L.3.2.2 Comparison with an action level (Cont.)

UCL = x + ( t 0.95,v )( s 2/n )

(L-26)

As in the first approach, the MSE is used in place of s2 if variances are not

significantly different, and the degrees of freedom (v) are N - k. If variances are

significantly different, s2 for the individual treatment is used, and v for each

treatment i is ni - 1. There is a 0.95 probability that the true population mean

tissue level is below the UCL. If the UCL is below the action level, there is a

$0.95 probability that the population mean tissue level for the dredged material

is below the action level, and we conclude that the action level is not exceeded.

If the UCL is above the action level, we cannot be sure that the mean population

tissue level does not exceed the action level.

Either of the above procedures may be used with data that have failed the

normality test, but the results should be considered approximate.

The choice of which approach to use depends on the computer software and

the presentation method to be used. In SAS, it is more convenient to calculate

the UCL and compare with the action level, as in program BIOACC

(Section L.4.2). In SYSTAT, it is simpler to conduct a one-sample t-test. Both

approaches can easily be performed by hand. If these data are presented

graphically, as in Figure L-5, the confidence-level approach is used. If the

investigator wants to provide the exact probability that the mean tissue level is

less than the action level, then the one-sample t-test is used.

Figure L-5 presents a comparison of mean bioaccumulation from the three

dredged sediments (see Table L-6) with a hypothetical action level of 0.2 g/g.

There is no need to calculate the UCL for sediment 1 as the mean exceeds the

action level. Because variances were not significantly different for the

untransformed data (Table L-7), we use MSE = 0.003763 and t0.95,16 = 1.746 in

Equation L-21 to obtain:

UCL = 0.190 + 1.746(0.003763/5)2 = 0.238

(L-27)

for sediment 2, and UCL = 0.178 for sediment 3. SAS program BIOACC

(Section L.4.2) calculates UCL for both equal and unequal variances.

If the UCL lies below the action level, there is a >0.95 probability that the

true population mean tissue level for that sediment is less than the action level.

Thus, we would conclude that mean bioaccumulation for dredged sediment 3 is

less than the action level. Because the UCL for sediment 2 exceeds the action

level even though the sample mean does not, we cannot be sure that the true

population mean tissue level for this sediment is less than the action level.

L37

Appendix L Selected Resource Documents