1. ## validity of correlation

Hi,
I'm hoping someone can help me with a problem with correlations I've encountered with my research.

I use an instrument that gives out 4 different numbers (called IOPg, IOPcc, CRF, CH) which are suppose to represent different things when one reading is taken. These 4 different numbers are based on 2 'component' numbers (called P1 and P2, see below), but these are not immediately available but can be extracted later.

In other words:
-Press button to take measurement, machine finds out P1 and P2.
-4 different numbers come out. Mathematically they are:
1. IOPg = (P1+P2)/2
2. IOPcc = P1-(0.43*P2)
3. CRF = P1-(0.7*P2)
4. CH = P1-P2
-The actual values of P1 and P2 aren't displayed and can only be found out later. However, it is known that P1 is always higher than P2 and both are positive.

To give you an idea of the actual numbers, the population mean/SD of IOPg is 15.5+/-2.5mmHg and CH is about 12.0+/-1.5mmHg. You may be able to get an idea of P1 and P2 from this information.

With this background, my questions are:
-From the information above, do you expect P1 and P2 to be correlated? I am thinking moderately to strongly.

-The 4 variables listed above are supposed to represent different things about someone's eye. If I find that some or all of these variables are correlated, can I conclude that the correlation suggests a relationship between these parameters has some physical meaning, or could one argue that since they are all based on P1 and P2, the supposed relationship could be a mathematical artifact?

-If the answer to the above is 'yes', how can I determine if there is physical significance (if possible)?

-Conversely, if I find the correlations not significant: could there be physical significance but the result come out non-significant due to their mathematical form?

Any help would be appreciated
Thanks
William

2. Originally Posted by williaml
To give you an idea of the actual numbers, the population mean/SD of IOPg is 15.5+/-2.5mmHg and CH is about 12.0+/-1.5mmHg. You may be able to get an idea of P1 and P2 from this information.

With this background, my questions are:
-From the information above, do you expect P1 and P2 to be correlated? I am thinking moderately to strongly.

William

Yup. I expect P1 and P2 are correlated(moderately to strongly).
Using the equation below, we can come up with the idea of correlation.
Var(aX+bY) = a^2 Var(X)+ b^2 Var(Y) + 2ab*Cov(X,Y)
How do you define physical significance?.
May be the following link may helpful for the rest of the questions
http://en.wikipedia.org/wiki/Correla..._and_causality

3. Hi,
The other part to my question was that if the first 4 variables are correlated, could it be due to the fact that they all use P1 and P2?

As an example, let's look at IOPg and CH. IOPg is suppose to represent the measured intraocular pressure (the eye being a fluid filled sphere therefore has pressure, just like a water balloon). Note, the measured pressure may not be the same as true pressure due to measurement errors. CH is suppose to describe the viscoelasticity or material properties of the eye, which may or may not cause a measurement error.

From my previous post, IOPg = (P1+P2)/2 and CH = P1 - P2.
Let's say IOPg is found to have a significant correlation with CH. The physical interpretation would be that the material properties of the eye has caused an intraocular pressure measurement error because we have no reason to think there should be a relationship between true pressure and material properties of the eye. [Note, I am aware of the difference between correlation and causation, this is a standard assumption in the field]

However, if there is a correlation, could it be because both variables are derived from P1 and P2? Or should I really conclude that the material properties affect measured IOPg? In other words, if it is correlated, how to I tell if they are related because:
1. material properties of the eye affect pressure measurement
2. material properties of the eye don't affect pressure measurement but there is a correlation only because P1 and P2 are shared
3. a combination of the above 2 options

Also,
-Conversely, if I find the correlations not significant: could there be physical significance but the result come out non-significant due to their mathematical form?

Let me know if any of this is unclear
Thanks
William

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