Chapter 9, Problem 9.109CTC

Pollutants at a housing development. Polycyclic aromatic hydrocarbons (PAHs)—formed during the incomplete burning of oil. gas. or coal—are considered to be potential dangerous pollutants by the Environmental Protection Agency (EPA). Consider' an actual developer who purchased a large parcel of land in Florida that he planned to turn into a residential community. Because the parcel turned out to have significant deposits of PAHs, the developer was required to remove these pollutants from the site prior to commencing development. The clean-up was completed, but the housing bubble burst and the development was a bust. The developer blamed the failure of his plan on the discovery of the pollutants, and filed suit against two industries (named Industry A and B) that were within 25 miles of the site. Although both industries produced PAH waste materials as part of their industrial processes, both denied responsibility for the pollution. Experts were hired to investigate the decree of similarity between pollutants at the industrial sites and these at the development site. Soil specimens were collected at each of four locations: 7 at the housing development site, 6 at Industry A, 5 at Industry B, and 2 at Industry C. Two different molecular diagnostic ratios for measuring the level of PAH in soil were determined for each soil specimen. These data are displayed in the accompanying table.

a. A biochemical expert hired by Industry A chose to analyze the data using a series of t-tests for comparing two means. That is, he conducted a two-sample t-test (Section 8.2 ) using α = .05 for each possible pair of sites: Industry A vs. Industry B, Industry A vs. Industry C, Industry A vs. Development, Industry B vs. Industry C. Industry E vs. Development, and Industry C vs. Development. The results of these 6 t-tests for the second PAH ratio variable led the expert to conclude that (1) mean PAH2 ratio at the development site is statistically different from the corresponding mean at Industry A and (2) the mean PAH2 ratio at the development site is not statistically different from the corresponding mean at Industry B. Use the data in the PAH file to replicate these results.

b. The inferences derived in part a led the expert to argue that the source of the PAH contamination at the housing development site is more likely to have been derived from Industry A than from Industry B. A statistician, hired to rebut this testimony, argued that the analysis (and subsequent inference) was flawed. Explain why. multiple t-tests; inflated Type I error rate

c. Propose a better, more statistically valid, method of analyzing the data. Conduct this analysis for both dependent variables. PAH Ratio 1 and PAH Ratio 2. What do you conclude? Run ANOVA

d. According to the statistician s court testimony, “the results provide clear evidence that these samples are simply too small to make a reliable determination about the sites' similarity or dissimilarity with aspect to [PAH] diagnostic ratios.” The statistician went on to conclude that “the small samples relied upon by [the biochemical expert] shed to light on the issue of whether [Industry A and Industry B] are similar or dissimilar to the [development] site” Do you agree? [Concluding Note: The trial judge ultimate y decided that the biochemist’s statistical analyses and his opinions based on them would be excluded from the evidence used to decide the case. As of this date, the issue of responsibility for the pollution has still not been decided ]