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I am trying (operative word) to validate a scale composed of two highly correlated (~.7) subscales, let's call them A and B. In order to establish convergent validity with other measures, I am looking at a lot of correlations. Because the subscales are highly correlated, I am looking at partial correlations (i.e., correlation between A and X controlling for B; and B and X controlling for A) in addition to zero-order correlations between each of the measures and each of the subscales.

Here's my question: For one measure, the Satisfaction with Life Scale (SWLS), zero-order correlations (i.e., between SWLS and A and SWLS and B) are both positive and moderate, whereas partial correlations are null and weak, respectively.

How do I interpret this? I'm wondering because it would be very interesting to me to discover that neither A nor B is alone sufficient for predicting SWL-- that instead you need both. In other words, that the whole is more than the sum of its parts. Is that anything close to what it means, and if not, what does it mean? I've tried searching the internet but haven't come up with anything, so now I'm also just really perplexed/curious.

I should also probably say that, in case it isn't already abundantly clear, statistics is not my strong suit! Thank you in advance for bearing with me (and for any insight you can offer!).

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  • $\begingroup$ Okay, I think I see what you're saying but I'm still having a little trouble wrapping my head around it. If the partial correlations are each telling me the influence of A (or B, respectively) on Y without the influence of the other, then would a null or weak partial correlation mean that, alone A (or B, respectively) doesn't tell us much about Y? That instead its the common influence (i.e., whatever it is about both A and B that has them correlated so highly in the first place) that's really influencing Y? Maybe this is just another way of putting what you said, but I wanted to be sure. $\endgroup$ – Vanessa Aug 26 '15 at 14:50
  • $\begingroup$ Actually, I guess I've covered enough now to make it an answer. $\endgroup$ – Glen_b -Reinstate Monica Aug 26 '15 at 22:04
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Assuming all the dependence relationships (both marginal and conditional) are close to linear (without which correlation isn't really a suitable way to describe what's going on), I think it's actually telling you that you don't really need both - either on its own is useful, but once you have one of them in there, the other adds very little.

The partial correlations tell you the effect after removing the part of the relationship that can be accounted for by the other variable. As a result a weak partial correlation doesn't mean that on its own the variable doesn't tell you about the response. On their own either of them do tell you about the response (which is why the ordinary correlations are large). Variables A and B are telling you largely the same thing, so when one is there the second doesn't add much on top of the first. This is because they're highly correlated. (High correlation between A & B also says they have the same information.)

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