If we found that the case matched what the theory predicted, a literal replication of the theory would have been achieved (Yin,1989: 54). Since this outcome may be due to chance we could seek out some other schools in which the devolved system was introduced and examine its impact on the quality of education in those school. If the same patterns occur we have further literal replications.
We could then attempt to test the theory in a different way. Since we had concluded that the improvement in education was due to the introduction of the devolved system we would expect, on the basis of our theory, that where a centralized system was retained there would be no improvement in education. We would deliberately seek out instances of school still functioning with a centralized system to see whether our theoretical predictions were supported.
As a tougher test we might look for cases that run counter to the basic proposition: that is, cases of a failed devolved system. Alternatively, we might look for cases of centralized systems that, over the same period, also delivered improvements in educational quality. However, our theory may be such that it can account for these ‘deviant’ cases. It might specify that the basic relationship will only work under particular conditions. If we find that the basic propositions do not hold up and this is predictable on the basis of the theory we have added further support to our theory. This is called theoretical replication (Yin 1989: 54)