Dr. Don Hendricks
-6-
August 28, 1972
higher probability and larger samples will detect smaller errors.
AS a
working guide, we recommend that a power of .90 be the mininimal vatue used
to select sample sizes.
Thus to select the sample size necded to make com-
parisons between two islands (two areas, two groups of islands) first
determine what difference should be detected (e.g., 1.3 means roughly 30%
differences will be picked up) and choose a sample size Jarge enough to give
a power of .90 or better (about 130 in this case).
Lacking any firm choice
as to criterion as to difference to be detécted, one can simply browse
around in the table and get a general impression of what difference a
given sample size will serve to detect.
R (Ratio of “high" to "Tow" mean)
n
100
1.3
B
1.4
[nn
1.5;
efn
1.8
Bin
2.0
e{n
2.5
Bf{n
3.0
get
n
Bg
30
.691
22
.86
114
.80
9
83
4
54
«.83
50
.75
120
.89
75
89
47
881
25
.89
116
.85
11
.89
6
.76
130
.91
85
92
55
91]
27
9]
20
.91
12
92
8
89
140
.93
|100
.96
-93}
30
-94
422
-95
13
94
9
.93
60
In the above table, & denotes theprobability that samples of size n will detect
ratios of mean concentrations of size R.
As an example, if we expect the
concentrations in one area to be 1.3 times that in another and take 100
samples in each area, then the t-test will have a probability of .83 of
finding this difference (and probability of .17 of not identifying this
difference, even though one as great as this actually exists).
An inspection of the above table will show that one cannot have a high
probability of finding differences of less than about two-fold unless rather
large samples are used.
/
Sampling patterns
. In beginning this letter, we pointed out the necessity for using random
sampling if one is to be protected against criticism.
There is one rather
widely used alternative scheme, which is to locate samples in some systematic
pattern.
In a problem like the present one, a two-dimensional grid may be
the most likely pattern, so that the samples are located at, say, x-hundred
yard spacing.
One argument for using such a pattern is that it may provide
somewhat better estimates of the amount of soil to be moved in a clean-up