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).
 A: 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).
A: 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.
