# st: RE: Two problems: Pre-post intervention AND comparing z-score distribution in a specific poopulation v/s the normal distribution.

 From "Nick Cox" <[email protected]> To <[email protected]> Subject st: RE: Two problems: Pre-post intervention AND comparing z-score distribution in a specific poopulation v/s the normal distribution. Date Mon, 25 Jul 2005 21:19:43 +0100

```Your objection that expected frequencies don't
come out as integers is discussed in any good
textbook. Briefly, it is just the way the calculations
come out: it is not a cause for concern.

In my opinion by far the best way to check
for normality is to use -qnorm-.

Nick
[email protected]

Siddharth Kharkar

> 2)  Comparing Z-score distribution in a study group with
> mental difficulties
> against the normal population:
>
> Scores on a cognitive test were measured in a group of
> students drawn from
> an institution for the mentally challenged.
>
> z-scores were calculated for these cognitive scores using
> means and SD for
> this test in the general population.
>
> A person had a z-score of lesser than -2 (i.e. was below 2 SD
> on the curve
> for normal individuals) was considered to be "Cognitively deficient"
> A person with a z-score of -2 to -1 was labeled as
> "Borderline Cognitive
> functioning"
>
> Say the scores in the study group were as follows:
>
> Normal	(>-1SD)			50 % (8/16)
> Borderline (-1SD to -2SD)	25 % (4/16)
> Deficient (below -2 SD)		25 % (4/16)
>
>
> These values are obviously abnormal. The values expected based on the
> z-score distribution for normal people are: 84 %, 13.5 % and 2.5 %
> respectively.
>
> What is the best way to show that the distribution of Z-scores in the
> mentally challenged children was abnormal? What statistical
> test can be
> performed?
>
> I was thinking in terms of making another column "NUMBER of
> people expected
> if the distribution was normal, given a sample size of 16"
> and then doing a
> chi2 on the observed v/s expected categories.
>
> The problem is that the "Number of expected people" will be a
> decimal number
> e.g. 2.5/100 x 16 = 0.4. which doesn't make much sense..

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```