Geoscience Reference
In-Depth Information
Krebs (1999) has reviewed tests for a random distribution of items and rec-
ommends one proposed by Hines and O'Hara Hines (1979). The test statistic
is then
h
T
= 2
n
[2Σ(
x
i
)² + Σ(
z
i
)²]/[2
½
Σ
x
i
+ Σ
z
i
]²
where
n
denotes the number of points in the sample. The test statistic is com-
pared to the critical values shown in Table 6.1, with the table entered with
TABLE 6.1
Critical Values for the Hines and O'Hara Hines (1979) Test Statistic
h
T
α
Regular Alternative
Aggregate Alternative
m
0.005
0.01
0.025
0.05
0.05
0.025
0.01
0.005
10
1.0340
1.0488
1.0719
1.0932
1.4593
1.5211
1.6054
1.6727
12
1.0501
1.0644
1.0865
1.1069
1.4472
1.5025
1.5769
1.6354
14
1.0632
1.0769
1.0983
1.1178
1.4368
1.4872
1.5540
1.6060
16
1.0740
1.0873
1.1080
1.1268
1.4280
1.4743
1.5352
1.5821
18
1.0832
1.0962
1.1162
1.1344
1.4203
1.4633
1.5195
1.5623
20
1.0912
1.1038
1.1232
1.1409
1.4136
1.4539
1.5061
1.5456
22
1.0982
1.1105
1.1293
1.1465
1.4078
1.4456
1.4945
1.5313
24
1.1044
1.1164
1.1348
1.1515
1.4025
1.4384
1.4844
1.5189
26
1.1099
1.1216
1.1396
1.1559
1.3978
1.4319
1.4755
1.5080
28
1.1149
1.1264
1.1439
1.1598
1.3936
1.4261
1.4675
1.4983
30
1.1195
1.1307
1.1479
1.1634
1.3898
1.4209
1.4604
1.4897
35
1.1292
1.1399
1.1563
1.1710
1.3815
1.4098
1.4454
1.4715
40
1.1372
1.1475
1.1631
1.1772
1.3748
1.4008
1.4333
1.4571
50
1.1498
1.1593
1.1738
1.1868
1.3644
1.3870
1.4151
1.4354
60
1.1593
1.1682
1.1818
1.1940
1.3565
1.3768
1.4017
1.4197
70
1.1668
1.1753
1.1882
1.1996
1.3504
1.3689
1.3915
1.4077
80
1.1730
1.1811
1.1933
1.2042
1.3455
1.3625
1.3833
1.3981
90
1.1782
1.1859
1.1976
1.2080
1.3414
1.3572
1.3765
1.3903
100
1.1826
1.1900
1.2013
1.2112
1.3379
1.3528
1.3709
1.3837
150
1.1979
1.2043
1.2139
1.2223
1.3260
1.3377
1.3519
1.3619
200
1.2073
1.2130
1.2215
1.2290
1.3189
1.3289
1.3408
1.3492
300
1.2187
1.2235
1.2307
1.2369
1.3105
1.3184
1.3279
1.3344
400
1.2257
1.2299
1.2362
1.2417
1.3055
1.3122
1.3203
1.3258
600
1.2341
1.2376
1.2429
1.2474
1.2995
1.3049
1.3113
1.3158
800
1.2391
1.2422
1.2468
1.2509
1.2960
1.3006
1.3061
1.3099
1000
1.2426
1.2454
1.2496
1.2532
1.2936
1.2977
1.3025
1.3059
Note:
Given
n
, the number of random points (sample size) in
T
T-square sampling, enter the table
with
m
= 2
n
; that is, with
n
= 10 points, enter this table with
m
= 20. Values of
h
T
below the
regular alternative value indicate significant departure from a random pattern in the
direction of a regular pattern, and values above the aggregate alternative indicate signifi-
cant departure from a random pattern in the direction of an aggregate pattern.
