In this graph, how strong (if any) is the correlation? The image is from a presentation of another speaker (source: http://imgur.com/SBU4bUY).



1 Answer 1


To answer this question we need to extract numbers with some plot digitizer and then compute correlation coefficient. I've used Engauge Digitizer and get answer r=-0.43. Such value is treated as moderate correlation in social sciences and as low correlation in nature sciences.

  • $\begingroup$ Digitizer looks like an interesting tool, thanks for pointer. $\endgroup$ May 8, 2014 at 13:44
  • $\begingroup$ Thanks a lot! I thought there might also be a method of calculating the angle of the line (given both ends, as of course the scales are not to scale). Isn't -0.43 treated as weak even in social sciences? E.g. Dancey and Reidy (2004) and also Salkin categorise as follows: 0.9 - 1 Very strong 0.7 - 0.89 Strong 0.5 - 0.69 Moderate Isn't it also that a correlation of .7 explains only 50% of your data, and so on (I read somewhere that the correlation coefficient squared times 100 yields the percentage of data explained by the hypothesis)? $\endgroup$
    – Mike
    May 8, 2014 at 15:37
  • $\begingroup$ @Mike The angle of the line has meaning provided the aspect ratio is 1:1. Specifically, the two scales have to be stretched so that one standard deviation on each has the same length. When any scatterplot is redrawn in this way, with a little practice one can estimate the correlation by eye reasonably well (reliably distinguishing absolute correlations of 0, .3, .5, .7, and .9). This is a basic skill; for resources in learning it, please visit causeweb.org/cwis/SPT--BrowseResources.php?ParentId=41. $\endgroup$
    – whuber
    May 8, 2014 at 15:45
  • $\begingroup$ @Mike The strength of correlation score is rather the matter of personal taste. You may see also this tables strath.ac.uk/aer/materials/4dataanalysisineducationalresearch/… $\endgroup$
    – O_Devinyak
    May 8, 2014 at 15:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.