The most atriking aspect of this data is the larger mean ratio Ry as compared to the other estimates (0.371 compared to 0.032, 0.045, 0.076, and 0.102). This is due to the two very large individual ratios and it illustrates the effect of using an arithmetic mean to estimate a "typical value" when data are highly skewed. ORDERED RATIOS: 0,050 0.013 0.029 0.031 0.050 0.055 0.061 0.061 0.064 0.076 0.080 0.088 0.089 0.11 0.22 025 20 3.0 NEVADA TEST SITE 0.040 235y VEG, The second set of data consists of 273° concentrations in soil and associated vegetation from 17 random locations in Area 11, A Site, NTS. Gilbert and Eberhardt (1974) report that the ratio of vegetation mean to 601] mean tends to decrease toward ground zero. However, the data from the three activity level strata are combined here to illustrate the effect on ratio estimators when a constant ratio is not present. The vegetation concentrations are plotted versus the corresponding soi1i1 concentrations in Figure 7. The individual ratios (at the top of Figure 7) are skewed with the bulk of the data lying below 0.10 with two moderately large values (0.22 and 0.25) and two exceedingly large values (2.0 and 3.0). The various ratio estimates, their standard errors, and the 95 percent confidence limits are given in Table 2. AREA 11 ° 022 oos9 F259 5 0.030 0.020 ° »4 Q a L Ll 020 _t 040 Ll to 060 The widest confidence interval for 238i) VEG. Comparing the ratio estimates in Table 3, we again see, due to the skewnese of the data, that the mean of the ratios (R; = 0.0689) is cutside the 95% confidence limits of each of the other estimates. The other estimates lie in the confidence intervals of all methods with the exception of the sample median which lies outside the confidence interval for Method 3, which is extremely narrow. l 0.80 —L i 1.0 a 1.2 oeytoe. 0.016 0.016 0.018 0.018 0.020 0.021 0.026 0.028 0.029 RATIOS: 9939 9.935 0.037 0,050 0.052 0.057 0.28 0.43 The plot of the a similar manner to the 735 data. L Vegetation vs Soil, 735U (ug/g Dry) FIGURE 7. The third set of data consists of 23% concentrations in soil and associated vegetation for the same 17 locations in Area 11, A Site, data is given in Figure 8 where similar to the 235y data, there seems to be no linear relationship between concentrations of associated 1 and vegetation samples. In addition, the ratios are skewed in 0.013 2354) SOIL Re = Y/X, (0.005, 0.085), using V(R2) does not contain the lognormal estimate (R, = 0.102), while the smallest interval (0.026, 0.065) using V'(R>2) does not contain the sample median ratio (Rs = 0.076). The estimated standard error for Rp using V''(R>) was impossible to calculate because of a negative variance. This set of data illustrates the diversity of average ratio estimates which is possible when the ratio does not remain constant throughout the data set, and when the distribution of the observations is skewed. as the 235U concentrations (Gilbert et al., 1975). 2 0.031 0.076 2 00.050 00.061 oofe The other estimates are not as similar as those for the Pu/Am data. Note, e.g. that the confidence interval for R; does not overlap thosefor Ry, Ry and Rs. 0.068 0.20 NEVADA TEST SITE ok oH 0.10 F a AREA 11 0.05 : O 0.057 "S 0,030 0.05 8 0.028 007 %°0.016 29.43 0 70.28 Oo 1 0.018” 0 FIGURE 8. 65 a rc 9gag9 oeoe—0018 1 No 020 2 238) SOIL | 3 Vegetation vs Soil, 738U (ug/g Dry) 614 615 , a