I think more can be said.
1. I suppose that Stas' implication is that Spearman rank correlation is
not a parameter in a model or distribution, but even so I don't see much
(informal) difficulty in regarding sample rank correlation as an
estimate of population rank correlation. As Roger Newson likes to point
out, other rank correlations have clear interpretations as differences
between probabilities and inference is also straightforward.
2. Spearman rank correlation may be regarded as a measure of
monotonicity of relationship just as Pearson rank correlation is a
measure of linearity of relationship. So, they are answers to different
questions.
3. Most books on nonparametric statistics carry accounts of rank
correlation. I also recommend Harold Jeffreys, "Theory of Probability",
Oxford University Press 1961, for a very good non-standard account. (The
book title is not an accurate guide to the contents.)
4. Inferences with Spearman rank correlation do depend on mutual
independence of observations.
5. Asymptotics are for the birds on the horizon.
Nick
[email protected]
Stas Kolenikov
Inference for Pearson's moment correlation relies on normality of the
data. Spearman rank correlation is free of any assumptions, but there
is no population characteristic that it estimates, which makes
interpretation and asymptotic inference somewhat weird. If one is
significant and the other is not, you are making either type I or type
II error somewhere.
On 10/6/09, Ashwin Ananthakrishnan <[email protected]> wrote:
> In examining the correlation between two variables, what is the
difference in utility of the Spearman correlation co-efficient (stata
command 'spearman') and the Pearson correlation co-efficient (stata
command "pwcorr" or "correlate")?
>
> Is there a situation where one is more applicable than the other?
What does it mean if the correlation is significant with one but not the
other?
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