Statistical Tables
265
II1. ORDER-STATISTIC
ESTIMATES IN SMALL SAMPLES
Table E.4 Unbiased estimate of ~ using the range w (variance to be
multiplied by a
2)
N KI w
Variance EJf
N KI w
Variance Eft.
2
0.886w
0.571
1.000
11
0.315w
0.0616
0.831
3
0.591w
0.275
0.992
12
0.307w
0.0571
0.814
4
0.486w
0.183
0.975
13
0.300w
0.0533
0.797
5
0.430w
0.138
0.955
14
0.294w
0.0502
0.781
6
0.395w
0.112
0.933
15
0.288w
0.0474
0.766
7
0.370w
0.0949
0.911
16
0.283w
0.0451
0.751
8
0.351w
0.0829
0.890
17
0.279w
0.0430
0.738
9
0.337w
0.0740
0.869
18
0.275w
0.0412
0.725
10
0.325w
0.0671
0.850
19
0.271w
0.0395
0.712
20
0.268w
0.0381
0.700
Adapted by permission of the Biometrika Trustees
Probability Integral of the Range in Samples of n
Biometrika, Vol. 32, 1942, p. 301.
from E.S. Pearson and H.O. Hartley, The
Observations From a Normal Population,
Table E.5 Modified linear estimate of ~r (variance to be multiplied by 2)
N
Estimate
Variance Eft.
2
0.8862(X2-Xl)
0.571
1.000
3
0.5908(X3-X1)
0.275
0.992
4
0.4857(X4-X~)
0.183
0.975
5
0.4299(Xs-X~)
0.138
0.955
6
0.2619(X6+Xs-X2-X1)
0.109
0.957
7
0.2370(X7 + X6-Xz-XI)
0.0895
0.967
8
0.2197(X8 + XT-X2-X~)
0.0761
0.970
9
0.2068(X9 + Xs-X2-X~)
0.0664
0.968
10
O.1968(X~o+X9-X~-XI)
0.0591
0.964
11
0.1608(X~ +X~0 +Xs-X4-Xz-XI)
0.0529
0.967
12
0.1524(X~2 +X~ +X9-X4-Xz-XI)
0.0478
0.972
13
0.1456(X~3 + X~2 + X~o-X4-Xz-X~)
0.0436
0.975
14
O.1399(X~4+X~3+X~-X4-X~-X~)
0.0401
0.977
15
0.1352(X~5 --~ z¥14 q- XlZ--~"4--~¥2-XI)
0.0372
0.977
16
0.131 l(XI6 + XI5 q- XI 3-X4-/2-Xl)
0.0347
0.975
17
O.1050(XI7q-X16q-X15.q-X13-Xs-X3-X2-X1)
0.0325
0.978
18
O.1020(X18-t-Xlyq-X16.q-X14-~5-X3-X2-X1)
0.0305
0.978
19
0.09939(X~9 + XI8 + X~7 + XIs-Xs-X3-X2-X~)
0.0288
0.979
20
0.09706(X20 + Xx9 + X~8 + X~6-Xs-X3-Xz-X~)
0.0272
0.978