The correction for attenuation The reliability of the task that I measured is very low for some sub-tasks. So, I tried to correct the correlation coefficient with Spearman's disattenuation formula: $r_{x'y'} = r_{xy}/\sqrt(r_{xx}r_{yy})$ where the raw correlation between $x$ and $y$ ($r_{xy}$) is divided by the square root of the product of the reliability of $x$ ($r_{xx}$) and the reliability of $y$ ($r_{yy}$).
My problem is that some of the values in the corrected matrix are greater than 1 and therefore dominating the pattern of the result. So as not to bias anything, I should probably correct values so that they are in the range of -1 and +1.
Do you have any suggestions for that?
 A: Correction for attenuation assumes that you have not violated any assumptions of the calculation of reliability.  Assuming you've used coefficient (Cronbach's) alpha, that means that you have a measurement model that is:

*

*reflective - the items should be the effects of the variables being measured, not the cause (e.g. is "I feel sad" a cause, or an effect, of depression).

*The measurement should fit a tau-equivalent model. That means that the covariances among items should be equal (not variances though).

*Errors should be independent. This is error both within and between scales. If you are measuring depression and have an item "I have trouble sleeping" and "I wake up in the night" the errors are likely to correlate. Similarly, if you are estimating the correlation between depression and PTSD and have an item that says "I have nightmares that wake me up" this is also likely to correlate.

You can test tau-equivalence and independence of errors in a structural equation modeling framework. There's no need, because they are violated in every non-trivial real dataset.
So what do you do? Don't use attenuation correction. At least don't use it in this way. Use it as a way to think about your correlations, but don't try to interpret them in this way, because you'll get out of bounds correlations.
