Statistics for Environmental Engineers

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Statistics are numerical values that are calculated from imperfect observations. A statistic estimates a quantity that we need to know about but cannot observe directly. Using statistics should help us move toward the truth, but it cannot guarantee that we will reach it, nor will it tell us whether we have done so. It can help us make scientifically honest statements about the likelihood of certain hypotheses being true.

The Learning Process


Richard Feynman said (1995), “ The principle of science, the definition almost, is the following. The test of all knowledge is experiment. Experiment is the sole judge of scientific truth. But what is the course of knowledge? Where do the laws that are to be tested come from? Experiment itself helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations — to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment again to check whether we have made the right guess.”


An experiment is like a window through which we view nature (Box, 1974). Our view is never perfect. The observations that we make are distorted. The imperfections that are included in observations are “noise.” A statistically efficient design reveals the magnitude and characteristics of the noise. It increases the size and improves the clarity of the experimental window. Using a poor design is like seeing blurred shadows behind the window curtains or, even worse, like looking out the wrong window.

Redefine hypothesis Redesign experiment

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