Statistics and Data Analysis for Microarrays Using R and Bioconductor, 2nd Edition

Classical approaches to data analysis 369

> za=qnorm(0.01,lower.tail=F)

> zb=qnorm(0.05)

> s=10

> mu=100

> mup=120

> za

[1] 2.326348

> zb

[1] -1.644854

> n=s^2*(za-zb)^2/(mup-mu)^2

> n

[1] 3.94261

This formula allows us to calculate the number of replicates needed in

order to detect a specific change in the gene expression assessed as a mean

of several replicate measurements, when the standard deviation is known and

specific thresholds have been chosen for the probability α of making a type I

error (false positives) and the power of the test 1 − β (the ability to detect

true positives).

Equation 12.13 is very meaning ful and illustrates several imp ortant phe-

nomena. First, the number of replicate measurements, or the sample size,

depe nds on the chosen significance ...