168 TRANSURANIC ELEMENTS IN THE ENVIRONMENT 



239,240p^ concentrations and accounted for approximately 20% of the variation. The 



95% confidence interval about a^ for Pu concentrations includes and suggests that 

 Oy^ may not be greater than 0; however, the inclusion of is the result of a slight 

 inaccuracy in confidence intervals calculated according to the formulas of Scheffe (1959, 

 pp. 231-235). An F-test of the null hypothesis, Hq : a^ = 0, indicated that a^ was 

 significantly greater than 0(F = 2.99; df= 10,15; P< 0.05). 



Alternate Statistical Models 



If each transect is considered separately, a one-way analysis of variance procedure can be 

 used to estimate a^ and o^ (Scheffe, 1959, pp. 221-224). These estimates, symbolized 

 Oy^ I and o\i, can be compared among transects to evaluate the assumptions of 

 independence of D/, My, and e,yyt- The a^,- and ol^t for ^^^Pu and 2 3 9,2 4 Op^ 

 concentrations for each transect are compared in Table 2. 



The aj^,/ for ^^^Pu concentrations range from -0.0003333 to 0.01674. Although 

 negative a^ ,• are impossible, negative a^ i can occur owing to the sampling variances of 

 mean-square' terms (Scheffe, 1959, pp. 228-229; Searle, 1971, pp. 406-408). The 95% 

 confidence intervals for all the a^ ,• overlapped and indicated that the estimates could 

 have been drawn from a common value of a^ ,• at all transects. The b\^i differed 

 significantly among transects (Fmax. = 85.6; df= 5,3; P < 0.05) (Kirk, 1968) and tended 

 to decrease as the mean concentration decreased. 



The a^ ,■ for 239,240p^ concentrations ranged from -0.004167 to 12.16 and were 

 significantly greater than for three of the five transects. Again, the 95% confidence 

 intervals for the a^ ,• overlapped. The broad confidence bands around the a^ ,■ in Table 2 

 for both ^-^^Pu and 2 3 9,2 4 0p^j concentrafions were due to the small number of degrees 



TABLE 1 Estimated Variance Components, 95% Confidence Intervals About the 



Estimates, and Intraclass Correlation Coefficients for the Model o^ = ap + a^ + Qg , 



Which Partitions the Total Variance of Soil Plutonium Concentrations (a^ ) into 



Components due to Distance from the Source (a^), Microtopographical 



Heterogeneity (a^), and Sampling Error (ag)* 



*Estimates were computed from 30 determinations of ^^*Pu and 2 3 9.2 4 op^ Concentrations are 

 in picocuries per gram. 



