Why are two correlations significantly different to zero but not significantly different from one another?

Is it 'normal' to have two Pearson correlation coefficients which are statistically significant on their own but not when compared with each other.

Example

• r=.9083 (n=45) for females who buy ice-cream and yoghurt
• r=.8382 (n=60) for males who buy ice-crean and yoghurt

(The above correlation is between buying ice-cream and buying yoghurt for the two groups)

Based on the above, my interpretation is that both males and females who buy more ice-cream also tend to buy more yoghurt but there is no difference whether one group buys more or less than the other group.

• I notice this is the latest in a long list of questions that use correlation coefficients to assess relationships. Using correlation coefficients in this way is at best a weak approach and at worst it is wrong and misleading. Have you considered using more conventional analyses?
– whuber
Commented Sep 15, 2011 at 16:28
• @whuber Thanks. Could you point me to some methods. I don't have a statistical background, so I am going for the simplest approach (which may not be appropriate, as you point out). Commented Sep 15, 2011 at 20:25
• After all these questions, I still don't know, because I haven't been able to figure out what your data look like (you have referred to them elsewhere as "responses," but that's too vague) or what your objectives are. Why don't you open a new question where you briefly describe your project, your data, and what you want to learn, and then ask (a) what an analysis of Pearson correlations could accomplish and (b) what some simple, effective approaches might be.
– whuber
Commented Sep 15, 2011 at 20:48
• @whuber I will do this! Commented Sep 16, 2011 at 4:11