Statistics for Environmental Engineers

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0.51


0.67


0.83


0.06


0.22


0.38


0.53


0.69


0.85


0.08


0.24


0.40


0.55


0.71


0.87


0.10


0.26


0.42


0.57


0.73


0.89


0.12


0.28


0.44


0.59


0.75


0.91


0.14


0.30


0.46


0.61


0.77


0.93


0.16


0.32


0.48


0.63


0.79


0.95

5.4 Wastewater Lead. What is the distribution of the influent lead and the effluent lead data in Exercise 3.7?

6

External Reference Distributions


KEY WORDS histogram, reference distribution, moving average, normal distribution, serial correlation, t distribution.


When data are analyzed to decide whether conditions are as they should be, or whether the level of some variable has changed, the fundamental strategy is to compare the current condition or level with an appropriate reference distribution. The reference distribution shows how things should be, or how they used to be. Sometimes an external reference distribution should be created, instead of simply using one of the well-known and nicely tabulated statistical reference distributions, such as the normal or t distribution. Most statistical methods that rely upon these distributions assume that the data are random, normally distributed, and independent. Many sets of environmental data violate these requirements.


A specially constructed reference distribution will not be based on assumptions about properties of the data that may not be true. It will be based on the data themselves, whatever their properties. If serial correlation or nonnormality affects the data, it will be incorporated into the external reference distribution.

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