Statistics for Environmental Engineers

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16.0 20 1.3X 1 =


There is no need to make more than one test per specimen unless more than 16 specimens are to be taken. The total cost of the scheme will be 16($1) + 1($20) = $36. The variance of the compositing scheme is a2 = 1- + —11.6) = 1.08. If we did not composite, the cost would be 16($1) + 16($20) = $336. Change the costs so sampling and testing are each $20 and we get:


n



s



nt



16.0 20 1.3 х 20



3.5


Making one test on each specimen would require four specimens. This scheme would have a variance of a2 = 4 +    = 4.3, a = 2.07, and a cost of 4($20) + 4($20) = $160. If this variance is too large,


we might try ns = 8 and nt = 2, which gives o2 = 1- +    = 2.08 and o = 1.44, at a cost of 8(S20) +


2(8)($20) = $480.    X

Comments


The variance components analysis is an effective method for quantifying the sources of variation in an experimental program. Obviously, this kind of study will be most useful if it is done at the beginning of a monitoring program. The information gained from the analysis can be used to plan a cost-effective program for collecting and analyzing samples. Cost-effective means that both the cost of the measurement program and the variance of the measurements produced are minimized.


It can happen in practice that some estimated variance components are negative. Such a nonsense result often can be interpreted as a sign of the variance component being zero or having some insignificant positive value. It may result from the lack of normality in the residual errors (Leone and Nelson, 1966). In any case, it should indicate that a review of the data structure and the basic assumptions of the components of the variance test should be made.

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