Supplement - Page 2.
t
a
138
100(1~a)% Upper
Limit on True Mean
. O01
2.35
20 pCi/g
05
1.66
19
-10
1.29
18
Since the decision to cleanup may be a function more of extreme values
rather than average concentrations the next section considers upper limits
on percentiles.
*
II.
Nonparametric Confidence Limits on Percentiles
Using "Practical Nonparametric Statistics” by W. J. Conover, John
Wiley, 1971, page 111, we compute upper one-sided confidence limits:
The probability is l-a that p percent of the soil concentrations
for the area from which samples were collected are less than or
equal to X.
Estimated values of X for various values of p and a for the data from
Janet are:
Pp.
_a_
50,
05
-50
.25
-90
-O1
- 90
225
50;
-50
.90
90
.95
95
95
-95
Interpretation:
.01
-10
X(pCi/g)
13
11
10
5]
.05
-10
46
4]
.O1
120
-10
25
57
52
.05
(median = 9.8 pCi/g)
1
(90°
th
percentile = 37 pCi/g)
4]
67
;
—
For p = .90 and a = .05 we state:
(95°
th
percentile = 46 pCi/q)
We are 95% sure that
90% of the soil concentrations on the island are < 46
pCi/gm.
These values of X for a = .01, .05, and .10 when p = .50 are nonparametric
equivalents of the 100(1-a)% upper limits on the median computed in Part I
above. The upper limits (X) obtained here do not require any assumption
about the distribution of the observations. Note that these limits are
consequently somewhat higher than the corresponding limits in Part I.