Posted by
Arthur Kramer on
Dec 19, 2006; 9:01pm
URL: http://spssx-discussion.165.s1.nabble.com/Significant-difference-Means-tp1072801p1072813.html
So, Richard is advocating for performing an independent groups t-test and
using the pooled standard error as the denominator, because he says both
groups are samples.
I am wondering, though, by what methodology was the sample of 500 drawn from
the sample of 1000 (was the original N 1500, or is one half of the group
being compared to the other half of the group?), is it a random sample or
was there a selection criterion?
There is another philosophical perspective at play also, and that is the
scale of 1 to 7, standing as the only measure of the construct, is at best
and ordinal scale because my distance between 1 and 2 may differ from your
distance between 1 and 2.
Arthur Kramer
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of
Richard Ristow
Sent: Tuesday, December 19, 2006 2:59 PM
To:
[hidden email]
Subject: Re: Significant difference - Means
To weigh in with two comments:
At 03:54 AM 12/19/2006, Spousta Jan wrote:
>The error of that 3.5 is about sqrt(1/1000) = 0,03 while the error of
>2.9 for students is about sqrt(1/500) = 0.045. That is both errors are
>of the same order of magnitude and the population error cannot be
>neglected in this case.
I'd like to second, and emphasize, this. Jan is clearly right here,
where the two groups are the same size. However, the same thing holds
when the sizes are quite different.
First, the t-test algorithm correctly allows for the increased
precision in measuring the mean in the larger group. Replacing it by a
constant only 'gains' you a little precision you don't really have.
Second, inequality of group size matters less than one might think.
Roughly, precision goes as the square root of sample size. (Under
'nice' conditions, that's exact: standard error of estimate goes as the
square root of sample size.) That means increasing the sample size
ten-fold leaves the SEE still 1/3 of the size it had - quite a long way
from letting it be considered a constant.
And at 10:42 AM 12/19/2006, Statisticsdoc (Stephen Brand) wrote:
>If your population consists of the 1000 students, then the mean of 3.5
>is a population parameter, and you would be justified is using the
>one-sample t-test suggested by John.
(This won't be quite fair to Stephen Brand, who'd also written
"Formally one should test the null hypothesis that the two samples have
the same mean, by using the independent groups t-test.")
There's a philosophical position, which I agree with, that will hardly
ever accept something like "[my] population consists of the 1000
students." The argument is that, even if those 1,000 students are all
you've ever seen or ever will see, their observed values constitute a
set generated by an underlying random mechanism, and that randomness
must be allowed for in estimation exactly as if you were aware of
100,000 similar students.
('Generated by an underlying random mechanism' is sometimes expressed
as 'drawn from a conceptually infinite population.' However, while this
is technically accurate, I don't blame anyone who considers a
'conceptually infinite population' a very odd notion.)
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