Statistics for Environmental Engineers

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b.    Ensure that the fitted value will be as close as possible to the true value


c.    Provide an internal estimate of the random experimental error


d.    Provide a check on the assumption of constant variance


Blocks of Time


Randomized Blocks of Time


° nO


о



о



о


• • •


time





A A A


B B B


C C C


C A B


A C B


B A C

time


(a) Good and bad designs for comparing treatments A, B, and C


cSffe


AAAA    BBBB    CCCC    DDDD


No blocking, no randomization


ABCD    BCDA    CDAB    DABC


Blocking and Randomization


(b) Good and bad designs for comparing treatments A, B, C, and D for pollution reduction in automobiles



(b) Good and bad designs for comparing treatments A, B, and C in a field of non-uniform soil type.



FIGURE 22.2 Successful strategies for blocking and randomization in three experimental situations.


One-Factor-At-a-Time (OFAT) Experiments


Most experimental problems investigate two or more factors (independent variables). The most inefficient approach to experimental design is, “Let’s just vary one factor at a time so we don’t get confused.” If this approach does find the best operating level for all factors, it will require more work than experimental designs that simultaneously vary two or more factors at once.


These are some advantages of a good multifactor experimental design compared to a one-factor-at-a-time (OFAT) design:

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