Statistics for Environmental Engineers

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The data were submitted (on computer tape) to an agency that intended to do a trend analysis to assess possible changes in water quality related to acid precipitation. The data were plotted before any regression analysis or time series modeling was begun. This plot was not expected to be useful in showing a trend because any trend would be small (subsequent analysis indicated that there was no trend). The purpose of plotting the data was to reveal any peculiarities in it.

Two features stand out: (1) the lowest pH values were observed in 1971-1974 and (2) the variation, which was large early in the series, decreased at about 150 weeks and seemed to decrease again at about 300 weeks. The second observation prompted the data analyst to ask two questions. Was there any natural phenomenon to explain this pattern of variability? Is there anything about the measurement process that could explain it? From this questioning, it was discovered that different instruments had been used to measure pH. The original pH meter was replaced at the beginning of 1974 with a more precise instrument, which was itself replaced by an improved model in 1976.

The change in variance over time influenced the subsequent data analysis. For example, if ordinary linear regression were used to assess the existence of a trend, the large variance in 1971-1973 would have given the early data more “weight” or “strength” in determining the position and slope of the trend line. This is not desirable because the latter data are the most precise.

Failure to plot the data initially might not have been fatal. The nonconstant variance might have been discovered later in the analysis, perhaps by plotting the residual errors (with respect to the average or to a fitted model), but by then considerable work would have been invested. However, this feature of the data might be overlooked because an analyst who does not start by plotting the data is not likely to make residual plots either. If the problem is overlooked, an improper conclusion is reported.

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