Hello ALLSTAT

 

 

  What we want to do is find the best of two ways of estimating the
proportion below:  

 

P= (# in AREA who are on Medicaid and are SMI)/  (# STATEWIDE who are on
Medicaid and are SMI)

 

 

 

There are two  ways under consideration of estimating the above proportion:

 

P_hat1  = (population of  AREA)/ (STATEWIDE population)

                       

P_hat2   =( medicaid-eligible population of  AREA)/ (STATEWIDE
medicaid-eligible population)

                      

 

We'd like to determine, statistically, whether P_hat1 or P_hat2  gives a
more accurate estimate of  P. 

 

The question is how to test that.  We have the values of  P_hat1,  P_hat2
and P for each AREA.    In practice, P is quite difficult to determine, but
for testing purposes we do have something.

 

Note that P_hat1 and P_hat2 are two different proportions from the SAME
sample. 

Note also that the denominators for P_hat1, P_hat2 and P are numbers from
the STATEWIDE population, ie for all AREAS combined.

 

Running two tests for each AREA, comparing P_hat1, P_hat2 to P and assuming
a binomial distribution with two independent samples doesn't seem like a
good idea.  P_hat1 and P_hat2 are two different proportions, both from the
same sample. 

 

Would a binomial paired-t test work? What does the formula for that look
like?  Could each AREA be treated like a person, so that each AREA
contributes one data point (one value of delta) to a given test? 

 

If this is unclear, please let me know. 

Any help would be greatly appreciated.   

Please go easy on me here, as I am very rusty on this and was an ignoramus
to begin with:  Zero minus something is a negative number. Maybe you can
bring me up into the small positive integers.

 

Thank you very much,

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