# How to quantify intraindividual variability between paired measurements?

I've collected data measuring several different parameters in several subjects at two time-points (t1 and t2).

X and Y are meausurements of two anatomical structures; X is an area measured in mm2, Y is a volume measured in mm3. For each one I can describe at least 4 variables: measuments at t1 and t2 (eg. X1, X2), absolute difference between the two measurements (X2-X1), percentual difference between the two.

I want to compare the "reliability" of X and Y in term of intraindividual variability. My intuitive choice would be to compare standard deviation or coefficient of variation between the two (or their variation). But:

• In the single time point measure (say, X1 vs Y1), a low SD/CV tells me only that different individuals tend to have roughly the same values, while high SD/CV tells me that different individuals tend to have very different values.
• Considering absolute difference between the two measurements does not seems to have much sense.
• Considering percentual difference between the two, low SD/CV in e.g. X tells me only that, in a population, X tend to change of roughly the same % in all the individuals, while an high SD/CV tells me that there is more variability in the entity of the change between individuals.

So, I'm not sure which statistic will tell me what I want to know. I was thinking of Pearson's r (or Spearman's rho) to quantify correlation between X1-X2 vs correlation between Y1-Y2 (if there is a stronger correlation between X1 and X2 than with Y1-Y2, it means X1 and X2 tend to increase/decrease in the same direction more thant Y1 and Y2 do, so they is less intraindividual variability).

• Am I correct in this assumption?
• If I were to calculate this in R, is it just a matter of cor.test(X1,X2) cor.test(Y1,Y2)

and then compare results?

Let $\rho_1$ and $\rho_2$ be Pearson's correlation between X1 and X2, and Y1 and Y2, respectively. By comparing the difference between two correlations, you test the $H_0: \rho_1 = \rho_2$. You are correct in that you reject the null if one correlation has a bigger value given both have the same sign (or if the two correlations have different signs). To do this, you need to perform the so-called Steiger Test because the two correlations in your study have no shared variable. In R you can use r.test in the psych package.