For the 3X3 correlation matrix that you describe to be a valid correlation matrix, it must be positive definite. An easy condition to work with is ensuring that the determinant of this matrix is positive. Say you organize your variables in A,B,C and call the missing correlation 'r'. Then your correlation matrix looks like:
well, i'm doing some research for my uni thesis and I wanted to see if there is any logic in connecting systemizing quotient (e-s theory) with different uses of music as outlined by Premuzic and Furnham (2007). my first hypothesis is that those who have a high SQ score would be more likely to use music in a cognitive fashion, and i wondered since both of those variables (systemizing and cognitive use of music) are positively correlated to openness to experience, could i use those correlations to support my hypothesis and even to predict whether or not my hypothesis would be accepted? in other words, is it okay to think high SQ and cognitive use would be correlated if they are both correlated to openness to experience?
edit: other big five traits as well as other uses of music are also correlated to either systemizing or empathizing or both.
what other info did you mean, spunky?
From the description of your research hypothesis I agree with noetsi that you may want to engage in some type of SEM or Path Analysis approach to test them. But not in predicting correlations because that value of r that I described previously can be negative and still give you a proper (i.e. positive definite) correlation matrix
unfortunately, i'm not very familiar with SEM. what I wrote in the previous post is more a rational/theoretical justification of my hypotheses, I meant to do the actual research through ANOVAs and correlation matrices. since my hypotheses NEED to be confirmed in order to finish college, I thought i could have the luxury of anticipating a certain result. Because i never intended to measure openness or other big five traits, just using it as a framework to connect SQ and cognitive use. am I missing something?
Well you are missing that ANOVA does not get at indirect effects. So if you are going to comment on the impact of A on C you will have to point out that using ANOVA you can only get at the direct effects of A on C not the indirect effects of A on C through B or other variable.
Sometimes its best to do the easy stuff to get done. So if you can just run direct effects just do that.
Basically what you can infer in this particular case is that corr(A,C) must be between -.762 and .999. In other words, there's a little constraint, but not much. The expression I used to get this is given in the thread I just linked above.