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hole 2 to the west and hole 17 to the east. The difference between these two mosaics
is greatest in the central part (between 14,250E and 14,400E) computed from holes
7-12 (between 14,200E and 14, 450E).
It is noted that the analysis of variance results shown in Table
7.1
differ from
those shown in the original table of Agterberg (
1966
, Table 4) that was based on the
same data with one exception. The original table shows separate estimates of the
first serial correlation coefficient (
r
1
) for each set of holes. These estimates vary
from 0.24 to 0.70 and
F
-ratios corrected using
n
0
based on these original estimates
of
r
1
. Later (in Agterberg
1974
), it was decided to use the same estimate (
r
1
¼
0.50)
based on the correlogram of Fig.
6.15a
for each set of holes. This single estimate is
probably more precise than the single smaller- sample estimates, because it is an
average for 24 drifts on different levels of the Whalesback Mine including those on
the 425-ft. level. This revision does not significantly change the original conclu-
sions drawn in Agterberg (
1966
).
Much information on the spatial distribution of copper in the Whalesback
Box 7.1: Degrees of Freedom for Autocorrelated Data
The variance of the mean of
n
autocorrelated data from a series with the first
order Markov property satisfies: var
X
¼
¼ σ
n
2
P
i¼
1
P
j¼
1
cov
X
i
;
2
X
j
h
n
o
i
2
ˁ
1
Þ
ˁ
1
n
1
n
1
is the autocorrelation
coefficient for adjoining values (
cf
. Cressie
1991
, p. 14). S
up
pose an equiv-
alent number of independent data (
n
0
) is defined as var
X
¼ σ
1
þ
ð
1
ð
1
ˁ
Þ=
n
=
n
where
ˁ
ˁ
ˁ
2
n
0
. For
=
10, the preceding equation then gives approximately
n
/
n
0
¼
n
>
1+2
r
1
[
n
/
r
1
)
2
]/
n
(
cf
. Agterberg
1974
, p. 302). For large
n
this gives
approximately
n
0
¼
(1
r
1
)
1/(1
r
1
)/(1 +
r
1
) illustrating that autocorrelation strongly
affects statistical inference even in large samples (also see Sect.
2.1
).
n
(1
deposit is for points outside subhorizontal levels such as the 425-ft. level used for
example earlier in this section. As an experiment, a 3-D analysis was performed on
all copper values for samples taken within a relatively small block extending from
the surface to the 425-ft. level and situated between the 14,000E and 14,500E
sections. In total, 516 values from both core samples and channel samples along
drifts were used. Figure
7.10a
shows a histogram of the 516 logarithmically
transformed copper values. It is clearly bi-modal. 3-D trend analysis gave the
following ESS-values: linear 18.0 %, quadratic 32.8 % and cubic 43.3 %. The
logarithmic variance of original data is 1.865. 3-D trend analysis reduced this
variance as follows: linear residuals 1.531, quadratic residuals 1.2070, and cubic
residuals 1.093. In Agterberg (
1968
) it is discussed in more detail that the cubic fit is
better than the quadratic fit in this example. A chi-square test for goodness of fit was
applied to test the cubic residuals (Fig.
7.10b
) for normality. It gave an estimated
chi-square of 17.3 for 17 degrees of freedom, well below the 27.6 representing the
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