# Generalized Mann-Whitney Type Tests

### Description

The function calculates p-values for different tests as presented in the paper "Generalized Mann-Whitney Type Tests for Microarray Experiments".

### Usage

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### Arguments

`X` |
Data matrix, each column corresponds to a variable, each row to an individual. Can also be a vector (one variable). |

`g` |
Vector of length |

`goi` |
Vector with elements of |

`test` |
Specifies the test statistic. |

`type` |
Permutation test ( |

`prob` |
This option is only for the Mann-Whitney test, see details. |

`nper` |
If type is |

`alternative` |
Specifies the alternative, the options are |

`mc` |
Multiple Cores, determines how many tests will be performed parallel (only available under Linux), see details. |

`output` |
Determines the level of the details in the output. |

`cluster` |
A vector of same length as |

`order` |
Boolean, shall all orders be calculated or only increasing orders? |

`keepPM` |
Boolean, keep the permutation matrices, required for Westfall & Young multiple testing adjustment. |

`mwAkw` |
Boolean or numeric, if |

`alg` |
Internal function, what permutation algorithm should be used. Shouln't be changed by the user. |

### Details

The object `X`

is the data vector (one variable) or the data matrix.
Each row refers to an observation, and each column to a variable. The tests are performed separately for all variables.

The vector `g`

gives the group number. The directional tests are based on this numbering of the group.

The `goi`

option defines, which treatment groups are used in the test constructions.
If no groups are specified (default), all groups are used.

The `test`

option specifies the test statistic. Possible options are `'uit'`

(union intersection test), `'triple'`

(test based on triple indicator functions),
`'jt'`

for Jonckheere-Terpstra test, `'jt*'`

for a modified Jonckheere-Terpstra test,
`'mw'`

for the Mann-Whitney / Wilcoxon test and
`'kw'`

for the Kruskal-Wallis test. See also reference [1] for further details.

The option `type`

is used to decide how the p-values are computed. For all tests are permutation type tests available
and the option for that is `type="permutation"`

. In addition for `test='mw'`

, `test='kw'`

or `test='jt'`

also the option `type='external'`

is available. This calls then the code from the base system or other, imported packages.
For `test='uit'`

there is also an asymptotic test (`type="asymptotic"`

) available. For `test='triple'`

or `test='jt*'`

asymptotic implementations are currently under development.

The `prob`

option is only for the Mann-Whitney test. For the option `"single"`

, the tests are to
compare a single group versus all the other groups. The option `"pair"`

makes all pair-wise comparisons
between the groups.

The option `alternative`

is used to specify whether one-sided or two-sided alternatives are used.
If the test is based on the PIs, the option `"greater"`

for example means that, according to the alternative,
the groups with larger group numbers tend to have larger observations as well. The function `createGroups`

may be used to renumber the groups, if needed.

The `mc`

option is only valid if `X`

is a matrix and the used OS is Linux, because the parallelisation is based
on the package parallel, and that again is based on the concept of forking, which is currently only supported under Linux.

The option `output`

can be used to control how detailed the output is. The default `"min"`

reports just
the matrix of p-values in a matrix (columns=variables, rows=tests). If `output="full"`

,
a list will be returned with items containing full test objects of class `htest`

.

The option `cluster`

is an additional object for the Kruskal-Wallis permutation test. For cluster-dependent
observation, only the permutations within clusters are acceptable for the p-value calculation.

In the `getSigTests`

function it is possible to apply the Westfall & Young multiple testing method. In this approach the
permutation matrix is used to adjust for multiple testing, hence if one wishes to apply this method, the only option for
`type`

is `"permutation"`

. In addition the boolean flag `keepPM`

has to be set to `TRUE`

. Is default is
to drop the permutation matrix after each run in order to save memory.

If a Kruskal-Wallis test is performed, there is also the option to perform afterwards paiwise Mann-Whitney tests to identify concrete, deviating groups.
If one wishes to do that just for significant variables one can set the option `mwAkw`

to the corresponding significance level. If `mwAkw`

is
set to `TRUE`

(or respective `1`

) the Mann-Whitney tests are performed for all variables.

There is also a function to choose the used calculation algorithm, options here are `"Rsubmat"`

, `"Rnaive"`

, `"Csubmat"`

, `"Cnaive"`

. The
purpose is just for validation.

### Value

A matrix or vector of p-values of the underlying hypothesis test(s). In case of `output="full"`

we give a list, and each list
item contains the `htest`

object for the column-wise performed test.

### Author(s)

Daniel Fischer

### References

Fischer, D., Oja, H., Schleutker, J., Sen, P.K., Wahlfors, T. (2013): Generalized Mann-Whitney Type Tests for Microarray Experiments, Scandinavian Journal of Statistic, doi: 10.1111/sjos.12055.

Daniel Fischer, Hannu Oja (2015). Mann-Whitney Type Tests for Microarray Experiments: The R Package gMWT. Journal of Statistical Software, 65(9), 1-19. URL http://www.jstatsoft.org/v65/i01/.

Westfall, P.H. and Young, S.S. (1993): Resampling-Based Multiple Testing: Examples and Methods for p-Value Adjustment. Wiley, New York.

### Examples

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