sample size. Thus, in such situations the derived statistics are not necessarily the best
indicator of "goodness of fit". Examination of residuals helps to reaffirm the "goodness
of fit" of the regression equation in conjunction with the R2 value. This examination
involved plotting the residuals vs. the dependent variable. If the residuals exhibit a
random distribution and have a more or less even split above and below the zero line then
it is possible to say that the equation describes the relationship well (Kirkup, 2002)
The other test requires formulating a null hypothesis and an alternate hypothesis,
which are then tested using ANOVA and t-statistic. This test helps to access the
suitability of the best-fit equation that describes the relationship between the variables
(Kirkup, 2002). The hypothesis test utilize in this analysis is a one-tailed ANOVA. In
this case the null and alternate hypotheses are,
Ho: the equation has a zero slope;
Ha: the equation has non-zero slope.
Since the linear regression equation relates porosity to permeability using the slope
and the intercept of the equation, the null hypothesis is that of zero slope, which yields a
constant function. The hypothesis tests were performed at the 95% confidence interval.
Results
Permeability values were plotted on an outline of Neuzil's (1994) compiled range
of permeabilities as a function of porosity for argillaceous sediments (Figure 2-5). The
majority of permeability values were enveloped within Neuzil's (1994) plot. However,
several samples from Site 1231 of Peru and Sites 1039 and 1040 of Costa Rica plotted
outside Neuzil's (1994) plotted area. These include non-argillaceous sediments of
calcareous oozes and few samples containing siliceous oozes.