Statistics for Environmental Engineers

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Estimated effects

1979 ban

1982 ban lift

Variances (log scale) ARIMA model parameter

<5 = -3353 ± 1201 lb/day O? = 0.006440 в = 0.64

5 = +1239 ± 959 lb/day ol = 0.001312

Month (Month 1 — January 1975)

FIGURE 54.3 Estimated effects of the interventions and the model (solid line) fitted to the data.

involved on the original scale. For the 1979 ban, this is 10.6% of (13,141 x 9788)и = 1200 lb/day. For the 1982 ban lifting, 10.6% of (8457 x 9696)1/2 = 960.

Based on the estimated shifts, phosphorus-based laundry detergents contributed about 25% of the influent P load prior to the ban and 13% after the ban was lifted. The post-ban shift is smaller because detergent products that reentered the market contained less phosphorus than those that were banned.

The weighting factor of the model was estimated to be в = 0.64. The weights used to estimate the pre-ban and post-ban averages and decay away from the intervention were as follows: 0.640, 0.230, 0.083, 0.03, etc., reducing each month by the factor 1 — в = 0.36. The first 3 months on either side of the gap account for more than 95% of the estimated value of the weighted average. This is why the level after the ban was lifted could be estimated so precisely (a2 = 0.002326), although the November 1982 level was estimated using only nine observations.

Having noted that relatively few observations actually entered into the estimated effect of an intervention, it is equally important to make clear that a fairly long record is necessary for computing reliable estimates of в, o’], and ol.

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