How to test the influence of an external factor?

I have two sets of independent measurements – these have been done on the same material but using different methods. They are not paired in any way. Means of samples are different and I’ve performed a t-test to see whether the difference is statistically significant and at 0.95 confidence level I got a p-value of $3.8times10^{-12}$.

Now I have a suspicion that there is a variable, let’s call it $X$, that causes this difference in means – it is used in weighting of results of one of the measurement methods but not the other and also I know that for a significant time the value of this variable has been consistently underestimated.

What methods should I try to use to establish the possible relationship between this variable $X$ and the analysis method that overestimates results?

I hope it’s not too vague and thanks in advance!