One of the most important points made in Chapter 9
concerns the interpretation of statistically significant correlations.
This point is so important that I'd like to reiterate it here.

On page 217, I've cautioned you that "many researchers
get carried away with the p-levels associated with their correlation
coefficients"
and that "discovering that a correlation coefficient is significant
may not really be very important--even if the results indicate p<.01
or
p<.001."
Such a result, I argued, "may be significant in a statistical sense
. . . but it may be quite insignificant in a practical sense."

Though you probably recall those statements (because
Chapter 9 is still "fresh" in your mind), do you remember
what was said at the end of Chapter 7? The final two paragraphs of
that early
chapter are worth considering once again.

Since you may not have our textbook handy, I'll type
here the final 10 sentences of Chapter 7. I highly recommend that you
carefully consider once again this important caution.

It is possible for a study to yield statistically
significant results even though there is a tiny difference between the
data and the null hypothesis. For example, in a recent study reported
in the Journal of Applied Psychology, the researcher
tested Ho: r
= 0 within the context of
a study dealing with correlation. After collecting and analyzing the sample
data, this null hypothesis was rejected, with the report indicating that
the result was "significant at the .001 level." The sample value
that produced this finding was -.03!

Even if the issue being investigated is crucial,
I cannot consider a correlation of -.03 to be very different in any
meaningful
way from the null value of 0. (With r = -.03, the proportion of explained
variance is equal to .0009!) As you will soon learn, a large sample
can
sometimes cause a trivial difference to end up being statistically significant--and
that is precisely what happened in the correlational study I am referring.
In that investigation, there were 21,644 individuals in the sample. Because
of the gigantic sample, a tiny correlation turned out to be statistically
significant. Although significant in a statistical sense, the r of -.03
was clearly insignificant in terms of its importance.