I recently used a self-designed survey tool to elicit perceived responses from a study population. I used the Chi-square goodness of fit test to show how the overall responses for each item on the scale differed from that for an expected standardized population. I was corrected by a colleague that a factor analysis should have been better statistical test. How is using a Chi-square goodness of fit test inferior in this regard and what is the advantage of doing a factor analysis?
The two are used for different purposes. It is necessary to know what your research goals/questions were in order to advise.
For survey-type psychometric data with a high risk of measurement error, using a measurement model in SEM IS a confirmatory factor analysis which allows you to test the extent to which your items load appropriately onto the factors (including estimates of error variance). CFA in SEM will give you various types of goodness of fit statistics of which model chi square (which is really a badness of fit measure) is NOT the most accurate as it is sensitive to both sample size and size of correlations...in SEM you need to take a failed chi square test very seriously, however, a "passed" test does not free you from looking at all the other goodness of fit indices to establish validity, reliability etc of your measurement model.
Hello Kenneth,
Some researchers call chi-square test (as a fit index) a test of "badness". It is a very crude test and as such should always be reported, and then usually ignored (as for example it is very sensitive to sample size - the more observations, the higher likelihood of obtaining sig value for chi-square). For more information I would recommend Tanaka paper from 1987.
Best wishes
It is better for you to rely on other fit indices, such as RMSEA and CFI, than rely solely on the chi-square value.
Article Fit Indices in Covariance Structure Modeling: Sensitivity to...
Thanks a lot everyone for your reply and especially Soon Li Lee for the article. It addressed my concerns and i am very happy you shared it with me. Bo Nielsen and Wirtold Orlik, i found your answers consistent with the article Lee shared. Orlik, i would be grateful if you can upload a link to the paper you talked about i.e by Tanaka. Thanks alot everyone.
Hello Kenneth,
Currently I am not able to get full text of this article. However, I provided a link below so hopefully through your library services you may obtain access.
Regards
http://psycnet.apa.org/psycinfo/1987-17621-001
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