Need a bread crumb...comparing two distributions



I'm looking for a recommendation on what statistical methods I should
look at to do some analysis. I have taken stats I & II and can
read...just looking for advice on where to read.

I have pairs of people, call them a1 and a2. Each have answered
various surveys, ranging from a few to hundreds, about different
services. I'm only interested in a one question. What I want to do
is find people who are similar based on how they answered this one
question.

They have not necessarily rated the same services or answered the same
number of surveys.

For example, let's say part of the data set is this:

a1:
service 1, rating is 1
service 2, rating is 3
service 3, rating is 2
a2:
service 1, rating is 2
service 2, rating is 4
service 4, rating is 5
service 14, rating is 2
service 251, rating is 3
service 327, rating is 3

So what are some statistics I could look at to see how similar these
customers are? Obviously I'm doing this in the large...there are
thousands of a1, a2 pairs and I'd like to compute a number that says
"a1 is similar to a2 is X" so I can find clusters.

I thought about using two numbers:
(a) comparing percentages for how many 1s, 2s, 3s, 4s, and 5s
(b) a correlation for the ones that do overlap, though this will range
from many pairs to only one pair

....but there may be better ways of doing this comparison.

Any ideas?

It's kind of a two-dimensional regression, if such a thing
exists...unfortunately, the service number is meaningless - it's just
a label - and the number of pairs is not the same.

Thanks!
-S.

.



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