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Paint manufacturer Color in a Can, with its evasive
quality manager, Walker Runn, is about to discover the pot of SPC
at the end of its rainbow.
Walker Runn, caught in a significant statistical error, was put on the sidelines, so to speak. His instructions were to take some time to learn a little more about statistical process control, and the perfect teacher was none other than Dan Druff, the vice president who uncovered Walker's incompetence in the first place. Dan Druff is himself a highly skilled statistician, though he's known to be a little flaky, and Walker has been following him around to learn enough to keep his job.
After several months of this apprenticeship, Dan
has given Walker a chance to demonstrate what he’s learned
by producing an analysis of variance (ANOVA) based on the output
of three Color in a Can plants.
The data related to his output is as follows:
"Aha," Walker says, realizing that even without
full understanding, he can simply enter the data into an easy-to-use
software program, DOEpack
EZ, for the calculations, then slip it into a PowerPoint
presentation he is preparing for Dan Druff's review.
Dan goes over the ANOVA analysis, reviewing for
Walker what he had learned from his disastrous hypothesis testing
assumptions last month. He wants to be sure that Walker understand
hypothesis testing as well as ANOVA, so he begins to question him
about the F value of 4.114 that is indicated on the ANOVA
"F" stands for 'facilities,'" Walker asserts confidently,
sure that the chart is self-explanatory and bears no deep statistical
secrets. Color in a Can has three facilities, or F's, he
continues. It's clear that this can't be the correct response, and
no doubt Walker Runn better walk or run to the nearest employment
agency after this debacle. But can you define F value?
Pick the correct response from the two given:
a) F value
refers to the ratio of variation between samples to the variation
b) F value
refers to the spread in the control limits for the data that is
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