On Thursday, May 06, 2010 11:29 AM, Annette Taylor wrote: >I am trying to explain to students with no or minimal stats knowledge >the difference between standard deviation and standard error. They >get SD pretty well because I can talk about average deviation about >a mean for a set of scores. SE, the more commonly accepted error >term these days, is a bit more complicated. Anyone have an "easy" >way to describe it to students?
As others have pointed out, you can say that the standard error is a standard deviation but of deviations of sample means relative to the population mean (or our best estimate of the population mean, the mean of the sample means). The key idea is that all of the sample means estimate the population mean but because they are based on subsets from the population, the sample means contain sampling error. If the samples were the same size as the population, there would be no sampling error and the sample means would always be equal to the population mean (standard deviation of sample means = 0). . But as the sample size gets smaller than the population size, the sampling error goes from zero to some measurable amount because some values are not included in the samples used to calculate that sample means.. In small samples, the amount of sampling error can be quite large and the standard deviation of the differences among sample means provides a measure of the amount of sampling error -- thus, the standard deviation for deviations of sample means around the population mean is a measure of error which we refer to as the "standard error of the mean". It might be useful to point out that standard errors can be calculated for most sample statistics and one will see standard errors for statistics like skewness and kurtosis when one uses SPSS for detailed descriptive statistics. -Mike Palij New York University [email protected] --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=2492 or send a blank email to leave-2492-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
