Re: chi-squared test. hypothesis confusion

eblabac@xxxxxxxxxxxxxxxxxxx wrote: 
This is a common question when starting to do hypothesis testing. Your
tests H0 is smoking and allergy are statistically independant, and Ha
is smoking and allergy are not independant. From your notes you have a
decision rule associated with this chisq test. You reject H0 if your
test statistic chi^2 >= chi^2 alpha (where chi^2 alpha, (r-1)(k-1) is
found in a table or generated from a program depending on your level of
alpha and r and k). Simply find the chi^2 alpha value from a table (in
any stat book), then calculate the chi^2 statistic using your data.
Then follow the rule ... if chi^2 >= chi^2 alpha  - reject Ho, i.e.
smoking and allergy are NOT independant, if chi^2 <  chi^2 alpha you
dont accept Ha, you "fail to reject H0", i.e. smoking and allergy are
independant. Its as easy as that. However, make sure your data
satisfies any assumptions of the test. This particular test has very
flexible assumptions, in that you only need your observations to be
independant of each other and that each cell of your 2x2 table is
greater than 0 (preferably bigger than 5, otherwise you could get
skewed results).
Hope that helps.

Eric B.


It is the expected frequencies, not observed, that need to be equal to 5 or more for a 2x2 chi-square. Here is a summary of the conditions under which chi-square tests perform reasonably well.

  www.angelfire.com/wv/bwhomedir/notes/chi_square_assumptions.txt

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

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