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Dear all,

There was an extended discussion on this list about fit indices and model

From this discussion  I memorized that chi-square test is the first and
most important test, and everybody seem to agree with that (although there
are some disagreement regarding usefulness of other fit indices).

Please help me interpret the following sentence:
 "The chi-square test again did not indicate an especially good fit in any
of the countries [chi-square p-value=0 for all the models].  However, the
other indices that were used indicated a good fit between model and data.
CFI was ranging from 0.977 to 0.997 and RMSEA from 0.024 to 0.062.   As the
indices of model fit did not differ much between the measurement model and
the structural model, the latter can be considered to offer a good
representation of relationships between variables."  ( Myrberg &  Rosén
(2008): A path model with mediating factors of parents' education on
students' reading achievement in seven countries, Educational Research and
Evaluation, 14:6, 507-520

Someone outside this list explained to me that In large samples  p-values
are often significant, expecially  when sample sizes reach the thousands --
then everything becomes significant.  In the paper I mention sample sized
are definitely very large , from 3500 to 6000.

I wonder why nobody in the discussion on the chi-square and other fit
indices never mentioned the relationship between p-values and sample size?
And does it mean that SEM is not applicable to very large samples?

Indeed, most of the sample sizes people mention  when asking practical
questions on this list are in the range of 100-400.

Could anyone give a reference where SEM was used on a very large sample
(several thousands)?


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