# Function for normalizing the mean and variance 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. 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.

### Usage

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

### 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 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. |

### Value

A vector of mean and variance 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

`norm2c`

,`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<-norm2d(lRctl,lRtxt,lIctl,lItxt)
``` |

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