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

http://imgur.com/SBU4bUY

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up vote 5 down vote accepted

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.

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+1 for the effort. –  Zhubarb May 8 at 12:57
    
Digitizer looks like an interesting tool, thanks for pointer. –  conjectures May 8 at 13:44
    
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)? –  Mike May 8 at 15:37
    
@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. –  whuber May 8 at 15:45
    
@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/… –  O_Devinyak May 8 at 15:51

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