# Is “standard error (SE)” the same as “standard error of the mean (SEM)”?

Can I assume the SE the same as SEM? Is SE just the abbreviation of SEM?

I am not talking about the standard deviation (SD).

• Well, you can have SE also of other statistics than the mean ... – kjetil b halvorsen Oct 29 '17 at 21:20
• can I ask examples? – lanselibai Oct 29 '17 at 21:23
• Well, you can have SE of the, median, of the 75th percentile, of maximum likelihood estimators, and many other statistics. But in case your statistic is a mean, then SE and SEM should be the same. – kjetil b halvorsen Oct 29 '17 at 21:33
• this makes sense – lanselibai Oct 29 '17 at 21:34

No. Standard Error is the standard deviation of the sampling distribution of a statistic. Confusingly, the estimate of this quantity is frequently also called "standard error". The [sample] mean is a statistic and therefore its standard error is called the Standard Error of the Mean (SEM).

• can you tell me the equation for the SE? – lanselibai Oct 29 '17 at 21:33
• There's not always a closed-form equation for the standard error of an estimator – call-in-co Oct 29 '17 at 21:41
• can you show me an open-form, or a link? – lanselibai Oct 29 '17 at 21:49
• I'm confused as to why you say no: from your link: "The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the parameter or the statistic is the mean, it is called the standard error of the mean (SEM)." Thus, the SEM is just a special case of the SE. – Cliff AB Oct 19 '19 at 1:44
• @CliffAB the last sentence is exactly right: but the question is asking if SE and SEM are the same. It's analogous to a square being a special case of a rectangle, but not being the same. – call-in-co Oct 19 '19 at 2:27

The "Standard Error" otherwise known as the SEmeasurement represents a measure of the net effect of all factors producing inconsistency in pupils performance. It is an index of the variability of the test scores of candidates having the same actual ability, i.e. a measure of the discrepancy between competence and performance on the day. About 67% of pupils' scores are 'correct' to within one standard error value, 95% to within two standard errors, and 99% within three standard errors. SEmeasurement = Std.Dev.(students' totals) * SQRT(1-alpha) where (Cronbach's) alpha is the internal consistency reliability value.

The "Standard Error of the Mean" SEmean measures how far the the mean of pupils' test totals for the sample is likely to vary from the true population mean. The standard error of the mean of a sample is an estimate of the standard deviation that would be obtained from the means of a large number of samples drawn from that population.
SEmean = Std.Dev.(students' totals) / SQRT(n).

Laurence Kiek Research Computing and Training Services, Jindabyne, Australia.