94
|
2.81
|
2.70
|
2.62
|
|
64
|
7.05
|
4.95
|
4.10
|
3.63
|
3.32
|
3.10
|
2.93
|
2.80
|
2.70
|
2.61
|
|
65
|
7.04
|
4.95
|
4.10
|
3.62
|
3.31
|
3.09
|
2.93
|
2.80
|
2.69
|
2.61
|
|
66
|
7.04
|
4.94
|
4.09
|
3.62
|
3.31
|
3.09
|
2.92
|
2.79
|
2.69
|
2.60
|
|
67
|
7.03
|
4.94
|
4.09
|
3.61
|
3.30
|
3.08
|
2.92
|
2.79
|
2.68
|
2.60
|
|
68
|
7.02
|
4.93
|
4.08
|
3.61
|
3.30
|
3.08
|
2.91
|
2.78
|
2.68
|
2.59
|
|
69
|
7.02
|
4.93
|
4.08
|
3.60
|
3.29
|
3.08
|
2.91
|
2.78
|
2.68
|
2.59
|
|
70
|
7.01
|
4.92
|
4.07
|
3.60
|
3.29
|
3.07
|
2.91
|
2.78
|
2.67
|
2.59
|
|
71
|
7.01
|
4.92
|
4.07
|
3.60
|
3.29
|
3.07
|
2.90
|
2.77
|
2.67
|
2.58
|
|
72
|
7.00
|
4.91
|
4.07
|
3.59
|
3.28
|
3.06
|
2.90
|
2.77
|
2.66
|
2.58
|
|
73
|
7.00
|
4.91
|
4.06
|
3.59
|
3.28
|
3.06
|
2.89
|
2.77
|
2.66
|
2.57
|
|
74
|
6.99
|
4.90
|
4.06
|
3.58
|
3.28
|
3.06
|
2.89
|
2.76
|
2.66
|
2.57
|
|
75
|
6.99
|
4.90
|
4.05
|
3.58
|
3.27
|
3.05
|
2.89
|
2.76
|
2.65
|
2.57
|
|
76
|
6.98
|
4.90
|
4.05
|
3.58
|
3.27
|
3.05
|
2.88
|
2.75
|
2.65
|
2.56
|
|
77
|
6.98
|
4.89
|
4.05
|
3.57
|
3.26
|
3.05
|
2.88
|
2.75
|
2.65
|
2.56
|
|
78
|
6.97
|
4.89
|
4.04
|
3.57
|
3.26
|
3.04
|
2.88
|
2.75
|
2.64
|
2.56
|
|
79
|
6.97
|
4.88
|
4.04
|
3.57
|
3.26
|
3.04
|
2.87
|
2.75
|
2.64
|
2.55
|
|
80
|
6.96
|
4.88
|
4.04
|
3.56
|
3.26
|
3.04
|
2.87
|
2.74
|
2.64
|
2.55
|
|
81
|
6.96
|
4.88
|
4.03
|
3.56
|
3.25
|
3.03
|
2.87
|
2.74
|
2.63
|
2.55
|
|
82
|
6.95
|
4.87
|
4.03
|
3.56
|
3.25
|
3.03
|
2.87
|
2.74
|
2.63
|
2.54
|
|
83
|
6.95
|
4.87
|
4.03
|
3.55
|
3.25
|
3.03
|
2.86
|
2.73
|
2.63
|
2.54
|
|
84
|
6.95
|
4.87
|
4.02
|
3.55
|
3.24
|
3.02
|
2.86
|
2.73
|
2.63
|
2.54
|
|
85
|
6.94
|
4.86
|
4.02
|
3.55
|
3.24
|
3.02
|
2.86
|
2.73
|
2.62
|
2.54
|
|
86
|
6.94
|
4.86
|
4.02
|
3.55
|
3.24
|
3.02
|
2.85
|
2.73
|
2.62
|
2.53
|
|
87
|
6.94
|
4.86
|
4.02
|
3.54
|
3.24
|
3.02
|
2.85
|
2.72
|
2.62
|
2.53
|
|
88
|
6.93
|
4.85
|
4.01
|
3.54
|
3.23
|
3.01
|
2.85
|
2.72
|
2.62
|
2.53
|
|
89
|
6.93
|
4.85
|
4.01
|
3.54
|
3.23
|
3.01
|
2.85
|
2.72
|
2.61
|
2.53
|
|
90
|
6.93
|
4.85
|
4.01
|
3.53
|
3.23
|
3.01
|
2.84
|
2.72
|
2.61
|
2.52
|
|
91
|
6.92
|
4.85
|
4.00
|
3.53
|
3.23
|
3.01
|
2.84
|
2.71
|
2.61
|
2.52
|
|
92
|
6.92
|
4.84
|
4.00
|
3.53
|
3.22
|
3.00
|
2.84
|
2.71
|
2.61
|
2.52
|
|
93
|
6.92
|
4.84
|
4.00
|
3.53
|
3.22
|
3.00
|
2.84
|
2.71
|
2.60
|
2.52
|
|
94
|
6.91
|
4.84
|
4.00
|
3.53
|
3.22
|
3.00
|
2.84
|
2.71
|
2.60
|
2.52
|
|
95
|
6.91
|
4.84
|
3.99
|
3.52
|
3.22
|
3.00
|
2.83
|
2.70
|
2.60
|
2.51
|
|
96
|
6.91
|
4.83
|
3.99
|
3.52
|
3.21
|
3.00
|
2.83
|
2.70
|
2.60
|
2.51
|
|
97
|
6.90
|
4.83
|
3.99
|
3.52
|
3.21
|
2.99
|
2.83
|
2.70
|
2.60
|
2.51
|
|
98
|
6.90
|
4.83
|
3.99
|
3.52
|
3.21
|
2.99
|
2.83
|
2.70
|
2.59
|
2.51
|
|
99
|
6.90
|
4.83
|
3.99
|
3.51
|
3.21
|
2.99
|
2.83
|
2.70
|
2.59
|
2.51
|
|
100
|
6.90
|
4.82
|
3.98
|
3.51
|
3.21
|
2.99
|
2.82
|
2.69
|
2.59
|
2.50
|
\(q\)
\(\alpha = 0.05\)
|
|
\(k\) (number of groups)
|
|
\(df_\epsilon\)
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
5
|
3.64
|
4.60
|
5.22
|
5.67
|
6.03
|
6.33
|
6.58
|
6.80
|
6.99
|
|
6
|
3.46
|
4.34
|
4.90
|
5.30
|
5.63
|
5.90
|
6.12
|
6.32
|
6.49
|
|
7
|
3.34
|
4.16
|
4.68
|
5.06
|
5.36
|
5.61
|
5.82
|
6.00
|
6.16
|
|
8
|
3.26
|
4.04
|
4.53
|
4.89
|
5.17
|
5.40
|
5.60
|
5.77
|
5.92
|
|
9
|
3.20
|
3.95
|
4.41
|
4.76
|
5.02
|
5.24
|
5.43
|
5.59
|
5.74
|
|
10
|
3.15
|
3.88
|
4.33
|
4.65
|
4.91
|
5.12
|
5.30
|
5.46
|
5.60
|
|
11
|
3.11
|
3.82
|
4.26
|
4.57
|
4.82
|
5.03
|
5.20
|
5.35
|
5.49
|
|
12
|
3.08
|
3.77
|
4.20
|
4.51
|
4.75
|
4.95
|
5.12
|
5.27
|
5.39
|
|
13
|
3.06
|
3.73
|
4.15
|
4.45
|
4.69
|
4.88
|
5.05
|
5.19
|
5.32
|
|
14
|
3.03
|
3.70
|
4.11
|
4.41
|
4.64
|
4.83
|
4.99
|
5.13
|
5.25
|
|
15
|
3.01
|
3.67
|
4.08
|
4.37
|
4.59
|
4.78
|
4.94
|
5.08
|
5.20
|
|
16
|
3.00
|
3.65
|
4.05
|
4.33
|
4.56
|
4.74
|
4.90
|
5.03
|
5.15
|
|
17
|
2.98
|
3.63
|
4.02
|
4.30
|
4.52
|
4.70
|
4.86
|
4.99
|
5.11
|
|
18
|
2.97
|
3.61
|
4.00
|
4.28
|
4.49
|
4.67
|
4.82
|
4.96
|
5.07
|
|
19
|
2.96
|
3.59
|
3.98
|
4.25
|
4.47
|
4.65
|
4.79
|
4.92
|
5.04
|
|
20
|
2.95
|
3.58
|
3.96
|
4.23
|
4.45
|
4.62
|
4.77
|
4.90
|
5.01
|
|
21
|
2.94
|
3.56
|
3.94
|
4.21
|
4.42
|
4.60
|
4.74
|
4.87
|
4.98
|
|
22
|
2.93
|
3.55
|
3.93
|
4.20
|
4.41
|
4.58
|
4.72
|
4.85
|
4.96
|
|
23
|
2.93
|
3.54
|
3.91
|
4.18
|
4.39
|
4.56
|
4.70
|
4.83
|
4.94
|
|
24
|
2.92
|
3.53
|
3.90
|
4.17
|
4.37
|
4.54
|
4.68
|
4.81
|
4.92
|
|
25
|
2.91
|
3.52
|
3.89
|
4.15
|
4.36
|
4.53
|
4.67
|
4.79
|
4.90
|
|
26
|
2.91
|
3.51
|
3.88
|
4.14
|
4.35
|
4.51
|
4.65
|
4.77
|
4.88
|
|
27
|
2.90
|
3.51
|
3.87
|
4.13
|
4.33
|
4.50
|
4.64
|
4.76
|
4.86
|
|
28
|
2.90
|
3.50
|
3.86
|
4.12
|
4.32
|
4.49
|
4.62
|
4.74
|
4.85
|
|
29
|
2.89
|
3.49
|
3.85
|
4.11
|
4.31
|
4.47
|
4.61
|
4.73
|
4.84
|
|
30
|
2.89
|
3.49
|
3.85
|
4.10
|
4.30
|
4.46
|
4.60
|
4.72
|
4.82
|
|
31
|
2.88
|
3.48
|
3.84
|
4.09
|
4.29
|
4.45
|
4.59
|
4.71
|
4.81
|
|
32
|
2.88
|
3.48
|
3.83
|
4.09
|
4.28
|
4.45
|
4.58
|
4.70
|
4.80
|
|
33
|
2.88
|
3.47
|
3.83
|
4.08
|
4.28
|
4.44
|
4.57
|
4.69
|
4.79
|
|
34
|
2.87
|
3.47
|
3.82
|
4.07
|
4.27
|
4.43
|
4.56
|
4.68
|
4.78
|
|
35
|
2.87
|
3.46
|
3.81
|
4.07
|
4.26
|
4.42
|
4.56
|
4.67
|
4.77
|
|
36
|
2.87
|
3.46
|
3.81
|
4.06
|
4.25
|
4.41
|
4.55
|
4.66
|
4.76
|
|
37
|
2.87
|
3.45
|
3.80
|
4.05
|
4.25
|
4.41
|
4.54
|
4.66
|
4.76
|
|
38
|
2.86
|
3.45
|
3.80
|
4.05
|
4.24
|
4.40
|
4.53
|
4.65
|
4.75
|
|
39
|
2.86
|
3.45
|
3.79
|
4.04
|
4.24
|
4.39
|
4.53
|
4.64
|
4.74
|
|
40
|
2.86
|
3.44
|
3.79
|
4.04
|
4.23
|
4.39
|
4.52
|
4.63
|
4.73
|
|
41
|
2.86
|
3.44
|
3.79
|
4.03
|
4.23
|
4.38
|
4.51
|
4.63
|
4.73
|
|
42
|
2.85
|
3.44
|
3.78
|
4.03
|
4.22
|
4.38
|
4.51
|
4.62
|
4.72
|
|
43
|
2.85
|
3.43
|
3.78
|
4.03
|
4.22
|
4.37
|
4.50
|
4.62
|
4.72
|
|
44
|
2.85
|
3.43
|
3.78
|
4.02
|
4.21
|
4.37
|
4.50
|
4.61
|
4.71
|
|
45
|
2.85
|
3.43
|
3.77
|
4.02
|
4.21
|
4.36
|
4.49
|
4.61
|
4.70
|
|
46
|
2.85
|
3.42
|
3.77
|
4.01
|
4.20
|
4.36
|
4.49
|
4.60
|
4.70
|
|
47
|
2.85
|
3.42
|
3.77
|
4.01
|
4.20
|
4.36
|
4.48
|
4.60
|
4.69
|
|
48
|
2.84
|
3.42
|
3.76
|
4.01
|
4.20
|
4.35
|
4.48
|
4.59
|
4.69
|
|
49
|
2.84
|
3.42
|
3.76
|
4.00
|
4.19
|
4.35
|
4.48
|
4.59
|
4.69
|
|
50
|
2.84
|
3.42
|
3.76
|
4.00
|
4.19
|
4.34
|
4.47
|
4.58
|
4.68
|
|
51
|
2.84
|
3.41
|
3.76
|
4.00
|
4.19
|
4.34
|
4.47
|
4.58
|
4.68
|
|
52
|
2.84
|
3.41
|
3.75
|
4.00
|
4.18
|
4.34
|
4.47
|
4.58
|
4.67
|
|
53
|
2.84
|
3.41
|
3.75
|
3.99
|
4.18
|
4.33
|
4.46
|
4.57
|
4.67
|
|
54
|
2.84
|
3.41
|
3.75
|
3.99
|
4.18
|
4.33
|
4.46
|
4.57
|
4.67
|
|
55
|
2.83
|
3.41
|
3.75
|
3.99
|
4.18
|
4.33
|
4.46
|
4.57
|
4.66
|
|
56
|
2.83
|
3.40
|
3.74
|
3.99
|
4.17
|
4.32
|
4.45
|
4.56
|
4.66
|
|
57
|
2.83
|
3.40
|
3.74
|
3.98
|
4.17
|
4.32
|
4.45
|
4.56
|
4.66
|
|
58
|
2.83
|
3.40
|
3.74
|
3.98
|
4.17
|
4.32
|
4.45
|
4.56
|
4.65
|
|
59
|
2.83
|
3.40
|
3.74
|
3.98
|
4.17
|
4.32
|
4.44
|
4.55
|
4.65
|
|
60
|
2.83
|
3.40
|
3.74
|
3.98
|
4.16
|
4.31
|
4.44
|
4.55
|
4.65
|
|
61
|
2.83
|
3.40
|
3.74
|
3.98
|
4.16
|
4.31
|
4.44
|
4.55
|
4.64
|
|
62
|
2.83
|
3.40
|
3.73
|
3.97
|
4.16
|
4.31
|
4.44
|
4.55
|
4.64
|
|
63
|
2.83
|
3.39
|
3.73
|
3.97
|
4.16
|
4.31
|
4.43
|
4.54
|
4.64
|
|
64
|
2.83
|
3.39
|
3.73
|
3.97
|
4.15
|
4.30
|
4.43
|
4.54
|
4.64
|
|
65
|
2.82
|
3.39
|
3.73
|
3.97
|
4.15
|
4.30
|
4.43
|
4.54
|
4.63
|
|
66
|
2.82
|
3.39
|
3.73
|
3.97
|
4.15
|
4.30
|
4.43
|
4.54
|
4.63
|
|
67
|
2.82
|
3.39
|
3.73
|
3.96
|
4.15
|
4.30
|
4.42
|
4.53
|
4.63
|
|
68
|
2.82
|
3.39
|
3.72
|
3.96
|
4.15
|
4.30
|
4.42
|
4.53
|
4.63
|
|
69
|
2.82
|
3.39
|
3.72
|
3.96
|
4.15
|
4.29
|
4.42
|
4.53
|
4.62
|
|
70
|
2.82
|
3.39
|
3.72
|
3.96
|
4.14
|
4.29
|
4.42
|
4.53
|
4.62
|
|
71
|
2.82
|
3.39
|
3.72
|
3.96
|
4.14
|
4.29
|
4.42
|
4.52
|
4.62
|
|
72
|
2.82
|
3.38
|
3.72
|
3.96
|
4.14
|
4.29
|
4.41
|
4.52
|
4.62
|
|
73
|
2.82
|
3.38
|
3.72
|
3.96
|
4.14
|
4.29
|
4.41
|
4.52
|
4.62
|
|
74
|
2.82
|
3.38
|
3.72
|
3.95
|
4.14
|
4.29
|
4.41
|
4.52
|
4.61
|
|
75
|
2.82
|
3.38
|
3.72
|
3.95
|
4.14
|
4.28
|
4.41
|
4.52
|
4.61
|
|
76
|
2.82
|
3.38
|
3.71
|
3.95
|
4.13
|
4.28
|
4.41
|
4.52
|
4.61
|
|
77
|
2.82
|
3.38
|
3.71
|
3.95
|
4.13
|
4.28
|
4.41
|
4.51
|
4.61
|
|
78
|
2.82
|
3.38
|
3.71
|
3.95
|
4.13
|
4.28
|
4.40
|
4.51
|
4.61
|
|
79
|
2.81
|
3.38
|
3.71
|
3.95
|
4.13
|
4.28
|
4.40
|
4.51
|
4.60
|
|
80
|
2.81
|
3.38
|
3.71
|
3.95
|
4.13
|
4.28
|
4.40
|
4.51
|
4.60
|
|
81
|
2.81
|
3.38
|
3.71
|
3.95
|
4.13
|
4.28
|
4.40
|
4.51
|
4.60
|
|
82
|
2.81
|
3.38
|
3.71
|
3.94
|
4.13
|
4.27
|
4.40
|
4.51
|
4.60
|
|
83
|
2.81
|
3.37
|
3.71
|
3.94
|
4.13
|
4.27
|
4.40
|
4.50
|
4.60
|
|
84
|
2.81
|
3.37
|
3.71
|
3.94
|
4.12
|
4.27
|
4.40
|
4.50
|
4.60
|
|
85
|
2.81
|
3.37
|
3.71
|
3.94
|
4.12
|
4.27
|
4.39
|
4.50
|
4.60
|
|
86
|
2.81
|
3.37
|
3.71
|
3.94
|
4.12
|
4.27
|
4.39
|
4.50
|
4.59
|
|
87
|
2.81
|
3.37
|
3.70
|
3.94
|
4.12
|
4.27
|
4.39
|
4.50
|
4.59
|
|
88
|
2.81
|
3.37
|
3.70
|
3.94
|
4.12
|
4.27
|
4.39
|
4.50
|
4.59
|
|
89
|
2.81
|
3.37
|
3.70
|
3.94
|
4.12
|
4.27
|
4.39
|
4.50
|
4.59
|
|
90
|
2.81
|
3.37
|
3.70
|
3.94
|
4.12
|
4.27
|
4.39
|
4.50
|
4.59
|
|
91
|
2.81
|
3.37
|
3.70
|
3.94
|
4.12
|
4.26
|
4.39
|
4.49
|
4.59
|
|
92
|
2.81
|
3.37
|
3.70
|
3.94
|
4.12
|
4.26
|
4.39
|
4.49
|
4.59
|
|
93
|
2.81
|
3.37
|
3.70
|
3.93
|
4.12
|
4.26
|
4.39
|
4.49
|
4.58
|
|
94
|
2.81
|
3.37
|
3.70
|
3.93
|
4.11
|
4.26
|
4.38
|
4.49
|
4.58
|
|
95
|
2.81
|
3.37
|
3.70
|
3.93
|
4.11
|
4.26
|
4.38
|
4.49
|
4.58
|
|
96
|
2.81
|
3.37
|
3.70
|
3.93
|
4.11
|
4.26
|
4.38
|
4.49
|
4.58
|
|
97
|
2.81
|
3.37
|
3.70
|
3.93
|
4.11
|
4.26
|
4.38
|
4.49
|
4.58
|
|
98
|
2.81
|
3.37
|
3.70
|
3.93
|
4.11
|
4.26
|
4.38
|
4.49
|
4.58
|
|
99
|
2.81
|
3.37
|
3.70
|
3.93
|
4.11
|
4.26
|
4.38
|
4.49
|
4.58
|
|
100
|
2.81
|
3.36
|
3.70
|
3.93
|
4.11
|
4.26
|
4.38
|
4.48
|
4.58
|
|
101
|
2.81
|
3.36
|
3.69
|
3.93
|
4.11
|
4.25
|
4.38
|
4.48
|
4.58
|
|
102
|
2.81
|
3.36
|
3.69
|
3.93
|
4.11
|
4.25
|
4.38
|
4.48
|
4.57
|
|
103
|
2.80
|
3.36
|
3.69
|
3.93
|
4.11
|
4.25
|
4.38
|
4.48
|
4.57
|
|
104
|
2.80
|
3.36
|
3.69
|
3.93
|
4.11
|
4.25
|
4.37
|
4.48
|
4.57
|
|
105
|
2.80
|
3.36
|
3.69
|
3.93
|
4.11
|
4.25
|
4.37
|
4.48
|
4.57
|
|
106
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.48
|
4.57
|
|
107
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.48
|
4.57
|
|
108
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.48
|
4.57
|
|
109
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.48
|
4.57
|
|
110
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.48
|
4.57
|
|
111
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.47
|
4.57
|
|
112
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.47
|
4.57
|
|
113
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.25
|
4.37
|
4.47
|
4.56
|
|
114
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.24
|
4.37
|
4.47
|
4.56
|
|
115
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.24
|
4.37
|
4.47
|
4.56
|
|
116
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.24
|
4.37
|
4.47
|
4.56
|
|
117
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.24
|
4.36
|
4.47
|
4.56
|
|
118
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.24
|
4.36
|
4.47
|
4.56
|
|
119
|
2.80
|
3.36
|
3.69
|
3.92
|
4.10
|
4.24
|
4.36
|
4.47
|
4.56
|
|
120
|
2.80
|
3.36
|
3.68
|
3.92
|
4.10
|
4.24
|
4.36
|
4.47
|
4.56
|
\(\alpha = 0.01\)
|
|
k (number of groups)
|
|
\(df_\epsilon\)
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
5
|
5.70
|
6.98
|
7.80
|
8.42
|
8.91
|
9.32
|
9.67
|
9.97
|
10.24
|
|
6
|
5.24
|
6.33
|
7.03
|
7.56
|
7.97
|
8.32
|
8.61
|
8.87
|
9.10
|
|
7
|
4.95
|
5.92
|
6.54
|
7.00
|
7.37
|
7.68
|
7.94
|
8.17
|
8.37
|
|
8
|
4.75
|
5.64
|
6.20
|
6.62
|
6.96
|
7.24
|
7.47
|
7.68
|
7.86
|
|
9
|
4.60
|
5.43
|
5.96
|
6.35
|
6.66
|
6.91
|
7.13
|
7.33
|
7.49
|
|
10
|
4.48
|
5.27
|
5.77
|
6.14
|
6.43
|
6.67
|
6.87
|
7.05
|
7.21
|
|
11
|
4.39
|
5.15
|
5.62
|
5.97
|
6.25
|
6.48
|
6.67
|
6.84
|
6.99
|
|
12
|
4.32
|
5.05
|
5.50
|
5.84
|
6.10
|
6.32
|
6.51
|
6.67
|
6.81
|
|
13
|
4.26
|
4.96
|
5.40
|
5.73
|
5.98
|
6.19
|
6.37
|
6.53
|
6.67
|
|
14
|
4.21
|
4.89
|
5.32
|
5.63
|
5.88
|
6.08
|
6.26
|
6.41
|
6.54
|
|
15
|
4.17
|
4.84
|
5.25
|
5.56
|
5.80
|
5.99
|
6.16
|
6.31
|
6.44
|
|
16
|
4.13
|
4.79
|
5.19
|
5.49
|
5.72
|
5.92
|
6.08
|
6.22
|
6.35
|
|
17
|
4.10
|
4.74
|
5.14
|
5.43
|
5.66
|
5.85
|
6.01
|
6.15
|
6.27
|
|
18
|
4.07
|
4.70
|
5.09
|
5.38
|
5.60
|
5.79
|
5.94
|
6.08
|
6.20
|
|
19
|
4.05
|
4.67
|
5.05
|
5.33
|
5.55
|
5.73
|
5.89
|
6.02
|
6.14
|
|
20
|
4.02
|
4.64
|
5.02
|
5.29
|
5.51
|
5.69
|
5.84
|
5.97
|
6.09
|
|
21
|
4.00
|
4.61
|
4.99
|
5.26
|
5.47
|
5.65
|
5.79
|
5.92
|
6.04
|
|
22
|
3.99
|
4.59
|
4.96
|
5.22
|
5.43
|
5.61
|
5.75
|
5.88
|
5.99
|
|
23
|
3.97
|
4.57
|
4.93
|
5.20
|
5.40
|
5.57
|
5.72
|
5.84
|
5.95
|
|
24
|
3.96
|
4.55
|
4.91
|
5.17
|
5.37
|
5.54
|
5.69
|
5.81
|
5.92
|
|
25
|
3.94
|
4.53
|
4.89
|
5.14
|
5.35
|
5.51
|
5.65
|
5.78
|
5.89
|
|
26
|
3.93
|
4.51
|
4.87
|
5.12
|
5.32
|
5.49
|
5.63
|
5.75
|
5.86
|
|
27
|
3.92
|
4.49
|
4.85
|
5.10
|
5.30
|
5.46
|
5.60
|
5.72
|
5.83
|
|
28
|
3.91
|
4.48
|
4.83
|
5.08
|
5.28
|
5.44
|
5.58
|
5.70
|
5.80
|
|
29
|
3.90
|
4.47
|
4.81
|
5.06
|
5.26
|
5.42
|
5.56
|
5.67
|
5.78
|
|
30
|
3.89
|
4.45
|
4.80
|
5.05
|
5.24
|
5.40
|
5.54
|
5.65
|
5.76
|
|
31
|
3.88
|
4.44
|
4.79
|
5.03
|
5.23
|
5.38
|
5.52
|
5.63
|
5.74
|
|
32
|
3.87
|
4.43
|
4.77
|
5.02
|
5.21
|
5.37
|
5.50
|
5.61
|
5.72
|
|
33
|
3.87
|
4.42
|
4.76
|
5.00
|
5.20
|
5.35
|
5.48
|
5.60
|
5.70
|
|
34
|
3.86
|
4.41
|
4.75
|
4.99
|
5.18
|
5.34
|
5.47
|
5.58
|
5.68
|
|
35
|
3.85
|
4.40
|
4.74
|
4.98
|
5.17
|
5.32
|
5.45
|
5.57
|
5.67
|
|
36
|
3.85
|
4.40
|
4.73
|
4.97
|
5.16
|
5.31
|
5.44
|
5.55
|
5.65
|
|
37
|
3.84
|
4.39
|
4.72
|
4.96
|
5.15
|
5.30
|
5.43
|
5.54
|
5.64
|
|
38
|
3.83
|
4.38
|
4.71
|
4.95
|
5.13
|
5.29
|
5.41
|
5.53
|
5.62
|
|
39
|
3.83
|
4.37
|
4.70
|
4.94
|
5.12
|
5.28
|
5.40
|
5.51
|
5.61
|
|
40
|
3.82
|
4.37
|
4.70
|
4.93
|
5.11
|
5.26
|
5.39
|
5.50
|
5.60
|
|
41
|
3.82
|
4.36
|
4.69
|
4.92
|
5.11
|
5.26
|
5.38
|
5.49
|
5.59
|
|
42
|
3.82
|
4.35
|
4.68
|
4.91
|
5.10
|
5.25
|
5.37
|
5.48
|
5.58
|
|
43
|
3.81
|
4.35
|
4.67
|
4.91
|
5.09
|
5.24
|
5.36
|
5.47
|
5.57
|
|
44
|
3.81
|
4.34
|
4.67
|
4.90
|
5.08
|
5.23
|
5.35
|
5.46
|
5.56
|
|
45
|
3.80
|
4.34
|
4.66
|
4.89
|
5.07
|
5.22
|
5.34
|
5.45
|
5.55
|
|
46
|
3.80
|
4.33
|
4.66
|
4.89
|
5.07
|
5.21
|
5.34
|
5.44
|
5.54
|
|
47
|
3.80
|
4.33
|
4.65
|
4.88
|
5.06
|
5.21
|
5.33
|
5.44
|
5.53
|
|
48
|
3.79
|
4.32
|
4.64
|
4.87
|
5.05
|
5.20
|
5.32
|
5.43
|
5.52
|
|
49
|
3.79
|
4.32
|
4.64
|
4.87
|
5.05
|
5.19
|
5.31
|
5.42
|
5.51
|
|
50
|
3.79
|
4.32
|
4.63
|
4.86
|
5.04
|
5.19
|
5.31
|
5.41
|
5.51
|
|
51
|
3.78
|
4.31
|
4.63
|
4.86
|
5.03
|
5.18
|
5.30
|
5.41
|
5.50
|
|
52
|
3.78
|
4.31
|
4.63
|
4.85
|
5.03
|
5.17
|
5.29
|
5.40
|
5.49
|
|
53
|
3.78
|
4.30
|
4.62
|
4.85
|
5.02
|
5.17
|
5.29
|
5.39
|
5.49
|
|
54
|
3.78
|
4.30
|
4.62
|
4.84
|
5.02
|
5.16
|
5.28
|
5.39
|
5.48
|
|
55
|
3.77
|
4.30
|
4.61
|
4.84
|
5.01
|
5.16
|
5.28
|
5.38
|
5.47
|
|
56
|
3.77
|
4.29
|
4.61
|
4.83
|
5.01
|
5.15
|
5.27
|
5.38
|
5.47
|
|
57
|
3.77
|
4.29
|
4.60
|
4.83
|
5.00
|
5.15
|
5.27
|
5.37
|
5.46
|
|
58
|
3.77
|
4.29
|
4.60
|
4.83
|
5.00
|
5.14
|
5.26
|
5.37
|
5.46
|
|
59
|
3.76
|
4.29
|
4.60
|
4.82
|
5.00
|
5.14
|
5.26
|
5.36
|
5.45
|
|
60
|
3.76
|
4.28
|
4.59
|
4.82
|
4.99
|
5.13
|
5.25
|
5.36
|
5.45
|
|
61
|
3.76
|
4.28
|
4.59
|
4.81
|
4.99
|
5.13
|
5.25
|
5.35
|
5.44
|
|
62
|
3.76
|
4.28
|
4.59
|
4.81
|
4.98
|
5.12
|
5.24
|
5.35
|
5.44
|
|
63
|
3.76
|
4.27
|
4.59
|
4.81
|
4.98
|
5.12
|
5.24
|
5.34
|
5.43
|
|
64
|
3.75
|
4.27
|
4.58
|
4.80
|
4.98
|
5.12
|
5.24
|
5.34
|
5.43
|
|
65
|
3.75
|
4.27
|
4.58
|
4.80
|
4.97
|
5.11
|
5.23
|
5.33
|
5.42
|
|
66
|
3.75
|
4.27
|
4.58
|
4.80
|
4.97
|
5.11
|
5.23
|
5.33
|
5.42
|
|
67
|
3.75
|
4.26
|
4.57
|
4.79
|
4.97
|
5.11
|
5.22
|
5.33
|
5.42
|
|
68
|
3.75
|
4.26
|
4.57
|
4.79
|
4.96
|
5.10
|
5.22
|
5.32
|
5.41
|
|
69
|
3.75
|
4.26
|
4.57
|
4.79
|
4.96
|
5.10
|
5.22
|
5.32
|
5.41
|
|
70
|
3.74
|
4.26
|
4.57
|
4.79
|
4.96
|
5.10
|
5.21
|
5.31
|
5.40
|
|
71
|
3.74
|
4.26
|
4.56
|
4.78
|
4.95
|
5.09
|
5.21
|
5.31
|
5.40
|
|
72
|
3.74
|
4.25
|
4.56
|
4.78
|
4.95
|
5.09
|
5.21
|
5.31
|
5.40
|
|
73
|
3.74
|
4.25
|
4.56
|
4.78
|
4.95
|
5.09
|
5.20
|
5.30
|
5.39
|
|
74
|
3.74
|
4.25
|
4.56
|
4.78
|
4.95
|
5.08
|
5.20
|
5.30
|
5.39
|
|
75
|
3.74
|
4.25
|
4.56
|
4.77
|
4.94
|
5.08
|
5.20
|
5.30
|
5.39
|
|
76
|
3.74
|
4.25
|
4.55
|
4.77
|
4.94
|
5.08
|
5.20
|
5.30
|
5.38
|
|
77
|
3.74
|
4.25
|
4.55
|
4.77
|
4.94
|
5.08
|
5.19
|
5.29
|
5.38
|
|
78
|
3.73
|
4.24
|
4.55
|
4.77
|
4.94
|
5.07
|
5.19
|
5.29
|
5.38
|
|
79
|
3.73
|
4.24
|
4.55
|
4.76
|
4.93
|
5.07
|
5.19
|
5.29
|
5.38
|
|
80
|
3.73
|
4.24
|
4.55
|
4.76
|
4.93
|
5.07
|
5.18
|
5.28
|
5.37
|
|
81
|
3.73
|
4.24
|
4.54
|
4.76
|
4.93
|
5.07
|
5.18
|
5.28
|
5.37
|
|
82
|
3.73
|
4.24
|
4.54
|
4.76
|
4.93
|
5.06
|
5.18
|
5.28
|
5.37
|
|
83
|
3.73
|
4.24
|
4.54
|
4.76
|
4.92
|
5.06
|
5.18
|
5.28
|
5.36
|
|
84
|
3.73
|
4.23
|
4.54
|
4.75
|
4.92
|
5.06
|
5.17
|
5.27
|
5.36
|
|
85
|
3.73
|
4.23
|
4.54
|
4.75
|
4.92
|
5.06
|
5.17
|
5.27
|
5.36
|
|
86
|
3.73
|
4.23
|
4.54
|
4.75
|
4.92
|
5.06
|
5.17
|
5.27
|
5.36
|
|
87
|
3.72
|
4.23
|
4.53
|
4.75
|
4.92
|
5.05
|
5.17
|
5.27
|
5.35
|
|
88
|
3.72
|
4.23
|
4.53
|
4.75
|
4.92
|
5.05
|
5.17
|
5.27
|
5.35
|
|
89
|
3.72
|
4.23
|
4.53
|
4.75
|
4.91
|
5.05
|
5.16
|
5.26
|
5.35
|
|
90
|
3.72
|
4.23
|
4.53
|
4.74
|
4.91
|
5.05
|
5.16
|
5.26
|
5.35
|
|
91
|
3.72
|
4.23
|
4.53
|
4.74
|
4.91
|
5.05
|
5.16
|
5.26
|
5.35
|
|
92
|
3.72
|
4.22
|
4.53
|
4.74
|
4.91
|
5.04
|
5.16
|
5.26
|
5.34
|
|
93
|
3.72
|
4.22
|
4.52
|
4.74
|
4.91
|
5.04
|
5.16
|
5.25
|
5.34
|
|
94
|
3.72
|
4.22
|
4.52
|
4.74
|
4.90
|
5.04
|
5.15
|
5.25
|
5.34
|
|
95
|
3.72
|
4.22
|
4.52
|
4.74
|
4.90
|
5.04
|
5.15
|
5.25
|
5.34
|
|
96
|
3.72
|
4.22
|
4.52
|
4.74
|
4.90
|
5.04
|
5.15
|
5.25
|
5.34
|
|
97
|
3.72
|
4.22
|
4.52
|
4.73
|
4.90
|
5.04
|
5.15
|
5.25
|
5.33
|
|
98
|
3.72
|
4.22
|
4.52
|
4.73
|
4.90
|
5.03
|
5.15
|
5.25
|
5.33
|
|
99
|
3.71
|
4.22
|
4.52
|
4.73
|
4.90
|
5.03
|
5.15
|
5.24
|
5.33
|
|
100
|
3.71
|
4.22
|
4.52
|
4.73
|
4.90
|
5.03
|
5.14
|
5.24
|
5.33
|
|
101
|
3.71
|
4.22
|
4.52
|
4.73
|
4.89
|
5.03
|
5.14
|
5.24
|
5.33
|
|
102
|
3.71
|
4.21
|
4.51
|
4.73
|
4.89
|
5.03
|
5.14
|
5.24
|
5.32
|
|
103
|
3.71
|
4.21
|
4.51
|
4.73
|
4.89
|
5.03
|
5.14
|
5.24
|
5.32
|
|
104
|
3.71
|
4.21
|
4.51
|
4.73
|
4.89
|
5.02
|
5.14
|
5.24
|
5.32
|
|
105
|
3.71
|
4.21
|
4.51
|
4.72
|
4.89
|
5.02
|
5.14
|
5.23
|
5.32
|
|
106
|
3.71
|
4.21
|
4.51
|
4.72
|
4.89
|
5.02
|
5.14
|
5.23
|
5.32
|
|
107
|
3.71
|
4.21
|
4.51
|
4.72
|
4.89
|
5.02
|
5.13
|
5.23
|
5.32
|
|
108
|
3.71
|
4.21
|
4.51
|
4.72
|
4.89
|
5.02
|
5.13
|
5.23
|
5.32
|
|
109
|
3.71
|
4.21
|
4.51
|
4.72
|
4.88
|
5.02
|
5.13
|
5.23
|
5.31
|
|
110
|
3.71
|
4.21
|
4.51
|
4.72
|
4.88
|
5.02
|
5.13
|
5.23
|
5.31
|
|
111
|
3.71
|
4.21
|
4.50
|
4.72
|
4.88
|
5.02
|
5.13
|
5.23
|
5.31
|
|
112
|
3.71
|
4.21
|
4.50
|
4.72
|
4.88
|
5.01
|
5.13
|
5.22
|
5.31
|
|
113
|
3.71
|
4.20
|
4.50
|
4.72
|
4.88
|
5.01
|
5.13
|
5.22
|
5.31
|
|
114
|
3.70
|
4.20
|
4.50
|
4.71
|
4.88
|
5.01
|
5.12
|
5.22
|
5.31
|
|
115
|
3.70
|
4.20
|
4.50
|
4.71
|
4.88
|
5.01
|
5.12
|
5.22
|
5.31
|
|
116
|
3.70
|
4.20
|
4.50
|
4.71
|
4.88
|
5.01
|
5.12
|
5.22
|
5.30
|
|
117
|
3.70
|
4.20
|
4.50
|
4.71
|
4.88
|
5.01
|
5.12
|
5.22
|
5.30
|
|
118
|
3.70
|
4.20
|
4.50
|
4.71
|
4.87
|
5.01
|
5.12
|
5.22
|
5.30
|
|
119
|
3.70
|
4.20
|
4.50
|
4.71
|
4.87
|
5.01
|
5.12
|
5.22
|
5.30
|
|
120
|
3.70
|
4.20
|
4.50
|
4.71
|
4.87
|
5.01
|
5.12
|
5.21
|
5.30
|
Upper-tail Quantiles of the \(\chi^2\) Distribution
|
|
Upper-tail Probabilities
|
|
df
|
0.99
|
0.975
|
0.95
|
0.90
|
0.80
|
0.50
|
0.20
|
0.10
|
0.05
|
0.025
|
0.01
|
|
1
|
0.00
|
0.00
|
0.00
|
0.02
|
0.06
|
0.45
|
1.64
|
2.71
|
3.84
|
5.02
|
6.63
|
|
2
|
0.02
|
0.05
|
0.10
|
0.21
|
0.45
|
1.39
|
3.22
|
4.61
|
5.99
|
7.38
|
9.21
|
|
3
|
0.11
|
0.22
|
0.35
|
0.58
|
1.01
|
2.37
|
4.64
|
6.25
|
7.81
|
9.35
|
11.34
|
|
4
|
0.30
|
0.48
|
0.71
|
1.06
|
1.65
|
3.36
|
5.99
|
7.78
|
9.49
|
11.14
|
13.28
|
|
5
|
0.55
|
0.83
|
1.15
|
1.61
|
2.34
|
4.35
|
7.29
|
9.24
|
11.07
|
12.83
|
15.09
|
|
6
|
0.87
|
1.24
|
1.64
|
2.20
|
3.07
|
5.35
|
8.56
|
10.64
|
12.59
|
14.45
|
16.81
|
|
7
|
1.24
|
1.69
|
2.17
|
2.83
|
3.82
|
6.35
|
9.80
|
12.02
|
14.07
|
16.01
|
18.48
|
|
8
|
1.65
|
2.18
|
2.73
|
3.49
|
4.59
|
7.34
|
11.03
|
13.36
|
15.51
|
17.53
|
20.09
|
|
9
|
2.09
|
2.70
|
3.33
|
4.17
|
5.38
|
8.34
|
12.24
|
14.68
|
16.92
|
19.02
|
21.67
|
|
10
|
2.56
|
3.25
|
3.94
|
4.87
|
6.18
|
9.34
|
13.44
|
15.99
|
18.31
|
20.48
|
23.21
|
|
11
|
3.05
|
3.82
|
4.57
|
5.58
|
6.99
|
10.34
|
14.63
|
17.28
|
19.68
|
21.92
|
24.72
|
|
12
|
3.57
|
4.40
|
5.23
|
6.30
|
7.81
|
11.34
|
15.81
|
18.55
|
21.03
|
23.34
|
26.22
|
|
13
|
4.11
|
5.01
|
5.89
|
7.04
|
8.63
|
12.34
|
16.98
|
19.81
|
22.36
|
24.74
|
27.69
|
|
14
|
4.66
|
5.63
|
6.57
|
7.79
|
9.47
|
13.34
|
18.15
|
21.06
|
23.68
|
26.12
|
29.14
|
|
15
|
5.23
|
6.26
|
7.26
|
8.55
|
10.31
|
14.34
|
19.31
|
22.31
|
25.00
|
27.49
|
30.58
|
|
16
|
5.81
|
6.91
|
7.96
|
9.31
|
11.15
|
15.34
|
20.47
|
23.54
|
26.30
|
28.85
|
32.00
|
|
17
|
6.41
|
7.56
|
8.67
|
10.09
|
12.00
|
16.34
|
21.61
|
24.77
|
27.59
|
30.19
|
33.41
|
|
18
|
7.01
|
8.23
|
9.39
|
10.86
|
12.86
|
17.34
|
22.76
|
25.99
|
28.87
|
31.53
|
34.81
|
|
19
|
7.63
|
8.91
|
10.12
|
11.65
|
13.72
|
18.34
|
23.90
|
27.20
|
30.14
|
32.85
|
36.19
|
|
20
|
8.26
|
9.59
|
10.85
|
12.44
|
14.58
|
19.34
|
25.04
|
28.41
|
31.41
|
34.17
|
37.57
|
|
21
|
8.90
|
10.28
|
11.59
|
13.24
|
15.44
|
20.34
|
26.17
|
29.62
|
32.67
|
35.48
|
38.93
|
|
22
|
9.54
|
10.98
|
12.34
|
14.04
|
16.31
|
21.34
|
27.30
|
30.81
|
33.92
|
36.78
|
40.29
|
|
23
|
10.20
|
11.69
|
13.09
|
14.85
|
17.19
|
22.34
|
28.43
|
32.01
|
35.17
|
38.08
|
41.64
|
|
24
|
10.86
|
12.40
|
13.85
|
15.66
|
18.06
|
23.34
|
29.55
|
33.20
|
36.42
|
39.36
|
42.98
|
|
25
|
11.52
|
13.12
|
14.61
|
16.47
|
18.94
|
24.34
|
30.68
|
34.38
|
37.65
|
40.65
|
44.31
|
|
26
|
12.20
|
13.84
|
15.38
|
17.29
|
19.82
|
25.34
|
31.79
|
35.56
|
38.89
|
41.92
|
45.64
|
|
27
|
12.88
|
14.57
|
16.15
|
18.11
|
20.70
|
26.34
|
32.91
|
36.74
|
40.11
|
43.19
|
46.96
|
|
28
|
13.56
|
15.31
|
16.93
|
18.94
|
21.59
|
27.34
|
34.03
|
37.92
|
41.34
|
44.46
|
48.28
|
|
29
|
14.26
|
16.05
|
17.71
|
19.77
|
22.48
|
28.34
|
35.14
|
39.09
|
42.56
|
45.72
|
49.59
|
|
30
|
14.95
|
16.79
|
18.49
|
20.60
|
23.36
|
29.34
|
36.25
|
40.26
|
43.77
|
46.98
|
50.89
|