    # st: RE: interpreting the significance level of spearmans rank correlation

 From "Maarten Buis" To Subject st: RE: interpreting the significance level of spearmans rank correlation Date Thu, 1 Jun 2006 17:45:37 +0200

```---Patric Mayer wrote:
> I have a question concerning the level of significance
> of Spearman´s rank correlation test. the calculated
> rank correlation ("rho") is 0.8804. the star indicates
> that this 0.8804 is significant at the 5% level
> (probability of error), right?
>
> however, the shown "Sig.level" value indicates 0.0000.
> so, what does this 0.0000 mean exactly? tells it that
> the probability of error is not only 5% but instead 0%?
> is this a good result?

The 5% is the type I error rate, the probability of
rejecting the null hypothesis when the null hypothesis
is actually true. It is not a number you calculate
from the data, it is a number you choose. In some
statistics books this is confusingly called the
significance level, but it is not the "Sig.level".
If you are thinking in terms of error rates than the
"Sig.level" is nothing more but a statistic, which
you can compare with the type I error rate you have
chosen, say 5%. The only interpretation you can than
give to this number is that if it is less than 5% you
reject the null hypothesis and otherwise you do not
reject.

A significant correlation means that you rejected the
null hypothesis that the correlation is zero. In this
case a "Sig.level" of .049 is no "better" than .00000.
A correlation is either significant or it is not, and
there is no middle ground.

This way of testing can be seen as a procedure for
choosing between two competing statements about that
correlation: it is zero, or it is not zero. The type
I error rate tells you something about the quality of
the procedure you used in making that decision: You
will incorrectly state that the  correlation is not
zero in 5% of the times that you use this procedure
(draw a random sample, compute "sig.level" and choose
to reject when "sig.level" is less than .05) This is
the Neyman-Pearson approach to statistical testing.

There does exist an alternative approach to
statistical testing, which states that "Sig.level"
is the probability of drawing a sample with the
observed correlation if the null hypothesis is true.
If that probability is smaller than some level you
have chosen beforehand (say 5%) than you are so
surprised that you will reconsider your original
believe in the null hypothesis. Hence this number
is sometimes called the degree of surprise. This
is the Fisher approach to statistical testing.

Note that Neyman-Pearson approach and Fisher
approach will both lead to the same conclusion.

HTH,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z214

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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