# Re: st: Chi-Square?

 From Marcello Pagano To statalist@hsphsun2.harvard.edu Subject Re: st: Chi-Square? Date Sat, 08 Jul 2006 14:08:09 -0400

Another question to ask is, how was that category chosen? If it was chosen ex post as the one providing the largest difference, then you need to look at the distribution of the largest; a different distribution from the normal chi-squared distribution. If it was chosen a priori and this is the only one you wish to test, then that is a different story.

m.p.

Maarten buis wrote:

--- Janelle Knox <babeerage@gmail.com> wrote:

I have a variable that asks whether retirement income is
less than expected and has five options(more, less, same, not sure,
etc). Is there a way to test whether one of the options (in this
case-2) retirement is less than expected) is significantly higher
than the variable mean? So of 2500 respondants 1700 suggest that
retirement is less than expected. How do I test if this is
signficant?
Significant means that you reject the null hypothesis, so you need a
nul hypothsesis. I read you line "Is there a way to test whether one of
the options (in this case-2) retirement is less than expected) is
significantly higher than the variable mean?" as meaning that your null
hypothesis is that you think that all categories receive the same
proportion of respondents, so each category should receive 500 cases.
Given the large deviation of the actual value (1700) and the sample
size I would be very surprised if you can not reject the null
hypothesis. That is not surprising since it is not a very reasonable
null hypothsis, I see no reason why such likert-like items would be
uniformly distributed. So rejecting that hypothesis is not very
informative and you might want to think up a more meaningful
hypothesis.
You can test it with a chi square test, remeber that the formula is
sum((O-E)^2/E), O is the observed value, E is the expected value. In
Stata you can type:
di (1700-500)^2/500 + (800-2000)^2/2000
which results in 3600, with in this case one degree of freedom. As
expected this is significant for any reasonable significance level.

HTH,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z214

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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