the probability of not having a significant relationship in the population is less than 1
percent. The results revealed a statistically significant negative correlation (r = -0.8654,
p =0 .0008) between nca and |E40*|, when controlling for nfa, implying that a high nca
results in a low E40o*.
Table 5-3. Partial correlation analysis for nca and |E40*| when controlling for nfa
nca
N r (Correlation Coefficient)
|E40*| 13 -0.8654**
p<0.05, ** p<0.01
Category Analysis of Power Law Parameters
In order to further evaluate the relationship between power law parameters (nca and
nfa) and the dynamic modulus, four simplified categories of power law parameters were
hypothesized. The four hypothesized categories to be tested are as follows:
Category 1 [Low nca (smaller than 0.50) and Low nfa (smaller than 0.59)].
Category 2 [Low nca (smaller than 0.50) and High nfa (greater than 0.59)].
Category 3 [High nca (greater than 0.50) and Low nfa (smaller than 0.59)].
Category 4 [High nca (greater than 0.50) and High nfa (greater than 0.59)].
Table 5-4 shows the Mean and Standard Deviation of E40*l for the four different
categories studied. Since the underlying power law parameters nfa and nca are slightly
correlated, a discriminate category analysis is not appropriate. Rather, a one-way
analysis of variance (ANOVA) is used to uncover the effects of the categorical variables
(i.e., four different categories) on the interval dependent variable (i.e., |E40*|). According
to Table 5-5, the results are statistically significant at an alpha level of 0.01 (F(3,9) =
7.64, p = 0.008). Since the results showed a significant omnibus F, a post-hoc analysis