I have a population of interest on which one numeric variable has been measured twice: before and after surgery. I did a paired t-test to compare means of the variable. However, there is a difference in sample size between the pre-op and post-op groups, ie not all patients had the variable measured after the surgery so that the post-op group is smaller. The pairs of the variable are known and linked by patient ID so that I was able to perform a paired t-test on the known differences. How should I report the mean of the variable in both samples? Should I report the mean of the paired-t test (ie the mean of the variable from the patients that were actually compared), or the mean of the actual sample size? I don't if I'm being clear, but hopefully someone can provide me with some insight.
You should report the mean of the paired t-test because reporting the mean of the actual sample will affect the t-test's validity.
For example, assume you were measuring BMI before and after surgery on 60 patients, half of which (30) are obese and half of which are not. If, for some reason, you didn't measure any of the obese patients after the surgery, you would end up with an extremely inaccurate measurement of the mean BMI after surgery (you'd only be measuring the non-obese patients). You would also find a difference in means that does not actually exist (the mean BMI has 'dropped' after surgery, because you didn't measure any of the obese patients).
This example is a little extreme, but it's possible that something similar might affect your t-test as well
What I think you should do is ignore the patients that were not measured afterwards; this will decrease your number of observations but will keep things more accurate.