TMM normalization examplified and explained

[LeonDK]

So according to the Robinson's 2010 paper on TMM normalization, the calculation of TMM factors, is given by:

If we then take this hypothetical count matrix:

    1   2   3   4   5
a 711 662 138 424 604
b 247 879 547 406 230
c 390 891 678 919 967
d  92 567 529 809 605
e 963 594  87 541 640
f  11 365 620 108 919
g 575 358  32 455 148
h 765 592 462  52 330
i 874 866 331 759 733
j  42 681 634  84 681

Could anyone briefly exemplify how to perform the calculation of the TMM factors manually?

I realise, that I can the normalization factors like so:

R
library(edgeR)
set.seed(13)
counts = as.data.frame(matrix( floor(runif(10*5,1,1001)), 10, 5))
rownames(counts) = letters[1:10]
colnames(counts) = seq(1,5)
d = DGEList(counts=counts)
d = calcNormFactors(d,method="TMM”)
d$samples$norm.factors
[1] 0.9412422 0.9510114 0.9604313 1.1794450 0.9862088

But i'd love to do a manual calculation, to understand the details of exactly how the TMM values are calculated

Cheers,
Leon

[dpryan]

Just look at the code for calcNormFactors. I recall it being fairly short.