1. the correlation is 0.3. that's not a high number.2. the correlation for facebook likes is 0.27. that's lower, but not by much.3. its possible the causality runs the other direction: high quality results get more +1s

 Yup, I love that the correlation for "Facebook shares, like, comments" (though those are three different things) is listed as 0.03 less, even though I've pointed out multiple times that Facebook doesn't exactly make it easy for Google to crawl Facebook to see that data.Your point #3 is critical: high quality things get more +1s (and tweets, and Facebook likes or comments or shares).
 Indeed, it's a little embarrassing. The tenuous conclusions reached based on correlation in the SEO industry are out of control. It should not be surprising that any metric of popularity (+1s, shares) will have some sort of correlation to another metric of popularity (links, brand searches?, editorial coverage, etc.) that Google might use in rankings.
 Correct me if I'm wrong, but isn't anything under .5 considered extremely weak correlation?
 The short answer is, "no, but it depends." If sample size is large and the sample is representative of what it claims to show, .5 is very significant correlation.The .3 correlation with a large sample size means something is happening. I agree with what Matt is saying: that content that gets +1s also gets links and mentions and everything else that Google might use to calculate rankings.
 The pearson correlation, when squared, gives the % of variance (in the strict mathematical sense) that is explained by this variable alone.So how much is 'weak' or not depends on the situation. If you have something that is influenced by multiple causes, then it is impossible to have any single high correlation. But any correlation, if statistically significant (i.e. highly unlikely to be caused by chance) can be important.The question is, how much is an 'interesting' amount of the total variance, in the given situation.(In the topic under discussion here, I have no idea.)
 Maybe rephrase "high quality things get more +1s" to "high ranking results get more +1s because they're found more often than low ranking results"This brings up the interesting question of why other social media is used less for promotion of effective pages. More zombie / spammers / scammers / PR firms manipulating facebook likes than +1s? This seems extremely likely given the known "underground" like-market and incentives WRT FB.
 I Like number 3. I think there's two ways this works: 1) Killer content is created and social shares quickly give signals of freshness and quality within an area. Combine that with early user metrics as the content moves up and you have a good idea of it's quality. However, if this content is not soon backed with corresponding signals (links, etc.) the ranking can fade. This is likely dependent on the industry and topic as to how it plays out.The other possibility is a good piece of content earns links, has great user metrics for certain keywords, lives on a great site, etc. and ranks well. It then accumulates social shares on top of that, further confirming the quality of the content. Thus...you get a situation like #3. Social signals make sense for indexation, but beyond that, until you start to understand the importance of the author (cough, AuthorRank, cough) then you can't use them for much more then understanding what the "mob" is finding valuable at the moment. And it might be a very fleeting fascination on a subject that really doesn't deserve to hold a ranking.
 Yes, at university they thought us that this is what you'd refer to as a "weak correlation".

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