Q:

Magnitude of a relationship

If I run Pearson correlation between Variable A (buyer/nonbuyer of ice-cream) and Variable B (buyer/nonbuyer of yoghurt) and have: 

Ho as "There is no relationship between...."
Ha as "There is a strong relationship..."

then what would "strong" mean in this context? 
Is the meaning of "strong" dependent on the context of my study or are there some guidelines on what is strong (as opposed to - I presume - "weak" or "average").
Is this something to do with "one-tail" and "two-tail" testing?

A:

An r of 0.822 means that the linear relationship between x and y accounts for $0.822^2 = 0.68$ or 68% of the variance in y. 
Is this strong? In some fields (e.g. psychology), it would be amazingly strong. In others (e.g. some aspects of physics) it would be disappointingly weak. 
The p < .001 means that, if, in the population from which this sample was drawn the true r was 0, then it is very unlikely that, in a sample the size of yours, you would get an r this high or higher. 

A:

It absolutely depends on context.  With pharmaceuticals, if use/non-use of a heart medicine is correlated at -.1 with occurrence/non-occurence of heart failure, this could save many lives and earn a drug maker millions of dollars.  In contrast, in educational testing, if SAT - Critical Reading score is not correlated at at least .65 with SAT - Math score in a large population, people will get very suspicious that something is wrong with the tests, which are important for many admissions and placement decisions and are huge money-makers in that industry.
Also, it is not uncommon to test an hypothesis that an r is at least, say, .4, that is, not necessarily a tiny value.

