Dear Tipsters,
And once the idea of the standard error is understood in the context of the
mean, it can be generalized to other statistics.
Sincerely,
Stuart
_____________________________________________________
"Floreat Labore"
"Recti cultus pectora roborant"
Stuart J. McKelvie, Ph.D., Phone: 819 822 9600 x 2402
Department of Psychology, Fax: 819 822 9661
Bishop's University,
2600 rue College,
Sherbrooke,
Québec J1M 1Z7,
Canada.
E-mail: [email protected] (or [email protected])
Bishop's University Psychology Department Web Page:
http://www.ubishops.ca/ccc/div/soc/psy
Floreat Labore"
_______________________________________________________
-----Original Message-----
From: Mike Palij [mailto:[email protected]]
Sent: May 6, 2010 1:28 PM
To: Teaching in the Psychological Sciences (TIPS)
Cc: Mike Palij
Subject: re:[tips] standard deviation versus standard error
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]
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