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Column1 | Column2 | Total | |

Row1 | a | b | r1 |

Row2 | c | d | r2 |

Total | s1 | s2 | N |

- a is the number of 1 values in group 1.
- b is the number of 1 values in group 2.
- c is the number of 0 values in group 1.
- d is the number of 0 values in group 2.
- r1 = a + b
- r2 = c + d
- s1 = a + c
- s2 = b + d
- N = r1 + r2 = s1 + s2

- Swap Row1 and Row2.
- Swap Column1 and Column2.

- Chi1:
- E:

- Chi2:
- E:

- Chi3:
- E:

- Chi4:
- E:

- Chi-Square: Chi1 + Chi2 + Chi3 + Chi4

Column1 | Column2 | Total | |

Row1 | 0 | B | r1 |

Row2 | C | D | r2 |

Total | s1 | s2 | N |

- Determine the number of table probabilities to calculate by finding the smallest marginal total (least value among r1, r2, s1, s2) and adding 1.
- Generate the table for "Set 0"
- A = 0
- B = b + a
- C = c + a
- D = d - a
- Totals remain unchanged.

- Calculate the probability of "Set 0"
- :
- This is because in "Set 0" A! = 1, = 1, and = 1.

- Calculate probabilities for other tables where A = {1, 2, ..., smallest marginal total}
- :

- P-value: where <= +

- When the P-value gets very close to 1 and should in fact be 1, it is necessary to make a correction.

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Topic revision: r5 - 09 Dec 2004, WillGray

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