Following is a brief synopsis and data collection for a project that I
am currently working on.  I would like, if at all possible, someone to
try and show me the correct statistical analysis that would be applied
to the following three hypothesis.

While most professionals in the medical and psychological fields agree
that the disease model is an effective approach to addiction, many
question the need for substance abuse treatment.  Dr. R. Westermyer is
one of those who ask the question “Is substance abuse treatment really
helping substance abusers or is it a racket designed primarily to make
money or to promote some other selfish goal, with little regard for
the health or well-being of patients?” (Westermeyer 2000)
In order to more effectively serve our clients,  Acton is always
interested in the latest research findings concerning treatment.  This
study seeks  to answer the question about whether or not treatment
centers are in fact a “revolving door,” designed primarily to make
money, and that the services offered at rehab are not substance
abusers.  This information will aid the management staff at Acton
Rehabilitation Centers to make informed decisions about their course
of treatment

The first hypothesis deals with a widely known observation in rehabs. 
Some addicts are not interested in treatment but only getting off the
streets when the weather turns cold.

Hypothesis 1  The mean number of clients entering Acton Rehabilitation
Center will increase as the temperature of the weather decreases.

Data was collected from the databases at Acton Rehabilitation Centers
for a period of five years.

Number of Clients Entering Acton

Year 		    Winter       Fall      Summer     Spring

2001                   900        	700          600           600
1999 		       800        	750          700           700
1998                   850	        700          700           700
1997		       900              650          600           650
1996	               900              750          650           650








The second hypothesis looks at how important 12 step meetings are to
the success of continued sobriety.  A.A. boasts millions have gotten
clean and remained that way through the attendance of 12 step
meetings.



Hypothesis 2  The mean number of clients that stay clean for a period
of one year by attending one meeting per day will be greater than the
mean number of clients who did not attend daily meetings.

Data was collected via personal and telephone interviews.  Question
asked:  How many meetings were attended in first year of sobriety.

Participants = 30


 

		Meetings Daily           Periodic Meetings           No Meetings
				          ( 4 per month) 

                            
Number of Clients      25                        4                    
    1







The last hypothesis looks at whether or not rehab treatment is really
necessary for addicts to get clean and to see whether or not those who
just attend meetings are just as or more successful at sobriety than
those who went through a rehab.



Hypothesis 3  Addicts who have gone through rehab will be found to
have longer sobriety time than those who did not go through rehab.

Data was collected via personal and telephone interviews.  Questions
asked:  How many  years of sobriety? And did you ever have treatment
in a rehab?

Participants = 30

         Clients Who Stayed Clean After Rehab Treatment (20 clients)


Number of Clients                  Years of Sobriety

         5                                 1
                                                                      
                  7                                 2
         2                                 3
         1                                 5
                                                                      
                  4                                 6
                                                                      
                  1                                 7



          Clients Who Stayed Clean Without Rehab Treatment (10
clients)


Number of Clients                  Years of Sobriety

        2                                  10
                                                                      
                 3                                  16
                                                                      
                 2                                  25
                                                                      
                 1                                  27
                                                                      
                 1                                  30
                                                                      
                 1                                  37

---

Clarification of Question by boobee-ga on 29 Sep 2002 11:30 PDT

When I posted my question, the data flew all over the place.  Here is
the data collected for each hypothesis.


DATA FOR HYPOTHESIS 1

Number of clients entering rehab during the Winter was: =: 
2001: 900,
1999: 800, 
1998: 850,
1997: 900, 
1996: 900
 

For the same years during the Fall clients entering rehab were: 700,
750, 700, 650, 750

 For same years during the Summer clients entering rehab were: 600,
700, 700, 600, 650

For same years during the Spring clients entering rehab were: 600,
700, 700, 650, 650


DATA FOR HYPOTHESIS 2

Out of 30 participants who had been clean/sober for a period of one
year, it was found that 25 clients attended daily meetings; 4 attended
meetings periodically (at least 4 per month); and 1 client had made no
meetings.

 
DATA FOR HYPOTHESIS 3

Out of 20 clients that had been through rehab sobriety times were: 5 =
one year; 7 = two years; 2 = three years; 1 = five years; 4 = six
years; and 1 = seven years. Of 10 clients that had not been through
rehab sobriety times were: 2 = ten years; 3 = sixteen years; 2 =
twenty-five years; 1 = twenty-seven years; 1 = thirty years; and 1 =
thirty-seven years.

Hi again boobee!

For each of these hypotheses, I will provide a framework for analysis.
However, it is important to remember that there is often no "correct"
way to analyze the problem (some creativity is often required).

HYPOTHESIS 1:

Null hypothesis: The mean number of clients entering Acton
Rehabilitation
Center will increase as the temperature of the weather decreases.

Alternative hypothesis: The mean number of clients entering Acton
Rehabilitation
Center will decrease or remain the same as the temperature of the
weather decreases.



What I would use here is a linear regression between temperature and
the number of clients entering rehab. Currently you do not have
sufficient data to do this. Although we could probably order the
seasons by average temperature, there is still no numeric
quantification.You will need to obtain the actual average temperatures
in each of the seasons in each year, otherwise you will be assuming
that all the Summer seasons, for example, have the same everage
temperature. If this is not possible, you can do a regression between
season and number of entries...note that this will have no explicit
connection to temperature and is therefore a secondary solution.

HYPOTHESIS 2:

Null hypothesis: The mean number of clients that stay clean for a
period
of one year by attending one meeting per day will be greater than the
mean number of clients who did not attend daily meetings.

Alternative hypothesis: The mean number of clients that stay clean for
a period
of one year by attending one meeting per day will be less than or
equal to the
mean number of clients who did not attend daily meetings.


You're dealing with a limited amount of data here as
well...essentially all you can do with this is find a correlation
(uni-directional) between the proportion of clients and the number of
meetings attended monthly. Of course, you could also obtain the mean
and standard deviation for the number of meetings attended by sober
individuals.

HYPOTHESIS 3:

Null hypothesis: Addicts who have gone through rehab have longer
sobriety time than those who did not go through rehab.

Alternative hypothesis: Addicts who have gone through rehab do not
have longer sobriety time than those who did not go through rehab.

This hypothesis can be (dis)proven using a simple linear regression;
you would need to calculate the mean of both sets of data and compare
the two in order to accept/reject the hypothesis. However, it is
obvious that the purpose of rehab is to "reform" the individual and so
it is unfair to compare the number of years of these two group
explicitly. After all, isn't the purpose of rehab to get a second
chance? Furthermore, all of these individuals are at different phases
of life and so the years of sobriety may be a small amount of the
total they will achieve, or it could just be the beginning. It would
make more sense to measure years of sobriety for people who WERE sober
and broke the streak. There are also other factors that need to be
considered; since the individuals that have been in rehab obviously
have an illness, there is a possibility that this could resurface.
Using statistical methods there is very little that you can do even
this unfair analysis using only the data given. Its like comparing
apples and oranges...you need data that will somehow link those who
went through rehab to those that have not had rehab.

In summary, I find that the data you have for this project is quite
weak...if possible, I would suggest obtaining additional data that did
more to prove/disprove the hypothesis tests that you would like to
conduct. Statistics are a powerful way of determining relationships
and making decisions, but the basis for all statistics is relevant and
accurate data.

Let me know if you have any problems understanding the information
above. Althogh it may not be prcisely what you expected, it is
important to realize when you should stop you analyses and retreat for
more suitable data.

Cheers!

answerguru-ga

I have already gave reason -- see prior reason provided -- also in
email sent to you.