Hello Allstatters
Sam Wilkinson wrote:
> Just a quick simple question probably with a similarly easy answer
> regarding the Chi-sqd. test for the two sample case.
> If I was looking at (say) comparing heights of children from different
> areas, and I obtained a Chi-sqd value using MILLIMETRES as my units, and
> then I used CENTIMETRES as my units, I would obtain two different
> Chi-sqd values (differing by a factor of 10).
> Therefore depending on the units I use, I could be in a situation where
> I can either accept of reject my null hypothesis.
This is the problem in converting from continuous to
discrete data for any goodness-of-fit test and may lead to different
conclusions to your hypothesis test. The more categories you create
the closer your discrete data is to the original data and there is
not much information lost. However a smaller number of
categories (eg changing from millimetres to centimetres, centimetres
to metres, and also to satisfy any assumptions your goodness-of-fit
test needs to make it valid) may make the goodness-of-fit test less
able to detect differences between observed and expected frequencies.
Also on the Chi-Square tests have a look at
http://faculty.vassar.edu/~lowry/chi_beta.html
for comments and simulations on the power of Chi-Square tests.
Michael Steele
Lecturer
Faculty of Environmental Sciences
Griffith University
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