# Statistics for Environmental Engineers

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Organisms will be put into (1) an aquarium containing effluent or (2) a control aquarium containing clean water. Equal numbers of organisms are assigned randomly to the control and effluent groups. The experimental response is a binary measure: presence or absence of some characteristic. In an acute bioassay, the binary characteristic is survival or death of the organism. In a chronic bioassay, the organisms are exposed to nonlethal conditions and the measured response might be loss of equilibrium, breathing rate, loss of reproductive capacity, rate of weight gain, formation of neoplasms, etc.

In our example, 80 organisms (nj = n2 = 80) were exposed to each treatment condition (control and effluent) and toxicity was measured in terms of survival. The data shown in Table 19.1 were observed. Are the survival proportions in the two groups so different that we can state with a high degree of confidence that the two treatments truly differ in toxicity?

### The Binomial Model

The data from a binomial process consist of two discrete outcomes (binary). A test organism is either dead or alive after a given period of time. An effluent is either in compliance or it is not. In a given year, a river floods or it does not flood. The binomial probability distribution gives the probability of observing an event x times in a set of n trials (experiment). If the event is observed, the trial is said to be successful. Success in this statistical sense does not mean that the outcome is desirable. A success may be the death of an organism, failure of a machine, or violation of a regulation. It means success in

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