Voltolini,
You have described the outcome of a small naturally-occurring experiment.
The important question is: what did your friend expect? You see, when you
submit these frequencies to a chi-square test, you are testing the "goodness
of fit" of the results to a particular theoretical model. In many cases,
the "expected frequencies" are those that would result from chance. For
example, the "default" chi-square test would compare the obtained
frequencies of 1 and 19 to a model of equal cell frequencies of 10 and 10.
However, this might not be a realistic random model in this case. Do you
know, on average, how often people show up for this sort of follow-up
medical treatment in this area? If so, then this information could help you
set up an appropriated set of expected frequencies, and then you could test
to see if the observed frequencies deviated significantly from these
expected frequencies.
In this case, the chi-square test and the one-sample test of proportion will
yield the same results (the Z will be equal to the square root of the
chi-square statistic). I think it would be conceptually more clear to use
the goodness-of-fit (chi square) test on the frequencies.
One more point. This sample is really too small for serious analysis and
interpretation. Most sources suggest that the chi-square statistic be
applied only when there is a frequency of at least 10 in each cell. If the
results of this analysis turn out to be interesting, your friend should
collect a larger sample of data and attempt to replicate the findings.
Best wishes.
Victor
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Victor L. Bissonnette
Charter School of Education and Human Sciences
Berry College
P.O. Box 495019
Mt. Berry, GA 30149-5019
(706) 290-2154
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----- Original Message -----
From: "Voltolini" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Monday, July 02, 2001 8:54 PM
Subject: advice in analizing small samples
Hi, a friend of mine are studying a desease (Tetano) and testing a
vaccine taken by patients twice but ... he is interested in to
investigate if people are returning to the hospital for the second dose.
In a pilot experiment, from 20 patients, only one had returned for the
second and last dose. The question is... how to test this ?
I was thinking in to use a test for independent proportions (1/20 and
19/20) but some friends are suggesting a chi-square test !
Any suggestions ?
Thanks,
Voltolini
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