I have a number of measurements of a data point which I want to compare to my model. I have the sample mean, sample standard deviation and therefore the SEM. It usually seems fairly obvious to me whether to use the std. dev. or SEM. I think in this case I want to use the std. dev. as I'm comparing my model to my data, not estimating a mean value. However it made me wonder, if I had no model and I was simply reporting an experimental error are there any hard a fast rules as to which one would use. I have probably been rather inconsistent in the past.
I tend to prefer the std. dev, as I generally use systems which can collect thousands of discrete data points a minute, so SEM tends to be rather implausibly small compared to the uncertainty present in the measurement system. Often this is to the point where the screen/printer resolution isn't sufficient to distinguish the upper and lower bounds using the SEM. If I work on an experiment where repeated measurements are hard to come by my mind seems to go to SEM. Is it simply a case of honesty? If stats are your dominating uncertainty quote SEM and if its measurment error quote std. dev.?
I feel like I should not be running on auto-pilot on what seems like an important question.