I think that your the general understanding of the meaning of SD and SEM is correct.  I also have a problem with a general comment that the SEM "should NEVER be used."  But whether the SEM or SD should be used depends on what is being conveyed, and most often you'll want to use the SD to convey the amount of variation of the data about the mean (especially when approaching a data set parametrically).  If your objective of your experiment is to obtain the mean and you wish to show its uncertainty (for example a series of laboratory measurements of some fixed physical quantity), then using SEM makes sense.  The SD will show the variation in your measurements, but the SEM will indicate how well you determined the quantity sought.  On the other hand, if you wish to describe a data set using values for central tendency and dispersion, then mean and SD are usually the best metrics, respectively, especially for symmetric distributions (cf., Normal distribution).   I agree with most of the points made at the website given, but some are a bit dogmatic (unlike the 007 movie or the Justin Bieber song, a statistician probably should not say "never").  For instance, you can use the SEM to test whether means are significantly different if, again, the means were the main objective of the experiment.  But, admittedly, I rarely use this metric otherwise.  I hope this helps.

To complement the above response: since SD and SEM are easily converted into each-other in a sample, I don't see the point of arguing very much if the one given is clearly stated as SD or SEM and the sample size is given.

The drawback of SEM is that it is much less informative than for instance a 95 % (or other stated level) confidence interval of the mean in all problematics involving mean comparisons or mean precision... So the need of SEM seems quite limited...

Thanks for your answers, confirms what I thought. Richard.

Hi

In order to differentiate between standard error and standard deviation, the following points are developed:

The standard error(SE) is very similar to standard deviation. Both are measures of spread. The higher the number, the more spread out your data is. To put it simply, the two terms are essentially equal — but there is one important difference. While the standard error uses statistics (sample data) standard deviations use parameters (population data).

1. The standard error is the estimated standard deviation or measure of variability in the sampling distribution of a statistic. A low standard error means there is relatively less spread in the sampling distribution. The standard error indicates the likely accuracy of the sample mean as compared with the population mean. The standard error decreases as the sample size increases and approaches the size of the population. Sigma (σ) denotes the standard error; a subscript indicates the statistic. For example, the standard error of the mean is represented by σM. To find the standard error of the mean, divide the standard deviation by the square root of the sample size: , where σ is the standard deviation of the original sampling distribution and N is the sample size.

2. In order to quantify the standard error, a good sample has to be drawn from the target population. The key to a good sample is that it has to be typical of the population from which it is drawn.

3. These are the few factor need to be controlled, in order to get good sample and to quantify the errors and variation:

• Proper planning of the study
• Use of appropriate statistical design and methods for study
• Appropriate sampling methods
• Randomization
• Reduce investigator bias
• Use appropriate and large sample size with consideration of power for the calculation
• Use of Standardized procedures
• Appropriate statistical Techniques