# An implementation of the Wilcox rank sum test / Mann-Whitney test that takes into account the direction / sign of gene set members and possibly the correlation between cases

### Description

This test evaluates whether the mean rank of statistics of gene set members is greater or less than the mean rank of the remaining statistic values. It extends the rankSumTestWithCorrelation function from the 'limma' package by taking into account the 'sign' of gene set members by reversing the ranks of down-regulated genes.

### Usage

1 2 |

### Arguments

`statistics` |
numeric vector giving values of the test statistic. |

`index.up` |
an index vector such that statistics[index.up] contains the values of the statistic for the up-regulated genes. |

`index.down` |
an index vector such that statistics[index.down] contains the values of the statistic for the down-regulated genes. |

`correlation` |
numeric scalar, average correlation between cases in the test group. Cases in the second group are assumed independent of each other and the first group. |

`df` |
degrees of freedom which the correlation has been estimated. |

`adjust.ties` |
logical: correct for ties ? |

`input.is.ranks` |
logical: is 'statistics' a vector of ranks ? If FALSE (default), ranks are computed. If FALSE, 'statistics' is assumed to represent ranks and is used directly. |

### Details

Please see the rankSumTestWithCorrelation function from the limma package for details.

### Value

Numeric vector containing U-statistic, z-score and p-value.

### Author(s)

Thomas Sandmann

### References

Wu, D, and Smyth, GK (2012). Camera: a competitive gene set test accounting for inter-gene correlation. Submitted.

Barry, W.T., Nobel, A.B., and Wright, F.A. (2008). A statistical framework for testing functional categories in microarray data. Annals of Applied Statistics 2, 286-315.

Zar, JH (1999). Biostatistical Analysis 4th Edition. Prentice-Hall International, Upper Saddle River, New Jersey.

### See Also

`rankSumTestWithCorrelation`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
genes.up <- c(1:10)
genes.down <- c(21:30)
set.seed(123)
scores <- matrix(rnorm(200), ncol=2)
## the first gene set receives increased /
## decreased scores in the first experiment
scores[genes.up,1] <- scores[genes.up ,1] + 1
scores[genes.down,1] <- scores[genes.down,1] - 1
## significantly greater
signedRankSumTest( statistics = scores[,1],
index.up = genes.up,
index.down = genes.down)
## not signficant
signedRankSumTest( statistics = scores[,2],
index.up = genes.up,
index.down = genes.down)
``` |