# Statistics for Environmental Engineers

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Statistical procedures that rely directly on comparing means, such as t tests to compare two means and analysis of variance tests to compare several means, are robust to nonnormality but may be adversely affected by a lack of independence.

Hypothesis tests are useful methods of statistical inference but they are often unnecessarily complicated in making simple comparisons. Confidence intervals are statistically equivalent alternatives to hypothesis testing, and they are simple and straightforward. They give the interval (range) within which the population parameter value is expected to fall.

These basic concepts are discussed in any introductory statistics book (Devore, 2000; Johnson, 2000). A careful discussion of the material in this chapter, with special attention to the importance regarding normality and independence, is found in Chapters 2, 3, and 4 of Box et al. (1978).

### References

Box, G. E. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, New York, Wiley Interscience.

Devore, J. (2000). Probability and Statistics for Engineers, 5th ed., Duxbury.

Johnson, R. A. (2000). Probability and Statistics for Engineers, 6th ed., Englewood Cliffs, NJ, Prentice-Hall.

Taylor, J. K. (1987). Quality Assurance of Chemical Measurements, Chelsea, MI: Lewis Publishers, Inc. Watts, D. G. (1991). “Why Is Introductory Statistics Difficult to Learn? And What Can We Do to Make It Easier?” Am. Statistician, 45, 4, 290-291.

### Exercises

2.1    Concepts I. Define (a) population, (b) sample, and (c) random variable.

2.2    Concepts II. Define (a) random error, (b) noise, and (c) experimental error.

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