The 'corrected' correlation for the inputs you gave is:


              
Please see the 'Explanation' tab for my health warning about this 'correction'.

            

            

              
This is ancient psychometrics but still of some use.  For more information, see:

              https://www.psyctc.org/psyctc/glossary2/attenuation-by-unreliability-of-measurement/
              
 

              
The formula is simple:

              
 

              $$correctedR = \frac{obsR}{\sqrt{rel_{x} * rel_{y}}}$$
              
              
The short summary is that unreliability in the measurement of both variables involved in a correlation always reduces the observed correlation between the variables from what it would have been had the variables been measured with no unreliability (which is essentially impossible for any self-report measures and pretty much any measures used in our fields.)

              
I am putting 'scare quotes' round 'corrected' throughout this app because I think it's important to be very cautious about this 'correction' as it can return a correlation above 1.0 where you have a reasonable observed correlation and low reliabilities and as for any observed correlation, the lower your reliabilities the higher the 'corrected' correlation which feels uncomfortable to me for all I see the logic!

            

            

              

                App created 13.x.24 by Chris Evans
                PSYCTC.org
              

              
Last updated 13.x.24.

              

                Licenced under a 
                Creative Commons, Attribution Licence-ShareAlike
                 Please respect that and put an acknowledgement and link back to here if re-using anything from here.
              

              


  
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