(16 + 22) (100)

(2 - 0.5) (100)

= 32.8%,

= 7.50% ,

116

20

which is plotted vs. 0.795, etc. (see Fig. 2c). Fig-

etc. Benzene (Fig. 2e) has several points at each

ures 2a, 2b, 2c, and 2d are log-cumulative prob-

extreme that deviate a good deal from linearity.

ability plots of QC/QA ratios for soil As, Ba, Cr,

and Pb respectively. Although a few points devi-

satisfactory. Chloroform and ethylbenzene (Fig.

ate slightly from the linear ideal for lognormal

2f and 2g) fit the lognormal model with only mini-

results, the fits are quite good and justify analyz-

mal scatter while toluene (Fig. 2h) provides a fair

ing the data as being lognormally distributed.

fit. Other VOCs not shown behaved similarly to

Plots for QC1/QC2 ratios behaved similarly, as

the ones shown. In view of these VOC plots, those

expected.

for other analytes, and the expected distribution

Lognormal plots for individual values rather

of ratios, we decided to treat all ratios by the same

than groups are illustrated using four VOCs in

computational procedures. Since the lognormal

groundwater (Fig. 2e2h). Individual rather than

model will be used, we must compute geometric

grouped probabilities were used because of the

means and geometric standard deviations as

relatively small number of ratios. Individual prob-

shown below.

abilities are calculated from

1. Compute QC1/QC2 ratios and their loga-

rithms when QC1/QC2 results are available.

(*i *- 0.5) (100)

2. Compute mean and standard deviation of

the logs.

where *n *is the total number of ratios in a set and *i*

3. Compute 95% confidence limits for the mean

is the rank after the ratios are arranged from low-

of the logs according to the equation

est to highest. Thus for 20 ratios ranging from

0.40 to 2.75, the first ranked one (0.40) would be

plotted on the abscissa vs. a probability of

(1 - 0.5) (100)

= 2.50%

where x is the mean of the logs, *t*0.95 is student's

20

alpha risk of 5% (α = 0.05), *S*x is the standard

and the next higher ratio would be plotted vs.

99.9

99.9

98

98

90

90

70

70

50

50

30

30

10

10

2

2

0.10

1.0

3.0

0.10

1.0

3.0

QC

QC

Barium QA Concentration Ratio

Arsenic QA Concentration Ratio

3