Re: What more info does the Standard Deviation give me?

On Fri, 28 Dec 2007 10:17:20 -0800 (PST), Maya <maya_souj@xxxxxxxxxxx>
wrote:

Consider these two statements:

1.) I measured the heights of 50 boys and 50 girls, and found that the
mean height of the boys was 1.5 meters, and the mean height of the
girls was 1 meter.

2.) I measured the heights of 50 boys and 50 girls, and found that the
mean height of the boys was 1.5 meters, and the mean height of the
girls was 1 meter, and that the mean of the boys' heights was a full x
Standard Deviations more than the mean of the girls' heights.

Statement 2 tells me something more than Statement 1. But 1 tells me
only one thing more than 2, right?

You see to have messed up your question.

"1 tells me only one thing more than 2, right?" is not
correct. What (2) tells is something about the internal
variation of (presumably) both samples

If you know that one SD is smaller than the other, it does
say something about the closeness of the scores generally, or
else about the presence of outliers. When the means are
for "growth", variation is often proportional to the means,
which is a reason for the log of measures to be used -- to achieve
equal variances and a more sensible metric.


Is it true that the only thing that a higher Standard Deviation of one
group (boys) tells me is that there was more variance among the boy
data points (more really tall, and more really short boys) than there
was among the girl data points (so each girl was closer to being about
the same height as each other girl, than each boy was to being about
the same height as each other boy)?

I should not gain anything more by comparing the SD of the boy data
set with the SD of the girl data set, right?

The comparison the means, above, is not a comparison
of the SDs, although they may happen to come out similar
in a particular pair of samples.

--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html
.

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