I have data for daily drug use (i.e. number of days out of the past 30
that an individual has used alcohol or other drugs) for adolescents
from 3 different substance use treatment programs.  I?d like to know
which of those programs has produced an effect of decreasing the total
number of days the youth uses alcohol or other drugs, and whether the
effect is different for males vs. females.  I do not have baseline
data.  Which statistical procedure would I use and why?

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Clarification of Question by threeblindmice-ga on 08 Nov 2004 15:11 PST

I only have data for the number of days out of the thirty.  (Not
whether someone was using drugs or alcohol on day 14 for example).  Is
there maybe some non-parametric test out there for this?

Analyse your data into two halves: Days 1-15 and Days 16-30 and by
treatment prescribed and sex.

Aggregate the totals and compare.

What else can you do? You don't have much data to work with.

Without baseline data, you're sort of hosed.  Sure, maybe program C
kids have the lowest counts after treatment (let's say 3 days/kid on
average), but maybe their numbers weren't very high before treatment
(say, 4 days/kid)?  Meanwhile, kids in A might have been binging
fiends before the program (30/30 days), but got down to 10 days out of
30 after treatment.  Pretty good improvement, but without the baseline
data, program C would look better.

Let's pretend you had baseline data though (so we have before and after data):

What you'd want to do is sort the data into 12 different sets (I hope
you have a lot of data): one set for each combination of before/after,
male/female, program A, B, and C.

Then, for each combo of male/female vs. A/B/C, you'd apply dependent
t-tests to the before/after data to check whether the difference in
means of each data set, before and after, was found to be
'statistically significant'.

T-tests have constraints regarding the distribution of the data; a
non-parametric alternative is Wilcoxon's matched pairs (see, e.g.,
http://www.graphpad.com/articles/interpret/Analyzing_two_groups/wilcoxon_matched_pairs.htm).

Another good reference is http://www.statsoftinc.com/textbook/stathome.html.