# Function for normalizing the mean of average-across-replicates log ratio differences

### Description

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. The normalization is done for each gene by subtracting from its average-across-replicates log ratio difference the loess estimated mean for average-across-replicates log ratio difference based on the loess regression of average-across-replicates log ratio differences on average-across-replicates log total intensities.

### Usage

1 2 | ```
norm2c(control.logratio, txt.logratio, control.logintensity, txt.logintensity,
span = 0.6)
``` |

### Arguments

`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 total intensities. |

### Value

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

### Author(s)

N. Dean and A. E. Raftery

### References

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.

### See Also

`norm2d`

,`norm1a`

,`norm1b`

,`norm1c`

,`norm1d`

### Examples

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<-norm2c(lRctl,lRtxt,lIctl,lItxt)
``` |

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