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| Fisher's exact test |
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| The statistical significance of the difference between two bisulfite sequence groups at each CpG site is evaluated with Fisher's exact test that is non-parametric statistical significance test to determine if there are nonrandom associations between two categorical data. Fisher's exact test can use the same way as the Chi-square test for independence and more exact for small number of methylated CpGs or unmethylated CpGs, that is usually detected in CpG methylation analysis. Two-tailed p-value of Fisher's exact test is calculated from the 2 x 2 tables (exampled below) at each CpG site. This p-value is used to show the independence of CpG methylation between two groups at the CpG site. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Example 2 x 2 table for CpG methylation status |
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a: number of methylated CpGs of group1 at the CpG site b: number of unmethylated CpGs of group1 at the CpG site c: number of methylated CpGs of group2 at the CpG site d: number of unmethylated CpGs of group2 at the CpG site |
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| In case of sample data show in table1, this data can be transformed as table2. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| The probability p of this table can be determined by following formula: p = a+bCa * c+dCc / a+b+c+dCa+c = 13C12 10C4 / 23C16 = (13! 10! 16! 7!) / (12! 1! 4! 6! 23!) = 0.0111357212 where the symbol ! indicates the factorial operator. |
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| When the marginal totals are fixed, there are 9 cases indicated below. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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