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---+ Permutation TTest Algorithm Performed on a set of non-negative numbers and labels of size N. There must be two specific labels. Label 1 must be 1 and label 2 must be 2. There can also be any other labels that will be ignored. ---++++ Permutation T value 1 Find the number and sum of each group. * Na: number of values in group 1 * Nb: number of values in group 2 * Sa: %$\sum X_i$% * Sb: %$\sum Y_i$% * SSa: %$\sum {X_i}^2$% * SSb: %$\sum {Y_i}^2$% 1 Compute the sample mean of each group. * Ma: %$\frac{Sa}{Na}$% * Mb: %$\frac{Sb}{Nb}$% 1 Compute the variance for each group. 1 Estimate the variance * varA: %$SSa - \frac{Sa^2}{Na}$% * varB: %$SSb - \frac{Sb^2}{Nb}$% * Var: %$\frac{varA + varB}{Na + Nb - 2}$% 1 Estimate the standard deviation (stDev): %$\sqrt{\frac{Var}{Na} + \frac{Var}{Nb}}$% 1 t: %$\frac{Ma - Mb}{stDev}$% ---++++ Permutation T probability 1 Calculate raw P value based on original grouping of each gene. <br> %$P_0$% = %$2 * (1 - probt(|t|, Na + Nb - 2))$% 1 Randomly regrouping each gene. <br> The size in each group stays the same as the original, each sample can only appare once in each group, number of regrouping depends on user. 1 For each regrouped gene, recalculate P value. <br> %$P_n$% = %$2 * (1 - probt(|t|, Na + Nb - 2))$% 1 Count if %$P_n$% less than or equals to %$P_0$%.<br> count = number of %$P_n$% <= %$P_0$% 1 Calculate permutation P value. <br> PP-value = %$ \frac{count}{NumRegrouping}$% 1 Rank PP-value by ascending order, calculate False Discovery Rate P value. <br> FDR P-value = %$ \frac{TotalNumOfGene}{rank}$%*PP-value ---++++ summary of running time | sample size | group size | permutation time | running time | | 10| 5 vs. 5| 252 | 0.01 | | 10| 5 vs. 5| 5,000 | 0.406 | | 20| 10 vs. 10| 10,000 | 0.56 | | 20| 10 vs. 10| 1,847,560 | 87.746 | | 50| 25 vs. 25| 10,000 | 1.261 | | 50| 25 vs. 25| 50,000 | 14.703 | -- Main.JoanZhang - 16 Aug 2004
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Topic revision: r3 - 02 Sep 2004,
JoanZhang
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