Re: Comparing fractions (or proportions)

Jack Tomsky wrote:

*** The Fisher test is based on the hypergeometric distribution, which has no parameter for the degrees of freedom. The Fisher test is UMP unbiased. This is in comparison with the Afonso Exact Test, which according to claims made by its author, has less power than a randomized test which ignores the data. Jack***


My response


1) LOL!
In the Hypergeometric Distribution there are the parameters:
___ n= the total number of objects
___n1=the number of objects of the FIRST CLASS
____r=the number of objects taken (without replacement)
If we draw r objects the probability to have x objects of the first class is:
______p(X=x; n, n1, r) =n1Cx * (n-n1)C(r-x) / nCr

which TOTALISE THREE PARAMETERS.


2) In the 2X2 CONTINGENCY TABLE

*** df are the quantities that can be freely got in a Distribution, therefore, owing to the marginal totals are fixed, is ONLY ONE DEGREE OF FREEDOM as I explained yet.


If the columns have NOT FIXED TOTALS, the df
is TWO:

___a11________a12________L1=a11+a12
___a21________a22________L2=a21+a22
___C1_________C2________N=C1 + C2=L1 + L2

Because N must be a fixed value, a11 AND a21 can vary, subjected to the conditions:
_______0<a11<L1______0<a12<L2
in order the table not to have NEGATIVE values or ZEROS.

For example
_2_4______5_1____
_1_8______5_4____


Elementary, WISE MAN (one of the three), elementary.

________licas (Luis A. Afonso)
.

Relevant Pages
Quantcast