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 Statistical software packages may also provide functions to determine t-
values or their associated probabilities. In SAS, these functions are TINV and
PROBT.
L.1.2 Hypothesis testing
The goal in analyzing data from certain CDF pathway tests, such as
bioaccumulation, is to determine whether the mean effect of exposure to a
dredged material is significantly greater than the mean effect of exposure to a
reference. Two formal hypotheses underlie the statistical analysis of data in the
two-sample situation. Let FR denote the mean effect of exposure to a reference
R, and let FD denote the mean effect of exposure to a dredged material D. Then,
these two hypotheses are defined as follows:
Null hypothesis.
H0: FD = FR
Case 0:
There is no difference in mean effect between the
treatment and the reference.
Alternative hypotheses.
H1: FD < FR
Case 1:
The mean effect of the treatment is less than the
mean effect of the reference (e.g., survival in the
100 percent elutriate is less than survival in the
control water).
OR
H1: FD > FR
Case 2:
The mean effect of the treatment is greater than
the mean effect of the reference (e.g.,
bioaccumulation from the dredged material is
greater than bioaccumulation from the reference).
Our hypothesis test will either reject H0 for H1 (Case 1 or Case 2), or will be
unable to reject H0 (Case 0). A one-tailed test is used because there is little
concern about identifying a lesser negative effect from the treatment than from
the reference.
In performing the hypothesis test, and in determining the sample size to use
in the test, the investigator must be aware of the probabilities for two types of
errors that can occur in the conclusion. Type I errors occur if, after analysis of
the data, H0 is rejected when it was actually true. In Case 1 for example, a Type
I error occurs when it is concluded that the mean effect (e.g., survival) of the
treatment is less than the mean effect of the reference when, in fact, the true
L6
Appendix L
Statistical Methods
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