# Spatial sign and rank tests of multivariate location

### 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 |

### 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 |

`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, seija.sirkia@iki.fi

### References

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

### See Also

Spatial signs and ranks

### Examples

1 2 3 4 5 6 |

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