fuzzy.ranksum.test {fuzzyRankTests} | R Documentation |

Calculate the fuzzy P-value, the fuzzy decision, or the fuzzy confidence interval associated with the Mann-Whitney-Wilcoxon rank sum test.

fuzzy.ranksum.test(x, y, alternative = c("two.sided", "less", "greater"), mu = 0, tol = sqrt(.Machine$double.eps), alpha) fuzzy.ranksum.ci(x, y, alternative = c("two.sided", "less", "greater"), tol = sqrt(.Machine$double.eps), conf.level = 0.95)

`x` |
numeric vector of data values. |

`y` |
numeric vector of data values. |

`alternative` |
a character string specifying the alternative
hypothesis, must be one of |

`mu` |
a number specifying the value of the median of the data distribution hypothesized under the null hypothesis. |

`tol` |
data values within |

`alpha` |
if missing, calculate the fuzzy P-value. If provided, must be between zero and one, then calculate the fuzzy decision. |

`conf.level` |
confidence level. |

The fuzzy P-value is a random variable taking values in the interval
*(0, 1)*. Its cumulative distribution function (CDF) is continuous
and piecewise linear. Hence its probability density function (PDF) is
piecewise constant (a step function). If *P* is the fuzzy P-value,
considered as a random variable, then the randomized test that rejects
the null hypothesis at significance level *alpha* when
*P < alpha* is an exact (randomized) test.

The fuzzy confidence interval is a fuzzy set,
whose “membership function” is a function on the parameter space
taking values in the interval *[0, 1]*. For rank tests, it is
piecewise constant (a step function). In the regular case, it is one
on a narrow interval and some number between zero and one on the part
of some wider interval not contained in the narrower interval, zero
outside the wider interval, and the values at jumps are the average of left
and right limits. In this case, the fuzzy interval can be easily interpreted
as a mixture of two confidence intervals (the narrow and the wide).
When no ties are possible, the values at the jumps do not matter.
Otherwise, they do. With ties, any or all of the intervals can be
degenerate, and the values at the jumps are not related to left and right
limits. If *I(mu)* is the membership function of the fuzzy
confidence interval, then the randomized test that rejects the null
hypothesis that *mu* is the true parameter value with probability
*1 - I(mu)* is an exact (randomized) test.

A list with class `"fuzzyranktest"`

or class `"fuzzyrankci"`

containing some of the
following components:

`knots` |
the vector of points at which the CDF of the fuzzy P-value,
which is continuous and piecewise linear, has discontinuous derivative
or the vector of points at which the membership function of the fuzzy
confidence is discontinuous and also |

`values` |
the values of the CDF of the fuzzy P-value at the knots. |

`knot.values` |
the values of the membership function of the fuzzy confidence interval at the knots. |

`interval.values` |
the values of the membership function of the fuzzy confidence interval between the knots. |

`reject.prob` |
if |

`alpha` |
the argument |

`null.value` |
the argument |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
the type of test applied. |

`data.name` |
a character string giving the names of the data. |

`conf.level` |
the argument |

`tol` |
the argument |

Charles J. Geyer (submitted).

Fuzzy P-values and Ties in Nonparametric Tests.

http://www.stat.umn.edu/geyer/fuzz/ties.pdf

Charles J. Geyer and Glen D. Meeden (2005).

Fuzzy and Randomized Confidence Intervals and P-values.

To appear in *Statistical Science* (with discussion).

http://www.stat.umn.edu/geyer/fuzz/fuzz5.pdf

`plot.fuzzyrankci`

,
`plot.fuzzyranktest`

,
`print.fuzzyrankci`

,
`print.fuzzyranktest`

.

#### make up data #### x <- c(1, 2, 3, 4, 4, 4, 5, 6, 7) y <- c(4, 5, 7, 7, 8, 9, 10, 11) fuzzy.ranksum.test(x, y) plot(fuzzy.ranksum.test(x, y)) fuzzy.ranksum.ci(x, y) plot(fuzzy.ranksum.ci(x, y))

[Package *fuzzyRankTests* version 0.3-10 Index]