# locationtests: Spatial sign and rank tests of multivariate location In SpatialNP: Multivariate Nonparametric Methods Based on Spatial Signs and Ranks

## Description

Multivariate tests of location of one or more samples based on spatial signs and (signed) ranks. In case of one sample the null hypothesis about a given location is tested. In case of several samples the null hypothesis is that all samples have the same location.

## Usage

 ```1 2 3``` ``` sr.loc.test(X, Y = NULL, g = NULL, score = c("sign", "rank"), nullvalue = NULL, cond = FALSE, cond.n = 1000, na.action = na.fail,...) ```

## Arguments

 `X` a matrix or a data frame `Y` an optional matrix or a data frame `g` a factor giving the groups (may contain just one level) `score` a character string indicating which transformation of the observations should be used `nullvalue` location to be tested in the one sample case (ignored if there is more than one sample) `cond` logical. Should the conditionally distribution free test be used? (Ignored if `score` is `"rank"`) `cond.n` number of permutations to use in the conditionally distribution free test `na.action` a function which indicates what should happen when the data contain 'NA's. Default is to fail. `...` further arguments to be passed to other functions

## Details

`X` should contain the the whole data set and `g` should describe the groups, or, if there is only one group, `g` may be missing. Alternatively, if there are two samples `X` may contain only the first sample while the second sample is given in `Y` and `g` is ignored. Note that in the one sample case when `rank` is chosen as `score` the function in fact uses signed ranks.

Note that the conditionally distribution free p-value is only provided for the sign based version of the test.

## Value

A list with class 'htest' containing the following components:

 `statistic ` the value of the statistic `parameter` the degrees of freedom for the statistic or the number of replications if conditionally distribution free p-value was used `p.value` the p-value for the test `null.value` the specified hypothesized value of the (common) location `alternative` a character string with the value 'two.sided'. `method` a character string indicating what type of test was performed `data.name` a character string giving the name of the data (and grouping vector)

## Author(s)

Seija Sirkia, [email protected]

## References

Oja, H., Randles R. (2004) Multivariate Nonparametric Tests. Statistical Science 19, 598-605.

 ```1 2 3 4 5 6``` ```A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3) X<-rbind(matrix(rnorm(1500),ncol=3),matrix(rnorm(750)+1,ncol=3))%*%t(A) sr.loc.test(X,cond=TRUE) X[1:250,]<-X[1:250,]+1 g<-factor(rep(c(1,2,3),each=250)) sr.loc.test(X,g=g,score="rank") ```