Unsure of how to compare non-paired values

[Richter915]

I am currently trying to show that two numbers are significantly different but I am unsure of how to do the statistics. I'll provide a brief description below.

I have 4 arrays: Array A Array B Array C and Array D
I can determine the difference between 2 arrays using a student's t-test
From each value within each array, I performed a simple mathematical calculation - let's just say I took the natural logarithm of each value.
I now have four new arrays which is from the calculations done on each value, Array A' Array B' Array C' and Array D'
Again, I can do a pairwise analysis of pairs of arrays using a student's t-test to determine significance.
What I want to do now is take the difference between two arrays (A' and B') and compare that to the difference between the other two arrays (C' and D'). Now, I can't simply take the difference in a pairwise manner (as in, value one of A' minus value one of B') so I have to take a difference of means.
So now I've generated the difference of these two means but I do not know how to do the variance of this value or to determine if these difference of means values are actually different from one another.

I've tried using propagation of uncertainty in order to determine uncertainty of these values but I am unsure if this is the best way. Either way, I am unsure if these values are significantly different.

Any help on this would be appreciated. Thanks.

 

[Stephen Tashi]

You haven't explained your problem clearly. I suggest you try again.

For example, you say you are trying to find if two numbers are significantly different, but you mention 4 arrays of numbers. Also, you say you transform the numbers in the arrays and get new arrays, but you say you "can't simply take the difference in a pairwise manner (as in, value one of A' minus value one of B' " and it isn't clear whether you mean that this operation is impossible or whether it is possible, but, for some reason, not meaningful.