Comparing difference of means due to individual variability So in our statistical test, we are using a dependent t-test because we are comparing the means between pre and post conditions in a physiology lab. Since there is a lot of variability between two subjects. For instance, one patient has pre/post values of 15.3 and 19.55% respectively while another has 2.74 and 3.02. My question is rather than find the means of both, can I simply compare the DIFFERENCE by making the pre condition always 1 and the post condition the difference between the two (i.e 19.55-15.3) meaning that when I run the test, the mean of pre condition will be exactly 1 and the post condition will be the difference between the two values. Is that appropriate? 
 A: One can use a paired t-test. As you can see in the link, the paired t-test is a comparison of differences, and that is indeed the appropriate test to perform, under one condition. That is, one should check to make sure that the difference between data pairs is not non-normally distributed. The paired t-test calculates the average difference between samples (which is also the difference of averages, but that is actually not as relevant.) Then, that average difference is divided by the standard error to make the t-statistic. That t-statistic is then the deviation from zero difference, so looking up what that statistic means in terms of probability, gives the likelihood of no difference.
If the paired differences are not normally distributed, then one can attempt to transform the data, by taking logs, square-roots, reciprocals and so forth of the original data sets to attempt to find a fairly normal difference histogram, or, one can just use a Wilcoxon signed-rank test, which, as it creates normal conditions by ranking the data, does not need normal conditions in the data itself.
