To find numerical evidence of lognormality, we chose the Filliben?’ r-test to reject if necessary the hypothesis that each data : Filliben's investigations have shown the r-test to be 98 percent as powerful as Shapiro and Wilk's omnibus W-test°® for Tejecting a lognormal hypothesis when the data are not 2 to 100. The r-test was validated?’ for sample numbers ranging from Computationally, the r-test is much more convenient than the W-test in that long lists of constants need not be stored. Ye approximate the r-probability levels by a second order polynozial in log (number of samples, N) for N 4. The maximum error for this approximation is + 0.004 in the region N = 10; elsewhere + 0.001. We tested al] data sets (greater than six measurements each) having more than half the samples greater than the minimus detectable activity (MDA) and found that 91 data sets out of 123 tested lognorme:. sets, Of the $i 56 percent had r-values greater than the 0.5 probability acceptance level; 36 percent, 0.1 < r <0.5; percent, r= 0.05. t-values (r $0.05). rejected data 7 percent 0.055 r < 0.1; and } The lognormal assumption was rejected for low The resulting inaccuracy is smali since those sets were near the MDA. Mean (X), standard variation (s), and cumulative probability were estimated by the (1) Krige's quantile version of tie maximun likelihood estimator, (2) log-probability graphical methods, and (3) arithmetic mean. a Pf > set is lognormally distributed. lognormal. f ee ~ Krige's method is used as outlined by Gilbert, 39 using the 5011118 e : ‘fs . Se “oY “i