# Statistics for Environmental Engineers

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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.

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.

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.

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

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

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

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11 + 1 + 111 + 1 = 0.

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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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