# Z.value: Calculate a Z score from a Wilcoxon statistic and a set of... In wgsea: Wilcoxon based gene set enrichment analysis

## Description

The mean of a Wilcoxon statistic is unaffected by correlation within the variable under test, but its variance is. This function uses a set of Wilcoxon statistics generated from permuted data to estimate the variance empirically, and thus calculate a Z score.

## Usage

 `1` ``` Z.value(W, Wstar, n.in, n.out) ```

## Arguments

 `W` Wilcoxon statistic for observed data. `Wstar` A vector of Wilcoxon statistics for a set of permuted data. `n.in` The number of items (SNPs) in the regions to be tested. `n.out` The number of items (SNPs) in the control regions.

## Value

A list with two elements:

Z.theoretical

which uses the theoretical mean of the Wilcoxon distribution under the null generated from n.in, n.out above

Z.empirical

which uses Wstar to calculate an empirical estimate of the mean of the Wilcoxon distribution under the null

## Note

The function can also deal with combining W statistics from multiple strata, as is typical in a meta analysis of GWAS data, using van Elteren's method. Strata may be defined by different geography or different SNP chips.

## Author(s)

Chris Wallace

`wilcoxon`

## Examples

 ```1 2 3 4 5 6 7 8``` ```x <- exp(-rexp(1000)) # uniform y <- exp(-rexp(1000,0.8)) # skewed towards 0 W <- wilcoxon(p=c(x,y),snps.in=1:1000) p.perm <- matrix(sample(c(x,y),replace=TRUE,size=10000),ncol=5) Wstar <- wilcoxon(p=p.perm,snps.in=1:1000) Z.value(W=W, Wstar=Wstar, n.in=1000, n.out=1000) ```

### Example output

```Loading required package: snpStats
\$Z.theoretical

Wilcoxon theoretical mean

data:  W
Z = 3.1023, p-value = 0.00192

\$Z.empirical

Wilcoxon empirical mean

data:  W
Z = 3.2212, p-value = 0.001277
```

wgsea documentation built on May 29, 2017, 7:02 p.m.