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st: RE: parameter estimation doubts


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: parameter estimation doubts
Date   Wed, 23 Aug 2006 22:05:39 +0100

Frankly, most of this appears unanswerable to me. 
As with another recent poster you seem to be 
expecting Statalist to play the same role as 
your advisor or committee of advisors. That's 
not fair on us -- or on them. 

I will peel off one point, as I am the author 
of the -chitest- command. 

It is difficult to comment without seeing what 
you typed or the output you got (compare advice
in the Statalist FAQ), but -chitest- is indicating 
a problem with your data. Is that right or is it wrong? 

For example, consider these observed frequencies, the 
frequencies of 0 to 9 in the first 608 digits 
in the decimal expansion of pi. Any hypothesis
to be considered by -chitest- should imply 
that the totals of observed and expected frequencies 
are identical. 

. l

     +------+
     | freq |
     |------|
  1. |   60 |
  2. |   62 |
  3. |   67 |
  4. |   68 |
  5. |   64 |
     |------|
  6. |   56 |
  7. |   62 |
  8. |   44 |
  9. |   58 |
 10. |   67 |
     +------+

Here the sum is 608 

. su freq, meanonly

. di r(sum)
608

and so a simple hypothesis of uniform frequencies
yields expected frequencies that are all

. gen exp = 60.8

. chitest freq exp

observed frequencies from freq; expected frequencies from exp

         Pearson chi2(9) =   7.4934   Pr =  0.586
likelihood-ratio chi2(9) =   7.9287   Pr =  0.541

  +-------------------------------------------+
  | observed   expected   obs - exp   Pearson |
  |-------------------------------------------|
  |       60     60.800      -0.800    -0.103 |
  |       62     60.800       1.200     0.154 |
  |       67     60.800       6.200     0.795 |
  |       68     60.800       7.200     0.923 |
  |       64     60.800       3.200     0.410 |
  |-------------------------------------------|
  |       56     60.800      -4.800    -0.616 |
  |       62     60.800       1.200     0.154 |
  |       44     60.800     -16.800    -2.155 |
  |       58     60.800      -2.800    -0.359 |
  |       67     60.800       6.200     0.795 |
  +-------------------------------------------+

Now the frequencies had added to 610, -chitest-
would have issued a warning 

. replace exp = 61
(10 real changes made)

. chitest freq exp

observed frequencies from freq; expected frequencies from exp

Warning: totals of freq and exp differ
              total
freq            608
exp             610

         Pearson chi2(9) =   7.4754   Pr =  0.588
likelihood-ratio chi2(9) =   3.9352   Pr =  0.916

  +-------------------------------------------+
  | observed   expected   obs - exp   Pearson |
  |-------------------------------------------|
  |       60     61.000      -1.000    -0.128 |
  |       62     61.000       1.000     0.128 |
  |       67     61.000       6.000     0.768 |
  |       68     61.000       7.000     0.896 |
  |       64     61.000       3.000     0.384 |
  |-------------------------------------------|
  |       56     61.000      -5.000    -0.640 |
  |       62     61.000       1.000     0.128 |
  |       44     61.000     -17.000    -2.177 |
  |       58     61.000      -3.000    -0.384 |
  |       67     61.000       6.000     0.768 |
  +-------------------------------------------+

which seems fair enough to me. The threshold for a warning is that 
| observed sum - expected sum | must not exceed 0.01. Thus it
is for the user to decide what is acceptable. 

Nick 
n.j.cox@durham.ac.uk 

Narasimhan Sowmyanarayanan
 
> 1. When I get values of expected success the sum of expected success
> does not equal the sum of actual success for some of my functions. Is
> this normal ? and what do you make out of it. When I do my Chi-Square
> tests it gives me a message in stata that the numbers dont match (I am
> using a downloaded script "chitest")
> 

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