At both sites for carp, we found there was at least one significant two-way interaction, so we used a linear model with two-way interactions to adjust the data. Two-way interactions were not significant for the bass at either site, nor was length. Bass at each site were adjusted using a linear model which included only time and lipid as factors. The model fitting results (including p-values) are summarized in Table 1.
Trend analyses were done on adjusted PCB concentrations for each site-species combination, with estimated parameters, predictions, and confidence limits on the predictions given in Table 2. Plots of the data along with the fitted model and prediction intervals are given in Figure 1.
We tested log standardized residuals for normality and found that for both species at Lake Allegan and carp at Plainwell Impoundment, the data were significantly different than normal (p<0.005). The distribution of transformed residuals for smallmouth bass at Plainwell Impoundment was similar to a normal distribution (p>0.1). Probability plots are given in Figure 2.
The simulations to evaluate whether the asymptotic coverage probability using the generalized likelihood ratio resulted in coverage probabilities of 96% and 99% for Lake Allegan and Plainwell Impoundment carp datasets respectively. Coverage probabilities generated with the empirical distribution simulations were 99.8% and 99.7% for Lake Allegan and Plainwell Impoundment carp, respectively. The full procedure empirical simulations had coverage of 73.9% for Lake Allegan carp and 77.8% for Plainwell Impoundment carp. The simulation results are summarized in Table 3.