Significance test between two samples when positions matter

Let's say that I have two samples:

A    B  C    D
100  5  17   12  #<- Method 1
90   2  4    15  #<- Method 2


And want to compare to test whether method 1 is different from method 2. However, that observations in the samples are tied together, say 100 and 90 come from the same market A. What is the proper way to test this?

I am pretty sure that lumping everything together and doing a t-test or Mann-Whitney U test is not the way to go.

• What do "A", "B", "C", "D" mean? Could they correspond to factors that have a natural order? What do the numbers mean? (Are they counts, measurements of physical quantities, percents, ...?) How were the numbers obtained--are they the result of a complete census of something, of random samples, of samples of convenience, or something else?
– whuber
Jul 2, 2014 at 16:54
• We can think of "A", "B", "C", "D" as events; they have no order, but values corresponding to those events are paired. I am very sure that paired t-test (as suggested by @Greg Snow) is what I need. Jul 2, 2014 at 17:09
• Exactly how would you apply the paired t-test to these data? It's still not possible to tell whether it would be appropriate or not because you haven't disclosed the (essential) information I mentioned.
– whuber
Jul 2, 2014 at 17:58
• @whuber Let's say we used marketing strategy method 1 in on half of customers in market A, and marketing strategy method 2 on the other half. Method 1 generated 100 purchases in market A, and method 2 generated 90 purchases in market A, and so on. Does this answer your question? Jul 2, 2014 at 18:32
• Sort of--at least it shows me this is not a matter for a paired t-test! You have 100+90+5+...+15 total results and they are not paired. Although you could (somewhat artificially) pair the groups and perform a t-test of the differences 10,3,13,-3 against 0, it would have little power and cannot be recommended. (It reports that $p=0.21,$ which is not significant.) Many people would routinely begin with a chi-squared test to see whether any differences between the methods seem to hold. (There is a difference at the 5% level: $\chi^2=8.1$, $p\approx 0.04$ via simulation.)
– whuber
Jul 2, 2014 at 18:48