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

 From "Siddharth Kharkar" <[email protected]> To <[email protected]> Subject st: Two problems: Pre-post intervention AND comparing z-score distribution in a specific poopulation v/s the normal distribution. Date Mon, 25 Jul 2005 09:09:18 -0400

```Hi,
I am most grateful for all the knowledge you people dispense on statalist. I
have learnt a lot through it.

I have two problems:

1) The first one concerns the effect of two different interventions:

At baseline, 20 % of patients admitted with disease X at Hospital 1 were
cured
At baseline, 30 % of patients admitted with disease X at Hospital 2 were
cured

Training 1 was given to doctors in Hospital 1
Training 2 was given to doctors in Hospital 2

In the Post-intervention period:
60 % of patients admitted to Hospital 1 were cured
55 % of patients admitted to Hospital 2 were cured

Obviously, Training 1 seems to work better than Training 2.

O How can it be shown that this "difference in improvement in cure rates" is
statistically significant? i.e. one training is better than the other?
(Note: This is NOT paired data.. the patients are different)
s Can a sample size be calculated for this situation?

I know its not a perfect study, but given the current situation, what can be
done?

The best I was able to do was to calculate the 95 % CI for the improvement
in cure for hospital 1, then calculate the 95 % CI for improvement in cure
for hospital 2. The CIs overlapped, indicating that the "improvement in cure
rates" were not statistically different.

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..

A big THANK YOU for any replies that follow. I have been a keen follower of
statalist and cant thank you guys enough for all that I have learnt through
it.

Thanks and regards,
Siddharth Kharkar.

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