30

e) One hundred and thirty-four data reports

tory, labeled V2-1 to V2-134, and 23 from the NPD

laboratory, labeled V3-1 to V3-23. These results

20

were from 39 project locations in more than 21

states and involved more than 15 laboratories.

10

0

The first approach considered was a plot of

QC concentration estimates vs. associated QA es-

timates. This is a very useful comparison tech-

nique. A linear regression line can be fitted by

QC

Cr

Ratios

minimizing the residual sum of squares for the

QA

QC estimates while assuming zero error in the

QA estimates. For an ideal system with perfect

agreement between QC and QA values, the fitted

model would be linear through the origin with a

TPH results, the percent exclusions were always

slope of 1.00. The extent of departure from this

less than 13% and often well below 10%.

ideal can be used to calculate confidence limits

We should not expect the QC/QA ratios to be

for individual measurements at some selected

normally distributed using linear coordinates. A

probability level. Confidence intervals for indi-

factor of 2 difference in QC and QA concentra-

vidual measurements are called tolerance bands.

tions would lead to a low side ratio of 0.50 and a

After reviewing the data sets submitted, we

high side ratio of 2.00. Obviously these two val-

decided that the concentration ranges were much

ues are not symmetrically distributed around the

too wide to be fitted to individual models. Fur-

ideal value of 1.00 for perfect agreement. A histo-

thermore, there is no basis for assigning referee

gram of the soil Cr QC/QA results (Fig. 1) shows

status to the QA values, and the data are not nor-

that the typical shape of these distributions is

mally distributed, which is the underlying as-

skewed toward the high end. This histogram sug-

sumption of this approach. It is also likely that

gests that a lognormal distribution should describe

the more complex computations required by this

the results. Simply stated, this means that the logs

approach might impede routine usage. Conse-

of the ratios will form a normal distribution when

quently, we decided to examine QC/QA concen-

plotted as shown in Figure 1.

tration ratios for between-laboratory comparisons

An effective method of testing the hypothesis

and QC1/QC2 ratios for comparison of within-

that the ratios are lognormally distributed is to

laboratory replicates. This approach is similar to

use Lognormal Probability graph paper in which

the first one considered except that no regression

the ordinate is a % probability scale and the ab-

model is fitted. When duplicate QC values were

scissa is a log scale. If the lognormal model is

given, the first listed value was always used for

correct, a straight line will result. To plot the Cr

the QC/QA computation. For metals in soils and

ratios shown in Figure 1, we convert the number

VOCs in groundwater, ratios below 0.30 and

of ratios in each cell to a cumulative probability.

above 3.00 were designated outliers and excluded

From Figure 1 there are 16 ratios between 0.395

from further computations. Because of the larger

and 0.595. Since the total number of ratios was

unavoidable uncertainties attached to the estima-

116, the probability of values in this cell is

tion of low concentration organic analytes in soils,

these limits were expanded to 0.254.00 for TPH

(16) (100)

= 13.8%.

and explosives and to 0.1010.0 for VOCs. While

116

this practice may seem arbitrary, exclusion of a

This value is plotted on the probability scale vs.

very few highly extreme values is necessary to

the upper boundary of the cell, 0.595. The next

avoid unreasonable increases of standard devia-

cell (0.5950.795) contained 22 ratios and the cu-

tions and the associated confidence bands for a

mulative percent was

data set. Except for VOCs in soils and one set of

2