When to use the standard error on the mean 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.
 A: Absolutely it is not just a question of honesty, or anything to do with stats v measurement error.  The standard error of the mean and the standard deviation of the population are two different things.
The mean of your sample is a random variable, because it would be different every time you ran the sampling process.  The sampling error of the mean is just the estimated standard deviation of the sample mean.
It's not quite clear what you mean by comparing data points to your model.  But if you mean you are interested in whether a particular data point is plausibly from the population you have modelled (eg to ask "is this number a really big outlier?), you need to compare it to your estimate of the population mean and your estimate of the population standard deviation (not the sample mean's standard deviation, also known as SEM).  So the standard deviation in this case.
More generally, it sounds like you are using the standard deviation inappropriately in some other circumstances.  If you are trying to report inferences about the population mean you should use the sample mean's standard deviation / standard error, not the population standard deviation.
A: I think of it this way;  the SEM is a measure of the precision of a sample mean.  But a sample mean from one experiment (say, with 3 -6 replicates) is hardly enough to gauge the precision of a population mean.  FOr me, one needs to do multiple independent experiments (each with replicates to generate a mean) and then each of these means are taken as individual n's.  So, instead of individual samples (replicates from an experiment), I only use the individual means of several (at least 3, more often 4-6) independent experiments to calculate the SEM and I use the STD of those averaged means in the calculation of an SEM.  SInce few (including me) perform experiments more than 3 times, I elect to use the STD of a "representative" experiment.  I think the SEM is not very useful and most people use it simply to reduce the size of the error bar.  Therefore, I do not like the SEM much and loathe its pervasive use in science. 
