Statistics
False Discovery Rate
False discovery rate control is a procedure that is less stringent than a classical Bonferroni correction.
Benjamini–Hochberg Controll Procedure
Rank the p-values from smallest to largest. Begin at 1, and increase the rank: 1, 2, 3, 4, 5, ... the rank is k.
Choose a false discovery rate q, for example q=0.1.
The total number of independent tests is m. If the level of gene expression for 20,000 genes is measured and tested then m=20,000.
Accept the tests with p-values lower than qk/m.
You estimate that a fraction q of these tests are false positives, due to random chance, but that the remaining ones are true positives.
Benjamini, Y., Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B. 57 (1): 289–300.
Normal Distribution
https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/stahl96.pdf
https://www.embedded.com/print/4413095
Derivation of the normal distribution from the binomial:
http://www.m-hikari.com/imf/imf-2017/9-12-2017/p/baguiIMF9-12-2017.pdf
