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Oplatek's external memory

Fishers test - true probability

We suppose $ a_{11} = min \{ a_{kl}; k \in 1..numberOfRows, l \in 1.. numberOfColumns\}$

$ P = \sum_{i=0}^{a_{11}} \frac{r_1! r_2! s_1! s_2!} { n! (a_{11}-i)! (a_{12}+1)! (a_{21}+i)! (a_{22}-i)!} $

Questions is why P represents PROBABILITY that random variables A,B are independent?

We usually reject hypothesis that that A,B are independent if the P is smaller $ \alpha = 0.05$

Example


  • Original table $ a_{11}$ represents that number of people injured on place A.






InjuredSurvived
A51015
B23840
74855



  • Switched rows to get minimum at $ a_{11}$:




    23840
    51015
    74855



  • P0:




    04040
    7815
    74855



  • P1:




    13940
    6915
    74855



  • P2:




    23840
    51015
    74855



  • Overall probability: $ P = P_0 + P_1 + P_2$