Statistics for Environmental Engineers

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3


For example, if y = xaz, a log transformation gives log y = a log x + b log z. Now the effects of factors x and z are additive. See Box et al. (1978) for an example of how this can be useful.


4


Six Sigma is the name for the statistical quality and productivity improvement programs used by such companies as Motorola, General Electric, Texas Instruments, Polaroid, and Allied Signal.


5


In Chapter 10, Shewhart charts were also called X (X-bar) charts and X was the notation used to indicate a measurement from a laboratory quality control setting. In all other parts of the book, we have used y to indicate the variable. Because the term F-bar chart is not in common use and we wish to use y instead of x, in this chapter we will call these X-bar charts Shewhart charts.


6


2 2 , 2 se vs. у used to estimate the parameters К and Ob.


7


   (12 — 11)7 + (10    — 11 )7 + (13 — 11 )7 + (9 — 11)7    10    =


8


1 Orthogonal means that the product of any two- column vectors is zero. For example, X3 • Xm = (—1)(-1) +——+ (+1)(+1) =


9


11 + 1 + 111 + 1 = 0.


10


Suppose that Method B measures 3.0 mg/L, which is 1.0986 on the log scale, and Method A measures 0.0477 less on the log scale, so it would give 1.0986 — 0.0477 = 1.0509. Transform this to the original metric by taking the antilog; exp(1.0509) = 2.86 mg/L. The difference 3.0 — 2.86 = 0.14, expressed as a percentage is 100(0.14/3.0) = 4.77%. This is the same as the effect of method (0.0477) on the log-scale that was computed in the analysis.

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