Influence of spatial autocorrelation on a fixed-effect model used to evaluate treatment of oil spills

Abstract

A study was conducted during 1989 by the EPA to evaluate the effectiveness of two methods of nitrogen fertilizer application to treat the Exxon oil spill on beaches of Alaska. The current study, using the data, was to determine the spatial relationship of oil residue on these beaches and to evaluate the influence of spatial autocorrelation on the power of a fixed-effect model used by EPA investigators. The distribution of residual dry weight (mg oil residue/kg of beach material), was found to be spatially independent on individual beaches and for individual sampling times. The presence of spatial autocorrelation resulted in an overestimation of treatment means and an underestimation of their respective standard errors. In turn, an increase in the significance of differences in individual treatments and in the power of the test resulted. A spatial autoregressive model was used to correct for the presence of spatially autocorrelated residuals and the model was used to obtain the best linear unbiased estimates of parameters. Analysis of variance showed that oil residue concentration was significantly higher on the control beach (Raven Beach) than on either of the beaches fertilized with two different nitrogen treatment applications (Kittiwake Beach or Tern Beach). These results also showed that the two fertilizer treatments reduced the concentration of oil residue significantly faster than would have occurred without treatment. The power of the experimental design, a randomized block design used by the EPA, adequately detected significant differences among treatments. A fixed-effect model was used to analyze the data. Furthermore, the current study also found that increasing the sampling intensity or replicating the experimental design could have decreased the power of the test because of the presence of spatially autocorrelated data. In general, the power of the fixed-effect model for the design to detect a significant difference among treatments increased over time. In contrast, the power of the fixed-effect model to detect a specified difference across all times decreased over time because of decreases in means and their associated standard errors.