Re: [office-formula] CHITEST definition

["Andreas J. Guelzow" <aguelzow@math.concordia.ab.ca>]

On Mon, 2007-12-03 at 19:10 +0100, Eike Rathke wrote:
> Hi Andreas,
> 
> On Friday, 2007-03-09 14:36:03 -0700, Andreas J. Guelzow wrote:
> 
> > > > Furthermore, Ecma/Excel's definition of degrees of freedom looks weird,
> > > > for rows>1 and cols>1 they say it would be (rows-1)*(cols-1). Why?!?
> > > 
> > > Btw, OOo does the same. Probably because it was documented as such.
> > 
> > Which test is CHITEST supposed to perform?
> > 
> > In the cases of a test for independence or a test of homogeneity, these
> > degrees of freedom make sense. (But we should have only one regular
> > region).
> 
> It claims to be an independence test. 

I know. But then it shouldn't use the "expected values" but calculate
them from the row and column sums of the observed values.

> On the other hand ...
> 
> > In the case of a Goodness-of-Fit test one would have observed and
> > expected frequencies (corresponding to each other) and the degree of
> > freedom should be n-1.
> 
> ... it gets two arrays passed, one of actual/observed values and one of
> expected values. See also the current definition in the latest draft
> document uploaded on Friday. If each column of observed values would
> represent a different group, matching those of the expected values, what
> would n-1 be then? 

So you really are performing several chi-sq tests in a single call?

> For example:
> 
> observed: x,y   expected: X,Y   =CHITEST(A1:B4;D1:E4)
> 
>  | A  B  C  D  E
> -+--------------
> 1| x  y     X  Y
> 2| x  y     X  Y
> 3| x  y     X  Y
> 4| x  y     X  Y
> 
> How would the (rows-1)*(cols-1) fit in there?

I can't see how that fits.

Neter/Wasserman/Whitmore:

When the sampled population has the probability distribution specified
in H0 and the samepl size n is resonably large then
X^2 is chi^2 distributed with k-m-1 degrees of freedom where k is the
number of classes and m the number of parameters estimated from the
sample data.

Andreas
> 
-- 
Andreas J. Guelzow, Professor
Dept. of Mathematical & Computing Sciences
Concordia University College of Alberta