how to interprete correlation coefficient

[Wang Xu-4]

Dear list members,

I s there any hands-on rules to interpret correlation coefficent? How can we categorize the diffeernces between the correlation coefficients as weak, medium and strong association? Thanks a lot for your litertature pointers and advice!

 

 

Wang Xu

[Kelly Vander Ley]

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[statisticsdoc]

Dear Wang,
The square of the correlation coefficient indicates the percentage of variance that is shared between two variables,  Jacob Cohen issued some general suggestions about the magnitude of effect sizes in correlational research that should be regarded as weak, medium, and large, although this approach to correlations has been criticized as treating effect sizes too generally.  The interpretation of an effect size is dependent on the literature that your work in embedded in, and the utility of certain effect sizes.  For example, David Funder has published a few papers in the field of personality psychology that illustrate the point that a correlation of .3 (commonly regarded as a quite modest correlation coefficient) can in certain contexts be very useful, if there is substantial value in accounting for even 9 percent of the variance in an outcome.  A correlation of .5 might seem quite substantial in some contexts, but it should worry you if the measures in question are supposed !
 to be parallel measures of the same cognitive skills used to make high-stakes decisions about an individual.
HTH,
Steve Brand
www.StatisticsDoc.com

---- dachengruoque <[hidden email]> wrote:
> Dear list members,
> I s there any hands-on rules to interpret correlation coefficent? How can we categorize the diffeernces between the correlation coefficients as weak, medium and strong association? Thanks a lot for your litertature pointers and advice!
>
>
> Wang Xu

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[Mike]

Just to follow up on a couple of points:

(1) Steve Brand below refers to Jack Cohen's criteria for evaluating
the size of a correlation coefficient which Jack usually presented in the
context of statistical power analysis.  One can refer to Jack's text on
power analysis or take a look at the following article:

Cohen, J. (1992).  A power primer. Psychological Bulletin, 112(1),
155-159.

The article is available through a number of sources, including copies
that some folks have on their website; see"
http://www.idi.ntnu.no/grupper/su/publ/ese/cohen-powerprimer92.pdf

The main idea is that of effect size (which can be represented by different
statistics) is critical in power analysis as well as meta-analysis.  Jack's
early work on the statistical power of published research led him to
suggest somewhat arbitrary guidelines but at least one could use such
standards in representing the effect size that a specific level of power
could detect (in addition to other isses).  Meta-analytic studies in an area
should provide a more refined set of values as guides.

(2)  As Brand mentions below, the interpretation of an effect size
has to be made in the context of the research and theory of an area.
If strong theories in an area imply that there should be no correlation
between certain variables, then the existence of any correlation, no
matter how small, are important because their existence (if replicated)
flasify the theory or at the very least identify critical flaws in the theory
that need to be addressed.  Knowing the research in an area is the
only sure guide for interpreting the magnitude as well as the importance
of a statistical result.

(3)  For those with www.jstor.org access, it might useful to take a
look at the following article which provides some of the history of the
Pearson r as well as 13 different interpretations of what a Pearson r
can mean:

  a.. Thirteen Ways to Look at the Correlation Coefficient
  b.. Joseph Lee Rodgers and W. Alan Nicewander
  c.. The American Statistician, Vol. 42, No. 1 (Feb., 1988), pp. 59-66
  (article consists of 8 pages)
  d.. Published by: American Statistical Association
  e.. Stable URL: http://www.jstor.org/stable/2685263
-Mike Palij
New York University
[hidden email]



----- Original Message -----
From: "Statisticsdoc Consulting" <[hidden email]>
To: <[hidden email]>
Sent: Sunday, April 18, 2010 11:49 PM
Subject: Re: how to interprete correlation coefficient


> Dear Wang,
> The square of the correlation coefficient indicates the percentage of variance that is shared between two variables,  Jacob Cohen issued some general suggestions about the magnitude of effect sizes in correlational research that should be regarded as weak, medium, and large, although this approach to correlations has been criticized as treating effect sizes too generally.  The interpretation of an effect size is dependent on the literature that your work in embedded in, and the utility of certain effect sizes.  For example, David Funder has published a few papers in the field of personality psychology that illustrate the point that a correlation of .3 (commonly regarded as a quite modest correlation coefficient) can in certain contexts be very useful, if there is substantial value in accounting for even 9 percent of the variance in an outcome.  A correlation of .5 might seem quite substantial in some contexts, but it should worry you if the measures in question are suppose!
 d !

> to be parallel measures of the same cognitive skills used to make high-stakes decisions about an individual.
> HTH,
> Steve Brand
> www.StatisticsDoc.com
>
> ---- dachengruoque <[hidden email]> wrote:
>> Dear list members,
>> I s there any hands-on rules to interpret correlation coefficent? How can we categorize the diffeernces between the correlation coefficients as weak, medium and strong association? Thanks a lot for your litertature pointers and advice!
>>
>>
>> Wang Xu
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
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[James Whanger]

See the following for alternative arguments about the appropriateness of interpreting r versus r-squared:

Ozer, D. J. (1985). Correlation and the coefficient of determination. Psychological Bulletin, 97, 307-315.

D'Andrade & Dart (2003). The interpretation of r versus r-squared. The Journal of Quantitative Anthropology, 2, 47-59.

2010/4/18 dachengruoque <[hidden email]>

Dear list members,

I s there any hands-on rules to interpret correlation coefficent? How can we categorize the diffeernces between the correlation coefficients as weak, medium and strong association? Thanks a lot for your litertature pointers and advice!

 

 

Wang Xu