Is it possible to distinguish two variables that are just correlated with each other but are not part of the same phenomenon, from two variables, that are part of the same phenomenon and share a common superior/higher latent factor? I mean a mathematical distinction and not a theoretical definition of a variable.
Let's say I measure the relationship between job quality and salary received, and I can assume that these are variables that measure other (separate) phenomena, different things; lets assume that they are correlated. On the other hand, I have the job quality measured by the employee's manager and job quality measured by self-report of the employee; let's assume that these two variables are also correlated with each other. Sooo... The first two measure separate phenomena, the next two measure one and the same phenomenon which is simply expressed or measured differently. The first two are simply just/only correlated, the next two have an higher factor or they are two variables expressing the same thing.
Do we have a mathematical, statistical or any other rule that can tell us (only by looking at the variables, their numerical values), do the two variables have an common latent factor OR are "just randomly correlated"? What's the mathematical difference between the factor items and correlated variables? PCA, CFA, SEM techniques can tell these things apart, or is it a completely theoretical problem? If these techniques can discriminate differences, what factors/indices should be considered?