lecture_10 - Three-way Contingency Tables Lecture 10 ILRST...

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    Three-way Contingency Tables Lecture 10 ILRST 212
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         Fishers exact test Fishers exact test is a procedure that you can use for data in  a two by two contingency table. It is an alternative to Chi- square test. A two by two table contingency table arises in a variety of  contexts, most often when a new therapy is compared to a  standard therapy (or a control group) and the outcome  measure is binary (live/dead, diseased/healthy,  infected/uninfected etc)
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      Fishers exact test Fishers exact test is based on exact probabilities from a specific  distribution (the hypergeometric distribution). The hypergeometric distribution is used for calculating probabilities for  samples drawn from relatively small populations and without replication.  The Chi-square test relies on a large sample approximation.  Therefore , you may prefer to use Fisher’s Exact test in situations where  a large sample approximation is inappropriate.
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        Fishers exact test There is really no lower bound on the amount of data that is needed for  Fisher’s Exact test.  We need to have atleast one data value in each row and one data value  in each column. We don’t have a 2 by 2 table if the entire row or column is zero. We can use Fishers exact test when one of the cells in the table has  zero. If one or two of the cells in a two by two table have large numbers in the  thousands and one or two of the other cells has number less than 5 , we  can still use Fishers Exact test.
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       Hypergeometric distribution A random variable  x  has a hypergeometric  distribution if its probability distribution is given by h ( x;n,N,k ) =                             for  x  = 0,1,2,..,n x k - - x n k N n N
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