Description Usage Arguments Details Author(s) References Examples

The function `qanova`

calculates the Wald-type statistic based on the
quantiles and/or their linear combinations, e.g. the interquartile range. Respective p-values
are obtained by a *χ^2*-approximation and a permutation approach, respectively.

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`formula` |
A model |

`data` |
A data.frame, list or environment containing the variables in formula
and the censoring status
indicator. Default option is |

`quantiles` |
A vector of probabilties corresponding to the quantiles of interest. By default is c(0.5), i.e. just the median is included. |

`lin_mat` |
A matrix specifying which linear combination of the quantiles should be
included for the analysis. By default ( |

`var_method` |
Method for the variance estimation of the sample quantiles. The default ("interval") is the interval-based estimator of Price and Bonett (2001). Additionally, the bootstrap method ("boot") of Efron (1987) or a kernel density approach ("kernel") can be chosen. |

`nperm` |
The number of permutations used for calculating the permuted p-value. The default option is 1999. |

`var_level` |
A number between 0 and 1 specifying the confidence level for the interval variance estimation method; the default value is 0.95. |

`nested.levels.unique` |
A logical specifying whether the levels of the nested factor(s) are labeled uniquely or not. Default is FALSE, i.e., the levels of the nested factor are the same for each level of the main factor. |

The `qanova`

function calculates the Wald-type statistic based on quantiles
and linear combinations of them for general factorial designs. The procedure is fully
nonparametric and no specific assumption of the underlying distribution is required.
In particular, heteroscedastic settings can be studied. The analysis can be based on a single
quantile (e.g. the median, default choice), a linear combination of quantiles (e.g. the
interquartile range, set `quantiles=c(0.25,0.75)`

and `lin_mat = matrix(c(-1,1),ncol=2)`

)
or on several (combinations of) quantiles simulatenously.

The `qanova`

function returns the test statistic as well as two
corresponding p-values: the first is based on a *chi^2* approximation and
the second one is based on a permutation procedure.

@return A `qanova`

object containing the following components:

pvalues_statThe p-values obtained by

*χ^2*-approximationpvalues_perThe p-values of the permutation approach

statisticsThe value of the qanova along with degrees of freedom of the central chi-square distribution and p-value, as well as the p-value of the permutation procedure.

npermThe number of permutations used for calculating the permuted p-value.

Philipp Steinhauer

Ditzhaus, M., Fried, R. and Pauly, M. (2021). QANOVA: Quantile-based Permutation Methods For General Factorial Designs. TEST (to appear, ArXiv preprint arXiv:1912.09146). Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Ann. Statist., 7:1-26. Price, R. and Bonett, D. (2001). Estimating the variance of the sample median. J. Stat. Comput. Simul, 68:295-305.

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