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

This function assesses the significance of spatial bias. 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 permutation tests. The significance is given by (adjusted) p-values derived in one-sided permutation test.

1 | ```
p.spatial(X,delta=2,N=-1,av="median",p.adjust.method="none")
``` |

`X` |
matrix of logged fold changes |

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

`N` |
number of samples for generation of empirical background distribution |

`av` |
averaging of |

`p.adjust.method` |
method for adjusting p-values due to multiple testing regime. The available
methods are “none”, “bonferroni”, “holm”, “hochberg”,
“hommel” and “fdr”. See also |

The function `p.spatial`

assesses the significance of spatial bias using an 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`

for `N`

random samples
of size ((2*delta+1)x(2*delta+1)). Note that this scheme defines a sampling with replacement
procedure whereas sampling without replacement is used for `fdr.spatial`

.
Comparing the 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}*,
p-values are calculated using Fisher's method. The p-value equals the fraction of values in the empirical
distribution which are larger than the observed value . The minimal p-value is set to `1/N`

.
Correspondingly, the significance
of observing negative deviations of *median/mean of \code{M}* can be determined.

A list of vectors containing the p-values for positive (`Pp`

)
and negative (`Pn`

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

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

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, "un-comment" them!
#
# 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.
# P <- p.spatial(M,delta=2,N=10000,av="median")
# sigxy.plot(P$Pp,P$Pn,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
# P <- p.spatial(M,delta=2,N=10000,av="median")
# VISUALISATION OF RESULTS
# sigxy.plot(P$Pp,P$Pn,color.lim=c(-5,5),main="FDR")
``` |

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