boonlert wrote:
>
> Dear all
> The result of paired sample t-test analysis from SPSS shows both a
> significance(sig.) of paired sample correlation and a significance of paired
> sample test but they are opposite interpretation (one is <.05, one >.05).
> Could any one tell me why they are different and how should I
> interpret this result?
Let's reverse your question. Why would you expect them to be the same?
The two tests are quite different statistics, with different sampling
distributions, testing different research questions. The correlation
coefficient measures the strength of the association between the two
variables. The null hypothesis being tested is that the correlation
value, r, could have been drawn from a population of correlations with a
mean of zero and approximately normally distributed between -1 and +1.
The paired sample t-test tests an entirely different question: whether
the difference between the means of the two variables could have been
drawn from a distribution with a mean of zero.
There is no logical reason to expect these two statistical tests to
yield similar results. Two variable X and Y might be highly correlated
and therefore yield a significant result (p>.05) when looking up a table
of critical values of the correlation coefficient. However, X and Y
could have similar means, and the difference between them could be
non-significant (p<.05) when looking up tables of critical values of t.
The reverse is equally possible. X and Y might not be correlated at
all, yet have quite different means.
Hope this helps,
Paul Gardner
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