Re: st: Question on stir

[Marcello Pagano <pagano@hsph.harvard.edu>]

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 
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> Fax:          +45 8613 1580 
> E-mail:       sj@soci.au.dk 
> _________________________________________________________ 
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