# Problem Coefficient of Variation and F-test

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Do not know if it is approp to ask this type of question…but any help would be appreciated.

1.  5 independent “factories” produce widgets and a rate of #of widgets per day (volume).

2.  The volume data for each individual factory is always positive; normally distributed; and not near zero.

3.  So for each factory i have a volume for 180 days; a mean and a SD.

4. Each factory has a different mean and SD. (some factories are big others are small).

I want to show that by combining the output from the 5 factories the relative day to day variation is reduced, e.g. on any given day factory 1 may be slow but factory 2 may be busy…by combining i “smooth out the variation”, e.g. if i put the output into one big pile…the relative day to day variation is less…

In a sense this may be a trivial result…but in my real world example i want to demonstrate it

Attempt #1:

I calculate the coeffient of variation for each factory and for the total.

Indeed the coeffience of variation is less for the total than for the individual sites.  This results holds pretty true for 6 different “widgets”.

Question:

Can I show this quantititively.  I know the f-statistic may be applicable in this instance.

I think i can compare the variation between individual factories…

but can I compare a single site to the total…my issues is that the individual factory data is part of the total…

attached is an example of the coefficient of variation data:

blue symbols are the factories.

each vertical column is a different “widget”…this graph holds multiple data sets on one graph

the red symbol is the is the CV for the total …

indeed the red is lower than the blue (for most widgets)

how can i investigate whether the red is truly lower than the blue…

is this graph good enough or can i get a p value…

for each widget, can do a single test that shows whether or not the red is lower than the blue for the group of 5 sites?

data.BMP

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