Re: Sample Means

Posted by Richard Ristow on Dec 21, 2006; 9:31pm
URL: http://spssx-discussion.165.s1.nabble.com/Sample-Means-tp1072828p1072831.html

At 03:01 AM 12/21/2006, Samir_Omerovi=E6?= wrote:

>I must admit that some of posts I had difficulty
>to follow so my reply comes late.

Yeah, well, we went down a bunch of paths, didn't we?

>I figure out that I did not find the solution to
>my problem, or rather I find so many I can not
>pick one that works best. Independent T test,
>Z-test, One sample test, Cohan d...

Well, at 11:56 AM 12/21/2006, Stephen Brand
(Statisticsdoc) suggested reformulating your question:

>I would suggest that you focus on the question
>of whether the mean answer of the 500 students
>differs from the mean answer of the 500 non-students.

instead your original question,

>What test should I use if I need to assess the
>significance of the mean of some subgroup in
>comparison the mean of the total population.

I think this is right: compare the two parts, not
one part with the whole. If you don't agree, ask
again, and we'll see what we can say.

To compare the two separate groups, the
independent-samples t-test is the best answer, as
Stephen Brand and Jan Spousta have both recommended.

Stephen wrote that using the t-test is "subject
to certain conditions," which it is, but in your
case those conditions will apply plenty well enough.

I'd say you can stop reading here, and go ahead.
....................
To speak to some other points that have been raised,

A) We talked a lot about whether your 1,000
should be considered the 'population' in the
statistical since. You just wrote,

>I have survey done with 1000 respondents and if
>among these 1000 I got 500 students (and the
>rest 500 are not students).

So the answer is clear: Your 1,000 are *NOT* the
population, in the sense we've been talking
about. They're a sample (with two sub-samples,
students and not). Our discussion about what
constitutes a 'population' is important in
general, but it's not relevant to you.

B) At 09:49 AM 12/21/2006, Arthur Kramer wrote:

>Another effect size you could examine is the correlation coefficient,

Arthur, can you help? *I* don't understand this
one. Correlation of what with what? The only
possibility I can see is the correlation of
response with the student/non student binary
variable, and I'd think testing for difference of
group means would be much more meaningful.

C) At 09:56 AM 12/21/2006, Rick Bello wrote:

>I would respectfully disagree with Jan's
>suggestion of using a t-test as the assumption
>of independence is violated.  Although within
>each group the samples are independent (each
>student or non-student is entered only once) the
>students contribute to both groups.

Quite right; but reformulating as a
between-groups comparison is probably the best solution.

D) Samir asked,

>Since I have answers at 7-point scale, I could
>maybe use Chi-square. If I take the frequency of
>answers of 1000 respondents as expected values
>and the frequency of answers of 500 students as
>test values. The problem is the same.
>Frequencies of 500 students are included in
>frequencies of 1000 respondents. And is it ok to
>use chi-square here or not at all?

That wouldn't solve your problem. As for the
t-test, you'd need to compare the students with
the (500) non-students, not with the whole 1,000.
That is, you need to compare the two separate
parts, not one part with the whole.

(As Jan Spousta wrote, the chi-square tests for a
different set of effects than the t-test does.
Sometimes comparing the results of the two is
illuminating, but that's for a further discussion sometime.)

E) Regarding this, at 09:35 AM 12/21/2006, Arthur Kramer wrote:

>The chi-square is a good way to go because your
>data are essentially non-parametric (i.e.,
>ordinal) in nature, unless you can document that
>the "space" between 1 and 2, 3 and 4, etc. are
>based on a common metric among all of your subjects.

True; but in cases like this, a rough-and-ready
assumption they're about equal usually works well enough.

If you don't trust that, use an ordinal
non-parametric test, not chi-square. Marta
García-Granero has prepared some tutorials on
non-parametric methods, including these.

-Good luck to you,
  Richard Ristow