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Topic: M&M's -Reply
Replies: 2   Last Post: Sep 18, 1996 12:03 PM

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Timothy Brown

Posts: 42
Registered: 12/6/04
M&M's -Reply
Posted: Sep 18, 1996 8:59 AM
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Bob--
Thanks for clarifying why I have been getting more and more
uncomfortable about this M&M's thing. I had pretty much come to the
conclusion that it was a terrible fit the the Chi-Square G.O.F.
model, since you aren't sampling individual candies, but bags of
them.

Do you (does anybody?) have any other ideas for a hands-on
application of Chi-Square?

Tim

Bob Hayden's Message Text:

This only hides the problem. You will now get a lot more variability
than sampling theory would suggest. Despite their claims to the
contrary, Mars does not mix the candies thoroughly enough for them to
be considered a random sample from a fixed population. I think they
are great for demonstrating sampling variability (especially when
they exaggerate it!) but not for any inference procedure based on
random sampling, i.e., not for any inference procedure in an
introductory course.

Here's one intuitive way to think about the problem. If the bags
were random samples, the sampling distribution of the proportion of
tan M&Ms would be close to normal. Suppose they mix them so badly
that virtually every bag contian only one color. Then the sampling
distribution of the proportion of tan ones has spikes at 0% and 100%
and virtually nothing around the population proportion of tan M&Ms.
It will not have the variance or shape that sampling theory predict
(and use as the basis for inference).

To see how bad the problem is, open many bags of M&Ms and compare the
empirical and theoretical variance of the sampling distribution of the
proportion of each color. (I did it many years ago.)







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