Theonly problem with applying Fisher's exact test to tables larger than 2x2 is that the calculations become much more difficult to do. The 2x2 version is the only one which is even feasible by hand, and so I doubt that Fisher ever imagined the test in larger tables because the computations would have been beyond anything he would have envisaged.
10 Matrix Mult: (2,3) entry; 11) Matrix Mult: Discovering I; 12) Matrix Mult: Inverses; 13) Matrix Mult: Showing Inverse; 14) Properties of Matrices; 15) Matrices, Systems of Equations, and AX=B; 16) Solving 2x2 System using AX=B; 17) Summary of Previous Solution; 18) Solve 3x3 System Using AX=B; 19) Definition AT (Transpose) 20) Practice AT
Tofind the p-value for a Fisher's exact test, we have to find all possible matrices of non-negative integers with the same row and column totals as the original table and then calculate the probability of each such table.The next step depends on whether you want to determine the one- or two-tailed p-value: two-tailed p-value. For a two-tailed test, you add together the probabilities of every
Sincepermutation matrices all satisfy the condition Pk = I P k = I (for some k k) the existence of a PLU P L U -decomposition for A A naturally suggests that Pk−1A = LU P k − 1 A = L U. Therefore, even when a LU L U decomposition is not available we can just flip a few rows to find a LU L U -decomposable matrix.
Remarks The identity matrix is the 3x2 matrix with ones on the main diagonal and zeros elsewhere. When an identity transform is applied to an object, it does not change the position, shape, or size of the object. It is similar to the way that multiplying a number by 1 does not change the number. Any transform other than the identity transform
45 - Fisher's Exact Test. The tests discussed so far that use the chi-square approximation, including the Pearson and LRT for nominal data as well as the Mantel-Haenszel test for ordinal data, perform well when the contingency tables have a reasonable number of observations in each cell, as already discussed in Lesson 1.
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can you add a 2x3 and a 3x2 matrix