Example 8-6. After using a log transformation Montgomery examines the normal probabilty plot of the residuals and says: “This plot is suggestive of slightly heavier than normal tails, so possibly other transformations should be considered.”
The Box-Cox plot for Montgomery’s model (A, B, AD) suggests an inverse transform which seems to clear up all the residual plots and clarify the model. Give it try.
#1 by Mark on February 7, 2006 - 11:36 am
In 6th Ed I find the example on p308. It details a fractional two-level factorial experiment with a CNC machine that produces an impeller for a jet turbine. The response is standard deviation difference of actual vs specified profile. Given the nature of the response, Montgomery applies the log transformation (generally apropos for std dev). However, in Fig 8-20 he shows a normal plot of resids that exhibits “heavier than normal” tails suggesting an alternative transformation like the one Pat found helpful. His inverse produces a much better normal plot of resids. It really clarifies the model selection A,B, D, AD.
#2 by Wayne on February 8, 2006 - 8:57 am
In the absence of the ability to easily generate a Box/Cox plot. The rule I always used is when the appropriate transformation (log for standard deviation, square root for counts, etc.) still left undesirable residual diagnostics you simply moved up to the next stronger transformation. In general the hierarchy of transformations goes as follows: square root, log, inverse, positive power > 1, and finally negative power < -1.