7945

• UCREFRP Catalog Number: 7945
• Author: Bovee, K. D. and T. Cochnauer.
• Title: Development And Evaluation Of Weighted Criteria Probability-Of-Use Curves For Instream Flow Assessments
• USFW Year: 1977.
• USFW - Doc Type: Fisheries, Instream Flow Information Paper No. 3.
• Copyright Material: NO

5. The optimum for a given hydraulic parameter was defined by
those incremental clusters which showed an obvious majority of obser-
vations, as well as being relatively uniform in frequency for each data
cluster.
6. The optimum was then tested for variance with chi-square, using
the null hypothesis that: within the area defined as the optimum for a
given parameter, there is no significant difference in the frequency of
observation within the optimum. If the null hypothesis could be re-
jected at any level of probability greater than 0.10, the optimum was
redefined (re-clustered, or some clusters omitted) and retested by
X2. In some cases, the variance was such that the null hypothesis
could be rejected at almost any level. Such cases were noted and treated
in the evaluation of the curve. Curve evaluations will be explained in
a later section.
7. Having defined the optimum, the mean or expected frequency
within the optimum was calculated. The total frequency of each incre-
ment cluster was also found.
8. The probability of use for those increments falling within the
optimum range was assigned a value of 1.0. Probabilities of use for
each clustered increment outside the optimum were calculated simply by
dividing the frequency for each cluster by the mean frequency for the
optimum. For two adjacent clusters with approximately the same fre-
quencies, the mean frequency for both was divided by the mean for the
optimum.
This entire procedure for frequency analysis is illustrated in
Table 4. The optimum was defined by the cluster groupings to the right
of the frequency column, rather than those to the left less for two
primary reasons: (1) clustering on the right resulted in less cluster-
to-cluster variance, and (2) clustering on the left resulted in several
secondary modes. Velocities of 1.7-1.8, and 2.3-2.4 feet per second,
were not included in the optimum range. Inclusion of these frequencies
introduced a statistically significant difference in the distribution.
Therefore, the optimum range was reduced to between 1.9 and 2.2 feet
per second.
Having defined the optimum range for a parameter, and having cal-
culated the probability of-use with respect to increments outside the
optimum, the probabilities were plotted and a curve fitted to the
distribution. Figure 2 shows such a plot for the data given in Table 4.
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