This normalization is used when the two samples (control and treatment, say) are not being directly compared on the slides but instead are being compared to a common reference sample. The quantity of interest for each gene is thus the average difference between control and treatment log ratios. This function performs a robust normalization of the variance of the (mean normalized) average-across-replicates log ratio differences by scaling the (mean normalized) average-across-replicates log ratio difference for each gene either by the standard deviation of the log ratio differences for that gene across replicates (if bigger than the absolute (mean normalized) average-across-replicates log ratio difference) or scaling by a constant (a quantile of the distribution of standard deviations of (mean normalized) average-across-replicates log ratio differences for all genes whose standard deviation was bigger than their absolute (mean normalized) average-across-replicates log ratio difference.

1 2 | ```
norm2d(control.logratio, txt.logratio, control.logintensity, txt.logintensity,
span = 0.6, quant = 0.99)
``` |

`control.logratio` |
A multiple-column matrix of replicates of log (base 2) ratios of gene expressions for the control versus reference slides. |

`txt.logratio` |
A multiple-column matrix of replicates of log (base 2) ratios of gene expressions for the treatment versus reference slides. |

`control.logintensity` |
A multiple-column matrix of replicates of log (base 2) total intensities (defined as the product) of gene expressions for the control versus reference slides. |

`txt.logintensity` |
A multiple-column matrix of replicates of log (base 2) total intensities (defined as the product) of gene expressions for the treatment versus reference slides. |

`span` |
Proportion of data used to fit the loess regression of the average-across-replicates log ratio differences on the average-across-replicates log intensities. |

`quant` |
Quantile to be used from the distribution of standard deviations of log ratio differences across replicates for all genes whose standard deviation was smaller than their absolute (mean normalized) average-across-replicates log ratio difference. |

A vector of mean and variance normalized average-across-replicates log ratio differences.

N. Dean and A. E. Raftery

N. Dean and A. E. Raftery (2005). Normal uniform mixture differential gene expression detection for cDNA microarrays. BMC Bioinformatics. 6, 173-186.

http://www.biomedcentral.com/1471-2105/6/173

S. Dudoit, Y. H. Yang, M. Callow and T. Speed (2002). Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments. Stat. Sin. 12, 111-139.

`norm2c`

,`norm1a`

,`norm1b`

,`norm1c`

,`norm1d`

1 2 3 4 5 6 7 8 9 10 11 12 | ```
apo<-read.csv("http://www.stat.berkeley.edu/users/terry/zarray/Data/ApoA1/rg_a1ko_morph.txt",
header=TRUE)
rownames(apo)<-apo[,1]
apo<-apo[,-1]
apo<-apo+1
lRctl<-log(apo[,c(seq(2,16,2))],2)-log(apo[,c(seq(1,15,2))],2)
lRtxt<-log(apo[,c(seq(18,32,2))],2)-log(apo[,c(seq(17,31,2))],2)
lIctl<-log(apo[,c(seq(2,16,2))],2)+log(apo[,c(seq(1,15,2))],2)
lItxt<-log(apo[,c(seq(18,32,2))],2)+log(apo[,c(seq(17,31,2))],2)
lRnorm<-norm2d(lRctl,lRtxt,lIctl,lItxt)
``` |

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