Statistics for Environmental Engineers

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References


Box, G. E. P. and D. R. Cox (1964). “An Analysis of Transformations,” J. Royal Stat. Soc., Series B, 26, 211. 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.


Elliot, J. (1977). Some Methods for the Statistical Analysis of Samples of Benthic Invertebrates, 2nd ed., Ambleside, England, Freshwater Biological Association.


Gilbert, R. O. (1987). Statistical Methods for Environmental Pollution Monitoring, New York, Van Nostrand Reinhold.


Land, C. E. (1975). “Tables of Confidence Limits for Linear Functions of the Normal Mean and Variance,” in Selected Tables in Mathematical Statistics, Vol. III, Am. Math. Soc., Providence, RI, 358-419. Landwehr, J. M. (1978). “Some Properties of the Geometric Mean and its Use in Water Quality Standards,” Water Resources Res., 14, 467-473.

Exercises


7.1    Plankton Counts. Transform the plankton data in Table 7.2 using a square root transformation x = sqrt( y) and a logarithmic transformation x = log( y) and compare the results with those shown in Figure 7.3.


7.2    Lead in Soil. Examine the distribution of the 36 measurements of lead (mg/kg) in soil and recommend a transformation that will make the data nearly symmetrical and normal.


7.6    32    5 4.2 14    18    2.3 52    10    3.3 38    3.4    4.3    0.10 5.7    0.10 0.10 4.4


0.42    0.10 16 2.0    12 0.10 3.2    0.43    1.4 5.9    0.23 0.10 0.10 0.23 0.29 5.3    2.0    1.0


7.3 Box-Cox Transformation. Use the Box-Cox power function to find a suitable value of Я to transform the 48 lead measurements given below. Note: All < MDL values were replaced by 0.05.

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