I'm trying to understand the meaning of stating the standard deviation (SD) of the mean difference (MD) [or otherwise called the absolute mean difference]. This is for a paper I'm writing up where other examples also quote the SD of the MD as part of the analysis summary.
While I understand what the mean difference represents, i.e., being a "measure of statistical dispersion", I'm not sure of the utility of reporting the standard deviation of this value. I can kind of conceptualise what it means, but again the issue is the utility.
For reference, the analysis is of repeated measures data for equivalence. I will be reporting the correlation coefficient and also the statistical probability for equivalence (with equivalence range) using a Two One Sided T-test (TOST). Thus my question regarding the utility of the standard deviation of the mean difference.
Maybe I'm lacking in statistical knowledge and please feel free to point out a suitable reference for me to consult.
Thanks in advance.
Update - example:
Machine A is the reference measurement system. Machine B is the new measurement system. A certain number of real life measurements are made with each machine (N) on a common object to understand how equivalent the machines are. Ideally they're identical - "of course" say the designers, and can even be expected - but this testing will be used to support the equivalence limit of +/- x units. (Given in reality it's not possible to say A is exactly equivalent to B.) So a paired measurement comparison.
When reporting these results it has been common to report the mean difference and the standard deviation of the mean difference, plus the correlation coefficient (Pearson's) with its p value.
Update - comments:
1. This question does indeed refer to the standard deviation of the mean difference, not simply the difference.
2. I well understand what the standard deviation means in terms of distributions. But my question is really "what is the meaning of the standard deviation of the mean difference in relation to the quantity being measured?"
3. If it's as simple as a guide to the variability of the difference, then so be it.
4. If the result was reported as A = B +/- x units with a p < 0.05 then I understand that this is different to quoting a standard deviation type number, but I still get it intuitively. I don't get the SD of a MD in regard to the original measurement entity nearly as well.