Statistics for Environmental Engineers

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A reference distribution for the difference between batches of 10 consecutive samples is needed. There are 111 differences of MA10 values that are 10 days apart that can be calculated from the data in Table 6.1. For example, the difference between the averages of the 10th and 20th batches is 6.81 — 6.76 =


0.05. The second value is the difference between the 11th and 21st is 6.74 — 6.80 = -0.06. Figure 6.4 is the reference distribution of the 111 differences of batches of 10 consecutive samples. A downward difference as large as -0.06 has occurred frequently. We conclude that the new condition is not different than the recent past.


Looking at the 10-day moving averages suggests that the stream pH may have changed. Looking at the differences in averages indicates that a noteworthy change has not occurred. Looking at the differences uses more information in the data record and gives a better indication of change.

Using a Reference Distribution for Monitoring


Treatment plant effluent standards and water quality criteria are usually defined in terms of 30-day averages and 7-day averages. The effluent data themselves typically have a lognormal distribution and are serially correlated. This makes it difficult to derive the statistical properties of the 30- and 7-day averages. Fortunately, if historical data are readily available at all treatment plants and we can construct external reference distributions, not only for 30- and 7-day averages, but also for any other statistics of interest.


The data in this example are effluent 5-day BOD measurements that have been made daily on 24-hour flow-weighted composite samples from an activated sludge treatment plant. We realize that BOD data are not timely for process control decisions, but they can be used to evaluate whether the plant has been performing at its normal level or whether effluent quality has changed. A more complete characterization of plant performance would include reference distributions for other variables, such as suspended solids, ammonia, and phosphorus.

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