Page 12 - Statistics for Environmental Engineers

L1592_frame_CH-01 Page 3 Tuesday, December 18, 2001 1:39 PM

NATURE
True models
Define problem
True variables
True values
Hypothesis
Experiment
Design
experiment
Redefine hypothesis
Data
Redesign experiment
Data
Collect Analysis
more data
Deduction

Problem is not solved Problem is solved

FIGURE 1.1 Nature is viewed through the experimental window. Knowledge increases by iterating between experimental
design, data collection, and data analysis. In each cycle the engineer may formulate a new hypothessis, add or drop variables,
change experimental settings, and try new methods of data analysis.
Learning is an iterative process, the key elements of which are shown in Figure 1.1. The cycle begins
with expression of a working hypothesis, which is typically based on a priori knowledge about the
system. The hypothesis is usually stated in the form of a mathematical model that will be tuned to the
present application while at the same time being placed in jeopardy by experimental verification.
Whatever form the hypothesis takes, it must be probed and given every chance to fail as data become
available. Hypotheses that are not “put to the test” are like good intentions that are never implemented.
They remain hypothetical.
Learning progresses most rapidly when the experimental design is statistically sound. If it is poor, so
little will be learned that intelligent revision of the hypothesis and the data collection process may be
impossible. A statistically efficient design may literally let us learn more from eight well-planned exper-
imental trials than from 80 that are badly placed. Good designs usually involve studying several variables
simultaneously in a group of experimental runs (instead of changing one variable at a time). Iterating
between data collection and data analysis provides the opportunity for improving precision by shifting
emphasis to different variables, making repeated observations, and adjusting experimental conditions.
We strongly prefer working with experimental conditions that are statistically designed. It is compar-
atively easy to arrange designed experiments in the laboratory. Unfortunately, in studies of natural systems
and treatment facilities it may be impossible to manipulate the independent variables to create conditions
of special interest. A range of conditions can be observed only by spacing observations or field studies over
a long period of time, perhaps several years. We may need to use historical data to assess changes that
have occurred over time and often the available data were not collected with a view toward assessing
these changes. A related problem is not being able to replicate experimental conditions. These are huge
stumbling blocks and it is important for us to recognize how they block our path toward discovery of
the truth. Hopes for successfully extracting information from such historical data are not often fulfilled.

Special Problems

Introductory statistics courses commonly deal with linear models and assume that available data are
normally distributed and independent. There are some problems in environmental engineering where
these fundamental assumptions are satisfied. Often the data are not normally distributed, they are serially
or spatially correlated, or nonlinear models are needed (Berthouex et al., 1981; Hunter, 1977, 1980, 1982).
Some specific problems encountered in data acquisition and analysis are:

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