Description Usage Arguments Details Value Note Author(s) See Also Examples

This function assesses the significance of spatial bias by a one-sided random permutation test. This is achieved by comparing the observed average values of logged fold-changes within a spot's spatial neighbourhood with an empirical distribution generated by random permutation. The significance of spatial bias is given by the false discovery rate.

1 | ```
fdr.spatial(X,delta=2,N=100,av="median",edgeNA=FALSE)
``` |

`X` |
matrix of logged fold changes.
For alternative input format, see |

`delta` |
integer determining the size of spot neighbourhoods
( |

`N` |
number of random permutations performed for generation of empirical background distribution |

`av` |
averaging of |

`edgeNA` |
treatment of edges of array: For |

The function `fdr.spatial`

assesses the significance of spatial bias using a one-sided random permutation test.
The null hypothesis states random spotting i.e. the independence of log ratio `M`

and spot location. First, a neighbourhood of a spot is defined by a two dimensional square window
of chosen size ((2*delta+1)x(2*delta+1)). Next, a test statistic is defined by calculating
the *median* or *mean* of `M`

within
a symmetrical spot's neighbourhood. An empirical distribution of *median/mean of \code{M}* is generated
based
`N`

random permutations of the spot locations on the array. The randomisation and calculation of
*median/mean of \code{M}* is repeated `N`

times.
Comparing this empirical distribution of *median/mean of \code{M}*
with the observed distribution of *median/mean of \code{M}*,
the independence of `M`

and spot location
can be assessed. If `M`

is independent of spot's location,
the empirical distribution can be expected to be
distributed around its mean value. To assess the significance of observing positive deviations of
*median/mean of \code{M}*,
the false discovery rate (*FDR*) is used. It indicates the expected proportion of false discoveries
among rejected null hypotheses. It is defined as *FDR=q*T/s*,
where *q* is the fraction of *median/mean of \code{M}* larger than chosen threshold *c*
for the empirical distribution, `s`

is the number of neighbourhoods with
*(median/mean of \code{M})> c*
for the distribution derived from the original data and `T`

is the total number of neighbourhoods on the array. FDRs equal zero are set to
*FDR=1/T*N*.
Varying threshold *c* determines the FDR for each spot neighbourhood. Correspondingly, the significance
of observing negative deviations of *median/mean of \code{M}* can be determined.

A list of matrices containing the false discovery rates for positive (`FDRp`

)
and negative (`FDRn`

) deviations of
*median/mean of \code{M}* of the spot's neighbourhood is produced.

The same functionality but with our input and output formats is offered by `fdr.spatial`

Matthias E. Futschik (http://itb.biologie.hu-berlin.de/~futschik)

`p.spatial`

, `fdr.int`

, `sigxy.plot`

, `fdr.spatial2`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
# To run these examples, delete the comment signs before the commands.
#
# LOADING DATA
# data(sw)
# M <- v2m(maM(sw)[,1],Ngc=maNgc(sw),Ngr=maNgr(sw),
# Nsc=maNsc(sw),Nsr=maNsr(sw),main="MXY plot of SW-array 1")
#
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# For this illustration, N was chosen rather small. For "real" analysis, it should be larger.
# FDR <- fdr.spatial(M,delta=2,N=10,av="median",edgeNA=TRUE)
# sigxy.plot(FDR$FDRp,FDR$FDRn,color.lim=c(-5,5),main="FDR")
#
# LOADING NORMALISED DATA
# data(sw.olin)
# M<- v2m(maM(sw.olin)[,1],Ngc=maNgc(sw.olin),Ngr=maNgr(sw.olin),
# Nsc=maNsc(sw.olin),Nsr=maNsr(sw.olin),main="MXY plot of SW-array 1")
#
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# FDR <- fdr.spatial(M,delta=2,N=10,av="median",edgeNA=TRUE)
# VISUALISATION OF RESULTS
# sigxy.plot(FDR$FDRp,FDR$FDRn,color.lim=c(-5,5),main="FDR")
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.