trend (version 1.1.6)

rrod.test: Robust Rank-Order Distributional Test

Description

Performs Fligner-Pollicello robust rank-order distributional test for location.

Usage

rrod.test(x, ...)
# S3 method for default
rrod.test(x, y, alternative = c("two.sided", "less", "greater"), ...)
# S3 method for formula
rrod.test(formula, data, subset, na.action, ...)

Value

A list with class "htest".

Arguments

x

a vector of data values.

...

further arguments to be passed to or from methods.

y

an optional numeric vector of data values.

alternative

the alternative hypothesis. Defaults to "two.sided".

formula

a formula of the form response ~ group where response gives the data values and group a vector or factor of the corresponding groups.

data

an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

Details

The non-parametric RROD two-sample test can be used to test for differences in location, whereas it does not assume variance homogeneity.

Let \(X\) and \(Y\) denote two samples with sizes \(n_x\) and \(n_y\) of a continuous variable.First, the combined sample is transformed into ranks in increasing order. Let \(S_{xi}\) and \(S_{yj}\) denote the counts of \(Y\) \((X)\) values having a lower rank than \(x_i\) \((y_j)\). The mean counts are:

$$\bar{S}_x = \sum_{i=1}^{n_x} S_{xi} / n_x$$

$$\bar{S}_y = \sum_{j=1}^{n_y} S_{yj} / n_y$$

The variances are: $$s^2_{Sx} = \sum_{i=1}^{n_x} \left( S_{xi} - \bar{S}_x \right)^2$$

$$s^2_{Sy} = \sum_{j=1}^{n_y} \left( S_{yj} - \bar{S}_y \right)^2$$

The test statistic is: $$ z = \frac{1}{2}~ \frac{n_x \bar{S}_x - n_y \bar{S}_y} {\left( \bar{S}_x \bar{S}_y + s^2_{Sx} + s^2_{Sy} \right)^{1/2}}$$

The two samples have significantly different location parameters, if \(|z| > z_{1-\alpha/2}\). The function calculates the \(p\)-values of the null hypothesis for the selected alternative than can be "two.sided", "greater" or "less".

References

Fligner, M. A., Pollicello, G. E. III. (1981), Robust Rank Procedures for the Behrens-Fisher Problem, Journal of the American Statistical Association, 76, 162--168.

Lanzante, J. R. (1996), Resistant, robust and non-parametric techniques for the analysis of climate data: Theory and examples, including applications to historical radiosonde station data, Int. J. Clim., 16, 1197--1226.

Siegel, S. and Castellan, N. (1988), Nonparametric Statistics For The Behavioural Sciences, New York: McCraw-Hill.

See Also

wilcox.test

Examples

## Two-sample test.
## Hollander & Wolfe (1973), 69f.
## Permeability constants of the human chorioamnion (a placental
##  membrane) at term (x) and between 12 to 26 weeks gestational
##  age (y).  The alternative of interest is greater permeability
##  of the human chorioamnion for the term pregnancy.
x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
rrod.test(x, y, alternative = "g")

## Formula interface.
boxplot(Ozone ~ Month, data = airquality)
rrod.test(Ozone ~ Month, data = airquality,
            subset = Month %in% c(5, 8))