By Dr. William M. Turner
Transmissivity data are plotted as cumulative probability of the occurrence of
transmissivity values having values greater than indicated on the graph. The plot is shown
in Figure 2.
Theoretical normal, lognormal and exponential distributions were next calculated based
on the estimates of population mean and standard deviation. For each statistical
distribution, a Chi-Square (C2) contingency table
was created to test for the goodness-of-fit between the proposed statistical frequency
distribution and the observed distribution of the data. The C2
test may be used to test the goodness-of-fit for any statistical distribution. If C2 = 0, there is a perfect match between the observed and
the expected values. The larger the value, the greater the departure of the observed from
the expected values.
In the present case a two-way contingency table was prepared representing frequency
classes and the number of transmissivity values within each frequency class. The null
hypothesis, Ho, being tested is that the distribution of observed
transmissivities in the Madera Limestone aquifer is lognormally distributed.
The C2 value for the contingency table
constructed from observed and expected values is 2.075. With 7 degrees of freedom, the C2 statistic at the 99 percent level is 16.08. Because C2 = 2.075 << 16.08, we conclude that the
disagreement between the observed and predicted cannot be rejected at the 0.01 level. We
are unable to reject the Ho hypothesis and we are, in the case of the Madera
Limestone aquifer, reasonably certain that the transmissivity distribution is very close
to the expected lognormal distribution.
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