Henry E. Schaffer said:
In articles various people say things like:
By the way, values of 0.48 and 0.45 are REALLY BAD.
and then argue over whether these are or should be publishable, etc.
In summary --- AARRGH! A correlation, in itself, is neither good/bad
nor publishable/unpublishable. One needs to know the "significance
level" and/or such extra information such as the design/size of
the experiment/survey yielding the correlation. One also needs to
know what is being claimed for the correlation (in terms of explanatory
or descriptive power) as to get some insight into the reaction of a
reviewer/editor.
You're spoiling all the fun! I wanted to see if he had learnt
enough in his stats classes to ask about the significance of the
results. Seriously, though, the statistical significance of Pearson's
r is somewhat problematical. We can work out the probability of
getting a value as large in magnitude if we had two independent normal
distributions. For the two cited correlations this probability is
about 0.1 (i.e borderline significance). But it seems unlikely that
gun ownership across nations is a normally distributed random
variable. After all, if I don't exclude outliers, the correlation
between handgun ownership and homicide is 0.73 with p=0.003.
I think it better to use Spearman's rank correlation coefficient to
test for significance.
For handguns vs homicide I get 0.38, p=0.18 (ie not significant)
For all guns vs homicide I get 0.7, p=0.02 (significant)