# Re: st: Question on stir

 From Marcello Pagano To statalist@hsphsun2.harvard.edu Subject Re: st: Question on stir Date Mon, 08 Aug 2005 11:59:05 -0400

```Svend Juul wrote:

```
Tim wrote:

But I have not heard that maximum likelihood asymptotic results systematically underestimates the standard error, as seems to be the case here. ---------------------------------------

I am not a statistician, so this is more by intuition:

A chi-square test consistently gives, with few observations, a too low P-value compared to an exact test.

The two p-values refer to two different distributions. The "exact" is not and it refers to the permutation distribution over whatever sample space you have created by conditioning; for example in the two by two table you condition on the row and column sums. The chi-squared, on the other hand, is the asymptotic, as sample size increases, distribution of the X-squared statistic defined by Pearson. It refers to the distribution over all possible samples.

I was not aware that the "chi-square test consistently gives, with few observations, a too low P-value...." so I would like to see proof of that. I have observed that this is not true.

A simple estimation of continuous data gives, with few observations, a too narrow confidence interval; that is why the t-distribution was invented.

The t-distribution was invented, discovered?, because it is the appropriate small sample distribution when sampling from a normal distribution and wishing to find the distribution of the deviations from the mean and not knowing the standard deviation. Do not know what the CI has to do with it?

m.p.

Isn't the same principle at play here?

As said: I am not a statistician, and somebody else must take over from here, if needed.

Svend

________________________________________________________
Svend Juul
Institut for Folkesundhed, Afdeling for Epidemiologi
(Institute of Public Health, Department of Epidemiology)
Vennelyst Boulevard 6 DK-8000 Aarhus C, Denmark Phone, work: +45 8942 6090 Phone, home: +45 8693 7796 Fax: +45 8613 1580 E-mail: sj@soci.au.dk _________________________________________________________
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