Is it always appropriate to convert paired data to unpaired data? This is a general question, which I have encountered regularly, but as it is seemingly very basic, I can not seem to find an answer / explanation for it.
Assume a situation in which we have paired data (repeated measures under different conditions on the same subject). In this situation, we want to do a kind of analysis or test (e.g. mediation analysis). The repeated measure variant of this method turns out to be quite involved, while I can understand the basic version. At the same time, several basic methods for paired data, such as a paired t-test, simply construct a single data set by using the difference instead of the individual values and then go on to use a basic variant of the method. Can I generally do the same for other methods without introducing errors into the data or are there any pitfalls I am missing? I expect tests to become less powerful, but at the same time be easier for me to handle and therefore have less potential for manual errors.

The question is whether the data set of differences appropriately reflects the information in the given situation. This may not be the case for example in situations where you have floor and ceiling effects. If your measurement scale has a maximum of 10, a difference of 1 probably has a different meaning if you start at 9 than if you start at 2.
Another issue is that if you have ordinal data, numerical differences may not be seen as meaningful (this is somewhat controversial in the literature and in my view may depend on the situation), so converting data to differences may be inappropriate.
