# Permutation One-Way ANOVA Test

### Description

Performs a permutation (randomization) test for location, using trimmed data (trim = 0 gives untrimmed data) on several independent samples.

### Usage

1 | ```
perm.oneway.anova(x, y, trim = 0, ford = NULL, R = 9999)
``` |

### Arguments

`x` |
a (non-empty) vector of observations of the (response) variable. |

`y` |
a vector of the corresponding populations (levels of the factor). |

`trim` |
the fraction (0 to 0.5) of observations to be trimmed from each sample; default is 0. |

`ford` |
an optional integer vector giving the change from alphabetical order of the populations to some other desired order. |

`R` |
number of replications (default = 9999). |

### Details

The null hypothesis is that the distributions of the variable are identical on all the populations. The alternative hypothesis is that the distributions of the variable have systematically larger values on some of the populations than on others.

### Value

A list with class "perm.oneway.anova" containing the following components:

`Perm.values ` |
the values of the test statistic obtained from the permutations. |

`Header ` |
the main title for the output. |

`Response ` |
the name of the (response) variable. |

`Factor ` |
the name of the factor. |

`Levels ` |
the populations (levels of the factor). |

`n ` |
the sample sizes. |

`Mean ` |
the sample means. |

`SD ` |
the sample standard deviations. |

`Statistic ` |
the test statistic; here, always F.trim. |

`Observed ` |
the observed value of the test statistic. |

`P.value ` |
the P-value or a statement like P < 0.001. |

`p.value ` |
the P-value. |

`Trim ` |
the trim value. |

### Author(s)

Neil A. Weiss

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 | ```
# Last year's energy consumptions, to the nearest 10 million BTU, for
# independent random samples of households in the four U.S. regions.
data("energy")
str(energy)
attach(energy)
# Permutation one-way ANOVA to decide whether the energy distributions
# have systematically larger values in some U.S. regions than in others.
# Regions ordered to Northeast, Midwest, South, and West; 999 replications.
perm.oneway.anova(ENERGY, REGION, ford = c(2,1,3,4), R = 999)
detach(energy) # clean up
``` |