# st: RE: parameter estimation doubts

 From "Nick Cox" To 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
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 |
+-------------------------------------------+

would have issued a warning

. replace exp = 61

. 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