If you want to describe the heterogeneity of your observed data, SD is the preferred choice. SEM is an inferential measure, describing the uncertainty of your measured effects (point estimates) and depends heavily on the sample size, whereas SD is largely independent of n, although the precision of this estimated SD again depends on n.

Depends upon data sets

If you want to describe the heterogeneity of your observed data, SD is the preferred choice. SEM is an inferential measure, describing the uncertainty of your measured effects (point estimates) and depends heavily on the sample size, whereas SD is largely independent of n, although the precision of this estimated SD again depends on n.

SD is a better measure and nowadays most of the high end journals require you to report in terms of SD. It gives one an idea about the spread of the data about the mean and is a better choice in my opinion.

SD is dependent of your sampling. SEM is an estimation of the whole population's SD. Both are acceptable in publications, as long as you specify clearly what you are showing.

it depends on your sample & how you collect your data

There is a paper about it. "Maintaining standards: differences between the standard deviation and standard error, and when to use each" Its found here: http://ww1.cpa-apc.org/Publications/Archives/PDF/1996/Oct/strein2.pdf

SEM is usually calculated from the sample variance (i.e. SD^2) divided by the sample size (n) [but you take the square root of both, ending up with SD/sqrt(n)], so if you present sample size and either SEM or SD, the reader can calculate one from the other...

You have to take the distribution of the data into account. Check them by the available methods (D'Agostino-Pearson, Kolmogorov-Smirnov, ...). Only in normally distributed data the SD (+average) is the correct. In all other cases median + SEM is fine.

Stephan, this is not about being correct or wrong. The SD is the square root of the variance, and the variance is the average squared difference to the mean. This is true and correct for all kinds of distributions. The only problem is the interpretation. For a normal distribution we know to expect about 63% of the values in the range mean plus/minus SD. This is different for other distributions. Further, the combination median and SEM is not sensible. SEM is a measure for the variability of the estimated mean. If the median is given, the variability should better be indicated by the interquartile range.

Jean-Nicolas, I'm sorry to say that, but what you wrote is plain wrong.

The weak law of large numbers states, that the sample mean converges toward the expected value (i.e.. the theoretical mean) with n -> infinity. As a consequence the SEM, which is calculated from the sample, tends to 0 with increasing n, which becomes clear from the formula Joacim pointed out.

Eik you are totally right. In fact, it would be the opposite (by oversimplifying...).

SD is the better measure to show the difference depends on the nature of data, SEM is always the measure of precision.

Sometimes the best way to show differences is to show them with graphics. Whether particular variation measures are reported or not - a picture of the distribution of measures of interest with graphical representation of measure variation around some central tendency measure is sometimes so much more satisfactory and informative.

Here is an example where variation in modeling methods across different years was the focal issue.

https://www.researchgate.net/publication/13161657_Discontinuity_in_the_Health_Care_Financing_Administration's_published_standardized_mortality_ratios_due_to_underestimation_bias_across_multiple_admissions_case_selection_methods?ev=prf_pub

Article Discontinuity in the Health Care Financing Administration's ...