(repost - problems at this end)
the discussion, a nd this post, have a real point. However, I'm not
sure that 'standard error' and 'standard deviation' are confused by
statistics people through the language all that much. There is a book
which gives the "official" definitions of terms, whose name escapes me
this minute. also, the text by John E. Freund and
Williams, Frank Jefferson, "Dictionary /outline of basic statistics,"
New York : Dover 1991 ISBN 0486667960, [Reprint. Originally
published: New York : McGraw-Hill, 1966.] was recommended on
allstat in the past.
The (true) standard deviation is defined as the square root of the
variance. the variance equals the sum of the squares of the
deviations of each measurement in a population from the mean of that
population, the whole divided by (n-1). Why n-1 and not n is for
another day; for very large n the question is superfluous. The
true standard deviation covers the whole population, which is usually
infinite anyway.
The _estimated_ standard deviation is the sum of the squares of the
deviations of each measurement in a _sample_ from the average of the sample.
Sample does not equal population, BTW. But we all knew that.
The 'standard error' is the standard deviation divided by the square
root of the specified sample size.
the std error, or the estimated std error, can estimate the variation
expected in a measured _average_ of a sample. We call this
'variation' the confidence interval. We can also use this confidence
interval to predict the location of the true mean of the population,
using the same confidence interval and the measured average
of the sample.
Thus, some people refer to the estimated standard deviation as the
standard deviation of a single measurement (the next one), and refer
to the standard error as the standard deviation of the average. While
the two terms perform the same assessment for the respective point
measurements, the terminology has just gotten quite
confusing. True?
I tell my students to make a table, with 'real' items on one side, and
'theoretical' items on the other. We also need to make the
distinction between estimating a mean (theoretical item) with one
measurement, and with the average of a sample of measurements.
Confused enough now? :)
Cheers,
Jay
Philip McShane wrote:
> This discussion of the meaning of 'Standard error' in relation to regression seems to me to highlight a serious problem in statistics: statisticians use different terms for the same thing, and the same term for different things, on an individualistic basis.
>
> Consider for example the different forms of the Akaike Information Criterion, or phrases such as 'the Wilcoxon-Mann-Whitney test'. To say they are 'mathematically equivalent' or 'easily converted' is no excuse; would anyone say that centimetres and inches are mathematically equivalent and use them interchangably?
>
> This does not happen so much in other areas of science: chemists know what 'propan-2-ol' is and zoologists what 'Drosophila melanogaster' is. They also know that if they use other terms (such as 'isopropanol') there is a danger of confusion or loss of precision. People even cope with changes, as long as these are agreed upon.
>
> A bit more standardisation would be a good idea.
>
> Regards
>
> Phil
>
> Phil McShane
> Nuffield dept of Surgery
> John Radcliffe Hosp
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> Oxford
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