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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.

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