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


From   "Maarten Buis" <M.Buis@fsw.vu.nl>
To   <statalist@hsphsun2.harvard.edu>
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 Spearmanīs 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

visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z214 

+31 20 5986715

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


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