Davis J.C. Statistics and Data Analysis in Geology (3rd ed.)
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Statistics and Data Analysis in Geology
Table
A.2.
Critical values
of
t
for
v
degrees
of
freedom and selected levels
of
significance.
For
critical values in the left-hand tail, change the sign
of the table value. Critical values are given for the right-hand tail.
Significance Level,
a,
for:
One-tailed Test
.001
.005
.01 .025 .05
.1
.2
No.
of
Degrees Two-tailed Test
of Freedom,
v
.002 .010 .02 .05
.1
.2
.4
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
3 18.3088
22.3271
10.2 145
7.1732
5.8934
5.2076
4.7853
4.5008
4.2968
4.1437
4.0247
3.9296
3.8520
3.7874
3.7328
3.6862
3.6458
3.6105
3.5794
3.5518
3.5272
3.5050
3.4850
3.4668
3.4502
3.4350
63.6567
9.9248
5.8409
4.6041
4.0322
3.7074
3.4995
3.3554
3.2498
3.1693
3.1058
3.0545
3.0123
2.9768
2.9467
2.9208
2.8982
2.8784
2.8609
2.8453
2.8314
2.8188
2.8073
2.7969
2.7874
2.7787
31.8205
6.9646
4.5407
3.7470
3.3649
3.1427
2.9980
2.8965
2.8214
2.7638
2.7181
2.6810
2.6503
2.6245
2.6025
2.5835
2.5669
2.5524
2.5395
2.5280
2.5176
2.5083
2.4999
2.4922
2.4851
2.4786
12.7062
4.3027
3.1824
2.7764
2.5706
2.4469
2.3646
2.3060
2.2622
2.2281
2.2010
2.1788
2.1604
2.1448
2.1314
2.1
199
2.1098
2.1009
2.0930
2.0860
2.0796
2.0739
2.0687
2.0639
2.0595
2.0555
6.3138
2.9200
2.3534
2.1318
2.0150
1.9432
1.8946
1.8595
1.8331
1.8125
1.7959
1.7823
1.7709
1.7613
1.7531
1.7459
1.7396
1.7341
1.7291
1.7247
1.7207
1.7171
1.7139
1.7109
1.7081
1.7056
3.0777
1.8856
1.6377
1.5332
1.4759
1.4398
1.4149
1.3968
1.3830
1.3722
1.3634
1.3562
1.3502
1.3450
1.3406
1.3368
1.3334
1.3304
1.3277
1.3253
1.3232
1.3212
1.3195
1.3178
1.3163
1.3150
1.3764
1.0607
0.9785
0.9410
0,9195
0.9057
0.8960
0.8889
0.8834
0.8791
0.8755
0.8726
0.8702
0.8681
0.8662
0.8647
0.8633
0.8620
0.8610
0.8600
0.8591
0.8583
0.8575
0.8569
0.8562
0.8557
(Continued)
602
Appendix
Table A.2.
Concluded.
Sigdicance Level,
a,
for:
One-tailed Test
No.
of
Degrees Two-tailed Test
.001
.005
.01 .025
.05
.1
.2
of
Freedom,
v
,002 ,010
.02
.05
.1
.2 .4
27
28
29
30
40
50
60
70
80
90
100
110
120
130
140
150
03
3.4210
3.4082
3.3962
3.3852
3.3069
3.2614
3.2317
3.2108
3.1953
3.1833
3.1737
3.1660
3.1595
3.1541
3.1495
3.1455
3.0902
2.7707
2.7633
2.7564
2.7500
2.7045
2.6778
2.6603
2.6479
2.6387
2.6316
2.6259
2.6213
2.6174
2.6142
2.61 14
2.6090
2.5758
2.4727
2.4671
2.4620
2.4573
2.4233
2.4033
2.3901
2.3808
2.3739
2.3685
2.3642
2.3607
2.3578
2.3554
2.3533
2.3515
2.2364
2.0518
2.0484
2.0452
2.0423
2.02
11
2.0086
2.0003
1.9944
1.9901
1.9867
1.9840
1.9818
1.9799
1.9784
1.9771
1.9759
1.9600
1.7033
1.7011
1.6991
1.6973
1.6839
1.6759
1.6706
1.6669
1.664
1
1.6620
1.6602
1.6588
1.6577
1.6567
1.6558
1.6551
1.6449
1.3137
1.3125
1.3114
1.3104
1.3031
1.2987
1.2958
1.2938
1.2922
1.2910
1.2901
1.2893
1.2886
1.2881
1.2876
1.2872
1.2816
0.8551
0.8546
0.8542
0.8538
0.8507
0.8489
0.8477
0.8468
0.8461
0.8456
0.8452
0.8449
0.8446
0.8444
0.8442
0.8440
0.8416
Table A.3a.
Critical values
of
F
for
v1
and
vz
degrees
of
freedom
and
5%
(a
=
0.05)
level of significance.
df1
2
3
4
5
6
7 8 91015202500
1
161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 245.95 248.01 249.26 250.10
2
18.51 19 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.43 19.45 19.46 19.46
3
10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.70 8.66 8.63 8.62
4 7.71 6.94 6.59 6.39 6.26
6.16
6.09 6.04
6.00
5.96 5.86 5.80 5.77 5.75
5
6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.62 4.56 4.52 4.50
6
5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 3.94 3.87 3.83 3.81
(Continued)
603
Statistics and Data Analysis in Geology
Table
A.3a.
Concluded.
df
12 3 4 5
6
7 8 9 1015202503
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
70
80
90
100
110
120
03
5.59 4.74
4.35 4.12 3.97 3.87 3.79
3.73 3.68
3.64 3.51
3.44 3.4 3.38
5.32
4.46 4.07 3.84 3.69 3.58 3.50
3.44 3.39 3.35
3.22 3.15
3.11 3.08
5.12 4.26
3.86 3.63 3.48 3.37 3.29
3.23 3.18
3.14 3.01
2.94 2.89 2.86
4.96 4.10
3.71
3.48
3.33 3.22 3.14
3.07
3.02 2.98
2.85 2.77 2.73 2.70
4.84 3.98
3.59 3.36
3.20 3.09 3.01
2.95 2.90
2.85 2.72 2.65 2.60 2.57
4.75
3.89 3.49
3.26 3.11
3.00 2.91
2.85
2.80 2.75
2.62 2.54
2.50 2.47
4.67 3.81
3.41
3.18
3.03
2.92
2.83 2.77 2.71
2.67 2.53
2.46 2.41 2.38
4.60 3.74
3.34
3.11
2.96
2.85
2.76 2.70 2.65
2.60
2.46 2.39
2.34 2.31
4.54 3.68
3.29
3.06
2.90 2.79 2.71 2.64 2.59 2.54
2.40 2.33
2.28 2.25
4.49 3.63
3.24 3.01 2.85 2.74 2.66
2.59 2.54
2.49
2.35 2.28
2.23
2.19
4.45 3.59
3.20 2.96 2.81 2.70 2.61
2.55
2.49 2.45
2.31
2.23 2.18
2.15
4.41 3.55
3.16 2.93 2.77 2.66 2.58
2.51
2.46 2.41
2.27
2.19 2.14
2.11
4.38 3.52
3.13 2.90 2.74
2.63 2.54
2.48
2.42
2.38
2.23 2.16
2.11 2.07
4.35 3.49
3.10
2.87 2.71
2.60 2.51
2.45
2.39 2.35
2.20
2.12 2.07
2.04
4.32 3.47
3.07
2.84
2.68
2.57 2.49
2.42
2.37 2.32
2.18
2.10 2.05
2.01
4.30 3.44
3.05 2.82 2.66
2.55
2.46 2.40
2.34 2.30
2.15 2.07
2.02 1.98
4.28 3.42 3.03 2.80 2.64 2.53 2.44
2.37 2.32
2.27
2.13 2.05
2.00 1.96
4.26 3.40
3.01 2.78 2.62 2.51 2.42
2.36 2.30
2.25
2.11 2.03
1.97 1.94
4.24 3.39
2.99
2.76
2.60
2.49 2.40
2.34 2.28
2.24 2.09
2.01 1.96
1.92
4.23 3.37
2.98 2.74 2.59
2.47 2.39
2.32 2.27 2.22
2.07 1.99
1.94 1.90
4.21 3.35
2.96 2.73 2.57
2.46 2.37
2.31
2.25 2.20
2.06 1.97
1.92 1.88
4.20 3.34
2.95
2.71
2.56
2.45 2.36
2.29
2.24 2.19
2.04 1.96
1.91 1.87
4.18 3.33
2.93
2.70
2.55
2.43 2.35
2.28
2.22 2.18
2.03
1.94 1.89 1.85
4.17 3.32
2.92
2.69
2.53
2.42 2.33
2.27
2.21 2.16
2.01 1.93
1.88 1.84
4.08 3.23
2.84 2.61 2.45
2.34
2.25 2.18
2.12 2.08
1.92 1.84
1.78 1.74
4.03 3.18
2.79 2.56
2.40 2.29 2.20
2.13
2.07 2.03
1.87 1.78
1.73 1.69
4.00 3.15
2.76
2.53
2.37
2.25 2.17
2.10
2.04 1.99
1.84 1.75
1.69 1.65
3.98 3.13
2.74
2.50
2.35
2.23 2.14
2.07 2.02
1.97
1.81
1.72
1.66
1.62
3.96 3.11 2.72 2.49 2.33 2.21 2.13
2.06 2.00
1.95
1.79 1.70
1.64
1.60
3.95 3.10
2.71 2.47 2.32 2.20 2.11 2.04 1.99 1.94
1.78
1.69 1.63 1.59
3.94 3.09
2.70 2.46 2.31 2.19 2.10
2.03 1.97
1.93
1.77 1.68
1.62 1.57
3.93 3.08
2.69 2.45 2.30
2.18 2.09
2.02 1.97
1.92 1.76
1.67 1.61 1.56
3.92 3.07
2.68 2.45 2.29
2.18 2.09
2.02
1.96 1.91
1.75 1.66
1.60 1.55
3.85 3.00 2.61 2.38 2.22
2.11
2.02
1.95 1.89
1.84 1.68
1.58 1.52 1.47
604
Appendix
Table
A.3b.
Critical values of
F
for
v1
and
vz
degrees of freedom
and 2.5%
(&
=
0.025) level
of
significance.
df1 2 3 4 5 6 7 8 9 1015202500
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
40
50
60
70
80
90
100
110
120
00
647.79
38.51
17.44
12.22
10.01
8.81
8.07
7.57
7.21
6.94
6.72
6.55
6.41
6.30
6.20
6.12
6.04
5.98
5.92
5.87
5.83
5.79
5.75
5.72
5.69
5.66
5.63
5.61
5.59
5.57
799.50 864.16 899.58 921.85 937.11 948.22 956.66 963.28 968.63 984.87 993.10 998.08 1001.41
39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.43 39.45 39.46 39.46
16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.25 14.17 14.12 14.08
10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.66 8.56 8.50 8.46
8.43 7.76
7.39 7.15 6.98 6.85
6.76 6.68
6.62 6.43 6.33
6.27 6.23
7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.27
5.17 5.11
5.07
6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82
4.76 4.57
4.47
4.40 4.36
6.06 5.42 5.05 4.82 4.65 4.53 4.43
4.36 4.30
4.10
4.00 3.94
3.89
5.71
5.08 4.72 4.48 4.32 4.20
4.10 4.03
3.96 3.77
3.67 3.60
3.56
5.46
4.83 4.47
4.24
4.07 3.95
3.85 3.78 3.72
3.52 3.42
3.35 3.31
5.26 4.63 4.28 4.04 3.88 3.76 3.66
3.59 3.53
3.33 3.23
3.16 3.12
5.10
4.47 4.12 3.89
3.73 3.61 3.51 3.44 3.37
3.18 3.07
3.01 2.96
4.97 4.35 4.00 3.77 3.60
3.48 3.39 3.31 3.25
3.05 2.95
2.88 2.84
4.86
4.24
3.89 3.66
3.50 3.38
3.29 3.21 3.15
2.95 2.84
2.78 2.73
4.77 4.15 3.80 3.58 3.41
3.29
3.20
3.12 3.06
2.86
2.76 2.69
2.64
4.69 4.08 3.73 3.50 3.34 3.22 3.12
3.05 2.99
2.79 2.68
2.61 2.57
4.62 4.01 3.66 3.44 3.28
3.16 3.06 2.98 2.92 2.72
2.62
2.55 2.50
4.56 3.95 3.61 3.38 3.22 3.10
3.01
2.93
2.87 2.67
2.56 2.49
2.44
4.51 3.90 3.56 3.33 3.17 3.05 2.96
2.88 2.82
2.62
2.51
2.44 2.39
4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84
2.77 2.57
2.46
2.40 2.35
4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80
2.73 2.53
2.42 2.36
2.31
4.38
3.78 3.44 3.22 3.05 2.93 2.84 2.76
2.70 2.50
2.39
2.32 2.27
4.35 3.75 3.41 3.18 3.02 2.90 2.81
2.73 2.67
2.47 2.36
2.29 2.24
4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70
2.64 2.44
2.33 2.26
2.21
4.29 3.69 3.35 3.13 2.97 2.85
2.75 2.68
2.61
2.41 2.30
2.23
2.18
4.27 3.67
3.33 3.10 2.94 2.82 2.73
2.65 2.59
2.39
2.28
2.21 2.16
4.24
3.65 3.31 3.08
2.92 2.80
2.71 2.63
2.57 2.36
2.25 2.18
2.13
4.22 3.63 3.29 3.06 2.90
2.78 2.69
2.61 2.55
2.34
2.23 2.16
2.11
4.20
3.61
3.27 3.04
2.88 2.76
2.67 2.59
2.53 2.32
2.21
2.14 2.09
4.18 3.59 3.25 3.03 2.87
2.75 2.65
2.57 2.51
2.31 2.20
2.12 2.07
5.42 4.05 3.46 3.13 2.90 2.74
2.62
2.53
2.45 2.39
2.18
2.07
1.99 1.94
5.34 3.97 3.39 3.05 2.83 2.67 2.55
2.46 2.38
2.32
2.11 1.99
1.92 1.87
5.29 3.93 3.34
3.01 2.79 2.63
2.51
2.41
2.33
2.27 2.06
1.94 1.87
1.82
5.25 3.89
3.31 2.97
2.75
2.59
2.47 2.38
2.30
2.24 2.03
1.91 1.83
1.78
5.22 3.86
3.28
2.95 2.73 2.57 2.45
2.35 2.28
2.21 2.00
1.88 1.81
1.75
5.20 3.84 3.26 2.93 2.71 2.55 2.43 2.34
2.26
2.19 1.98
1.86
1.79 1.73
5.18 3.83
3.25 2.92 2.70 2.54
2.42 2.32
2.24 2.18
1.97 1.85
1.77 1.71
5.16 3.82 3.24
2.90 2.68 2.53 2.40 2.31
2.23
2.17 1.96
1.84
1.76 1.70
5.15 3.80 3.23 2.89 2.67 2.52 2.39
2.30 2.22
2.16
1.94 1.82
1.75 1.69
5.04 3.70 3.13 2.80 2.58 2.42 2.30
2.20 2.13
2.06 1.85
1.72
1.64 1.58
605
Statistics and Data Analysis
in
Geology
Table
A.3c.
Critical
values
of
F
for
v1
and
vz
degrees of freedom
and
1%
((x
=
0.01)
level
of significance.
df
1
2 3 4 5
6
7 8 9 10 15 20 25
W
1
4052.18 4999.50 5403.35 5624.58 5763.65 5858.99 5928.36 5981.07 6022.47 6055.85 6157.28 6208.73 6239.83 6260.65
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
40
50
60
70
80
90
100
110
120
W
98.50
34.12
21.20
16.26
13.75
12.25
11.26
10.56
10.04
9.65
9.33
9.07
8.86
8.68
8.53
8.40
8.29
8.18
8.10
8.02
7.95
7.88
7.82
7.77
7.72
7.68
7.64
7.60
7.56
7.3
1
7.17
7.08
7.01
6.96
6.93
6.90
6.87
6.85
6.66
99.00
30.82
18.00
13.27
10.92
9.55
8.65
8.02
7.56
7.21
6.93
6.70
6.51
6.36
6.23
6.11
6.01
5.93
5.85
5.78
5.72
5.66
5.61
5.57
5.53
5.49
5.45
5.42
5.39
5.18
5.06
4.98
4.92
4.88
4.85
4.82
4.80
4.79
4.63
99.17
29.46
16.69
12.06
9.78
8.45
7.59
6.99
6.55
6.22
5.95
5.74
5.56
5.42
5.29
5.18
5.09
5.01
4.94
4.87
4.82
4.76
4.72
4.68
4.64
4.60
4.57
4.54
4.51
4.31
4.20
4.13
4.07
4.04
4.01
3.98
3.96
3.95
3.80
99.25
28.71
15.98
11.39
9.15
7.85
7.01
6.42
5.99
5.67
5.41
5.21
5.04
4.89
4.77
4.67
4.58
4.50
4.43
4.37
4.31
4.26
4.22
4.18
4.14
4.11
4.07
4.04
4.02
3.83
3.72
3.65
3.60
3.56
3.53
3.51
3.49
3.48
3.34
99.30
28.24
15.52
10.97
8.75
7.46
6.63
6.06
5.64
5.32
5.06
4.86
4.69
4.56
4.44
4.34
4.25
4.17
4.10
4.04
3.99
3.94
3.90
3.85
3.82
3.78
3.75
3.73
3.70
3.51
3.41
3.34
3.29
3.26
3.23
3.21
3.19
3.17
3.04
99.33
27.91
15.21
10.67
8.47
7.19
6.37
5.80
5.39
5.07
4.82
4.62
4.46
4.32
4.20
4.10
4.01
3.94
3.87
3.81
3.76
3.71
3.67
3.63
3.59
3.56
3.53
3.50
3.47
3.29
3.19
3.12
3.07
3.04
3.01
2.99
2.97
2.96
2.82
99.36
27.67
14.98
10.46
8.26
6.99
6.18
5.61
5.20
4.89
4.64
4.44
4.28
4.14
4.03
3.93
3.84
3.77
3.70
3.64
3.59
3.54
3.50
3.46
3.42
3.39
3.36
3.33
3.30
3.12
3.02
2.95
2.91
2.87
2.84
2.82
2.81
2.79
2.66
99.37
27.49
14.80
10.29
8.10
6.84
6.03
5.47
5.06
4.74
4.50
4.30
4.14
4.00
3.89
3.79
3.71
3.63
3.56
3.51
3.45
3.41
3.36
3.32
3.29
3.26
3.23
3.20
3.17
2.99
2.89
2.82
2.78
2.74
2.72
2.69
2.68
2.66
2.53
99.39
27.35
14.66
10.16
7.98
6.72
5.91
5.35
4.94
4.63
4.39
4.19
4.03
3.89
3.78
3.68
3.60
3.52
3.46
3.40
3.35
3.30
3.26
3.22
3.18
3.15
3.12
3.09
3.07
2.89
2.78
2.72
2.67
2.64
2.61
2.59
2.57
2.56
2.43
99.40
27.23
14.55
10.05
7.87
6.62
5.81
5.26
4.85
4.54
4.30
4.10
3.94
3.80
3.69
3.59
3.51
3.43
3.37
3.31
3.26
3.21
3.17
3.13
3.09
3.06
3.03
3.00
2.98
2.80
2.70
2.63
2.59
2.55
2.52
2.50
2.49
2.47
2.34
99.43
26.87
14.20
9.72
7.56
6.31
5.52
4.96
4.56
4.25
4.01
3.82
3.66
3.52
3.41
3.31
3.23
3.15
3.09
3.03
2.98
2.93
2.89
2.85
2.81
2.78
2.75
2.73
2.70
2.70
2.52
2.42
2.35
2.31
2.27
2.24
2.22
2.21
2.06
99.45
26.69
14.02
9.55
7.40
6.16
5.36
4.81
4.41
4.10
3.86
3.66
3.51
3.37
3.26
3.16
3.08
3.00
2.94
2.88
2.83
2.78
2.74
2.70
2.66
2.63
2.60
2.57
2.55
2.55
2.37
2.27
2.20
2.15
2.12
2.09
2.07
2.05
1.90
99.46
26.58
13.91
9.45
7.30
6.06
5.26
4.71
4.31
4.01
3.76
3.57
3.41
3.28
3.16
3.07
2.98
2.91
2.84
2.79
2.73
2.69
2.64
2.60
2.57
2.54
2.51
2.48
2.45
2.45
2.27
2.17
2.10
2.05
2.01
1.99
1.97
1.95
1.79
99.47
26.50
13.84
9.38
7.23
5.99
5.20
4.65
4.25
3.94
3.70
3.51
3.35
3.21
3.10
3.00
2.92
2.84
2.78
2.72
2.67
2.62
2.58
2.54
2.50
2.47
2.44
2.41
2.39
2.39
2.20
2.10
2.03
1.98
1.94
1.92
1.89
1.88
1.72
606
Appendix
Table
A.4.
Critical values of
x2
for
v
degrees of freedom
and selected levels
of
significance.
No.
of
Degrees
of
Freedom,
v
0.20 0.10 0.05 0.025
0.01
Significance
Level,
a
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
40
50
60
1.64
3.22
4.64
5.99
7.29
8.56
9.80
11.03
12.24
13.44
14.63
15.81
16.98
18.15
19.31
20.47
21.61
22.76
23.90
25.04
26.17
27.30
28.43
29.55
30.68
31.79
32.91
34.03
35.14
36.25
47.27
58.16
68.97
2.71
4.61
6.2
5
7.78
9.24
10.64
12.02
13.36
14.68
15.99
17.28
18.55
19.81
21.06
22.31
23.54
24.77
25.99
27.20
28.41
29.62
30.81
32.01
33.20
34.38
35.56
36.74
37.92
39.09
40.26
51.81
63.17
74.40
(Con
t
in
ued)
3.84
5.99
7.81
9.49
11.07
12.59
14.07
15.51
16.92
18.31
19.68
2
1.03
22.36
23.68
25.00
26.30
27.59
28.87
30.14
31.41
32.67
33.92
35.17
36.42
37.65
38.89
40.11
41.34
42.56
43.77
55.76
67.50
79.08
5.02
7.38
9.35
11.14
12.83
14.45
16.01
17.53
19.02
20.48
21.92
23.34
24.74
26.12
2
7.49
28.85
30.19
31.53
32.85
34.17
35.48
36.78
38.08
39.36
40.65
41.92
43.19
44.46
45.72
46.98
59.34
71.42
83.30
6.63
9.21
11.34
13.28
15.09
16.81
18.48
20.09
21.67
23.21
24.72
26.22
27.69
29.14
30.58
32.00
33.41
34.81
36.19
37.57
38.93
40.29
41.64
42.98
44.31
45.64
46.96
48.28
49.59
50.89
63.69
76.15
88.38
607
Statistics and Data Analysis in Geology
Table
A.4.
Concluded.
No.
of
Degrees
of
Freedom,
v
0.20 0.10 0.05 0.02 5 0.01
Significance
Level,
cx
70 79.71 85.53
90.5 3 95.02
100.43
80
90.41
96.58 101.88 106.63
112.33
90 101.05 107.57
113.15 118.14
124.12
100 111.67
118.50 124.34
129.56 135.81
110 122.25 129.39 135.48
140.92 147.41
120 132.81 140.23 146.57
152.21 158.95
Table
A.5.
Probabilities
of
occurrence of specified values
of
the Mann-Whitney
W,
statistic for testing the equality to
two
samples
of
size
n
and
m,
where
m
5
n
I
8.
CL
is the lower critical value and
Cu
is the upper critical value.'
m=3
CL
3
cu
4
cu
5
Cu
6
Cu
7
Cu
8
Cu
n
6
.0500
15
7
.lo00
14
8
.2000
13
9
.3500
12
10
.5000
11
11
.6500
10
12
.8000
9
13
.9000
8
14
.9500
7
15
1.0000
6
16
17
18
19
20
21
22
23
24
.0286
.0571
,1143
.zoo0
.3143
.4286
.5714
.6857
,8000
.8857
.942
.9714
1.0000
18
.0179
17
.0357
16
.0714
15
.1250
14
.1964
13
.2857
12
.3929
11
.5000
10
.6071
9
.7143
8
.8036
7
.8750
6
.9286
.9643
.982
1
1.0000
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
.0119
.0238
.0476
,0833
.1310
.1905
.2738
.3571
.4524
S476
.6429
.7262
.8095
.8690
.9167
.9524
.9762
.9881
1.0000
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
.0083
.0167
.0333
.0583
.0917
.1333
.1917
.2583
,3333
.4167
.5000
.5833
.6667
.7417
.8083
.8667
.9083
.94 17
.9667
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
.0061
.0121
.0242
.0424
.0667
.0970
.1394
.1879
.2485
,3152
.3879
.4606
.5394
.6121
.6848
.7515
.8121
.8606
.9030
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
'Adapted from
S.
Siege1 and
N.J.
Castellan,
Jr.,
1988,
Nonparametric
Statistics
for the Behavioral Sciences,
Zed.
Reproduced
by
permission
of
The McGraw-Hill Companies, New
York.
(Con tin ued)
608
Appendix
Table
A.5.
Continued.
m=4
n
CL
4
cu
5
Cu
6
Cu
7
Cu
8
Cu
10
.0143
26
.0079
30
.0048
34
.0030
38
.0020
42
11
.0286
25
.0159
29
.0095
33
.0061
37
.0040
41
12
,0571
24
,0317
28
.0190
32
.0121
36
.0081
40
13
.lo00
23
,0556
27
.0333
31
.0212
35
.0141
39
14
.1714
22
.0952
26
,0571
30
.0364
34
.0242
38
15
,2429
21
.1429
25
.0857
29
.0545
33
.0364
37
16
,3429
20
.2063
24
.1286
28
.0818
32
.0545
36
17
,4429
19
.2778
23
.1762
27
.1152
31
.0768
35
18
.5571
18
,3651
22
.2381
26
.1576
30
.lo71
34
19
.6571
17
,4524
21
.3048
25
.2061
29
.1414
33
20
,7571
16
.5476
20
.3810
24
.2636
28
.1838
32
21
.8286
15
.6349
19
.4571
23
.3242
27
.2303
31
22
,9000
14
.7222
18
.5429
22
.3939
26
.2848
30
23
.9429
13
.7937
17
.6190
21
.4636
25
.3414
29
24
.9714
12
.8571
16
.6952
20
.5364
24
.4040
28
25
,9857
11
.9048
15
.7619
19
.6061
23
.4667
27
26
1.0000
10
,9444
14
.8238
18
.6758
22
.5333
26
27
,9683
13
.8714
17
.7364
21
.5960
25
28
.9841
12
.9143
16
.7939
20
.6586
24
29
,9921
11
.9429
15
.8424
19
.7152
23
30
1.0000
10
.9667
14
.8848
18
.7697
22
31
,9810
13
.9182
17
.8162
21
32
.9905
12
.9455
16
.8586
20
33
.9952
11
.9636
15
.8929
19
34
1.0000
10
.9788
14
.9232
18
(Continued)
609
Statistics and Data Analysis in Geology
Table
A.5.
Continued.
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
,0040
40
,0079
39
.0159
38
.0278
37
,0476
36
.0754
35
,1111
34
.1548
33
.2103
32
.2738
31
.3452
30
.4206
29
.5000
28
.5794
27
.6548
26
.7262
25
,7897
24
.8452
23
,8889
22
.9246
21
,9524
20
.9722
19
.9841
18
.9921
17
.9960
16
1.0000
15
.0043
44
.0087
43
.0152
42
.0260
41
.0411
40
.0628
39
.0887
38
.1234
37
.1645
36
.2143
35
.2684
34
.3312
33
.3961
32
.4654
31
.5346
30
.6039
29
.6688
28
.7316
27
.7857
26
.8355
25
.8766
24
.9113
23
.9372
22
.9589
21
,9740
20
n
m=5
CL
5
cu
6
cu
7
cu
8
cu
.0013
50
.0008
55
.0022
45
.0025
49
.0051
48
.0088
47
.0152
46
.0240
45
,0366
44
,0530
43
.0745
42
,1010
41
.1338
40
,1717
39
,2159
38
,2652
37
,3194
36
,3775
35
.4381
34
,5000
33
.5619
32
,6225
31
.6806
30
.7348
29
.7841
28
.8283
27
.8662
26
.8990
25
.0016
54
.0031
53
.0054
52
.0093
51
.0148
50
.0225
49
.0326
48
.0466
47
.0637
46
.0855
45
.1111
44
.1422
43
.1772
42
.2176
41
.2618
40
.3108
39
.3621
38
.4165
37
.4716
36
.5284
35
.5835
34
.6379
33
.6892
32
.7382
31
.7824
30
(Continued)
610
Appendix
Table
A.5.
Continued.
m=6
n
CL
6
cu
7
cu
8
cu
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
.0011
57
.0022
56
.0043
55
.0076
54
,0130
53
.0206
52
.0325
51
.0465
50
.0660
49
.0898
48
.1201
47
,1548
46
.1970
45
,2424
44
.2944
43
.3496
42
,4091
41
.4686
40
,5314
39
.5909
38
.6504
37
.7056
36
.7576
35
.8030
34
A452
33
A799
32
.9102
31
.9340
30
.9535
29
.9675
28
.9794
27
.0006
63
,0012
62
,0023
61
,0041
60
.0070
59
.0111
58
.0175
57
.0256
56
.0367
55
.0507
54
.0688
53
.0903
52
,1171
51
.1474
50
.1830
49
,2226
48
.2669
47
.3141
46
.3654
45
,4178
44
.4726
43
.5274
42
.5822
41
.6346
40
.6859
39
.7331
38
.7774
37
A170
36
A526
35
.8829
34
.9097
33
.0003
69
.0007
68
.0013
67
.0023
66
.0040
65
.0063
64
.0100
63
.0147
62
,0213
61
.0296
60
.0406
59
.0539
58
.0709
57
.0906
56
.1142
55
.1412
54
.1725
53
.2068
52
.2454
51
.2864
50
.3310
49
.3773
48
.4259
47
.4749
46
.5251
45
.5741
44
.6227
43
.6690
42
.7136
41
.7546
40
.7932
39
(Continued)
611