st: quasi experimental design inquiry

[Omar Okasha <omarokasha@gmail.com>]

I am working on a quasi-experimental study, with an intervention to
reduce HIV stigma. A score has been constructed (scale 0-10) to
measure HIV stigma among healthcare workers in two hospitals: one
assigned for the intervention, and the other as control. Average
stigma score was calculated in the two hospitals, before and after
intervention, and we would like to see if the intervention has
succeeded to reduce stigma in the intervention hospital compared to
control. I am confused on which statistical test should be done, let's
say we have the following table with average scores:

....................................Before......................................After....................
...........................Control............Intervention.......Control............Intervention
Average Score........4.0(a).................4.0(b)............3.8(c)...............2.0(d).....

Note that individuals after intervention, in both hospitals, are not
the same ones before intervention, so it's independent on individual
level, but paired on hospital level

Now, we have two issues that need to be tested:
1. first is the change within each hospital (c-a) and (d-b): for
instance, in the intervention hospital, the difference between before
and after scores. that would translate to %reduction of score in each
hospital, and eventually whether reductions are significantly
different comparing the two hospitals

2. Second, is the difference between the two hospitals, before and
after intervention (b-a) and (d-c).

It seems to me there are two ways to do it but I am not sure which to use:
1. conducting paired ttest to test the difference within each hospital
before and after intervention, and independent ttest to test the
difference between the two hospital before and after intervention.
2. Difference in differences, the tests for the two issues at one step
((d-b)-(c-a))
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