Re: Sample Means

Posted by Richard Ristow on Dec 21, 2006; 10:47pm
URL: http://spssx-discussion.165.s1.nabble.com/Sample-Means-tp1072828p1072833.html

At 05:15 PM 12/21/2006, Arthur Kramer wrote:

>Since Samir is assuming the responses constitute a scale, I am
>suggesting correlate the students scores on the scale with the
>non-student scores on the scale.

You may have mis-phrased this. You can't correlate the values of one
variable between two groups; a correlation is of two variables over one
set of observations. Now,

>[The problem] can yield a Pearson correlation obtained by using group
>membership as a dummy coded predictor [correlated with] the scale
>score.  That might also be more appropriate with the large n, because
>as I said, with this many subjects any difference is apt to obtain
>significance.  The correlation is just another way of measuring effect
>size, isn't it?

Well, relative effect size. Since this is an ANOVA problem (the
independent-samples t-test is the one-factor, two-level special case of
ANOVA), one might want to give R^2 (the square of your correlation
coefficient), i.e. percent of variance explained, to follow standard
ANOVA terminology.

I said, 'relative effect size'. For absolute effect size, you'd
estimate a confidence interval for the difference of the group means:
"the 95% confidence interval for the difference is 0.8 to 2.1 scale
levels."

>If he does want to go the non-parametric route, a Mann-Whitney U may
>provide some insight into the "scale" score.

Marta has warned about Mann-Whitney U when there are few (like 7)
possible values of the dependent variable, so there will be many ties.
I haven't worked this up from her tutorials, but I'd look at them
before using Mann-Whitney incautiously. (I'd used it, incautiously, in
many cases like this, before Marta's warning.)

>Doing a Chi-Square may necessitate multiple goodness-fit
>analyses:  percent students saying "1" compared to the percentage of
>non-student saying "1", etc. up to seven--do you protect your type 1
>error then?

Well, the classic, basic, chi-square doesn't; it tests against the
single null hypothesis that the two categorical variables are
statistically independent.

But if the test non-independent, there's the question which cells are
most affected. For that, using the SPSS CROSSTABS procedure (and
borrowing from an earlier thread),

>Try adding, to subcommand CELLS, EXPECTED and ASRESID.
>
>EXPECTED is the expected number in the cell, if the null hypothesis is
>correct, and ASRESID is the adjusted standardized difference from
>observed and expected. Look for cells with ASRESID greater than 2 in
>absolute value; that will show cells where the difference is most
>important.