Blossom (version 1.4)

coverage: G-sample and goodness-of-fit tests based on empirical coverages

Description

G-sample and goodness-of-fit tests based on empirical coverages (COV) are for univariate comparisons of grouped data similar to the Kolmogorov-Smirnov family of statistics for comparing cumulative distribution functions (Mielke and Yao 1988, 1990). These statistics are appropriate for continuous univariate responses with no or few tied values. Options allow for testing goodness-of-fit to a uniform distribution on the unit circle, which is equivalent to a permutation version of Rao's spacing test (Rao 1976).

Usage

coverage(variable, group, expon = 1, interv = 0, number.perms, exact = FALSE,
save.test,data)

Arguments

variable

a vector for which the coverage test is to be performed.

group

the (optional) vector describing the grouping structure of the variable used in the analysis.

expon

allows selection of alternative exponents in distance calculations.

interv

tells the test how many units describe the circular units of measure recorded. This is only available for the 1-sample goodness-of-fit test.

number.perms

number of permutations used when not performing an exact test. The default is 4000 permutations.

exact

logical indicating whether to perform an exact coverage test. Only allowed for less than 24 observations.

save.test

logical indicating whether to return Monte Carlo resampled test statistic values.

data

the data.frame in which variable can be found.

Value

coverage returns an object of class CoverageObj.The functions summary as well as print can be used to obtain a summary of the test.Generic accessor functions pvalue and ResampVals can be used to obtain the p-value and Monte Carlo resampled test statistic values respectively.

Details

The default is to perform the test using Monte Carlo resampling. In this case two probabilities are reported, one which is the standard Monte Carlo approach of referencing the observed test statistic to those generated by the resampling, and a second which uses the resampled statistics to estimate the variance and skewness of the sampling distribution to be evaluated with the Pearson type III curve.

References

Mielke, P.W., and Y.C. Yao. 1988. A class of multiple sample tests based on empirical coverages. Annals of the Institute of Statistical Mathematics 40, 165--178.

Mielke, P.W. and Y.C. Yao. 1990. On g-sample empirical coverage tests: Exact and simulated null distributions of test statistics with small and moderate sample sizes. Journal Statistical Computation and Simulation 35, 31--39.

Rao, J.S. 1976. Some tests based on arc-lengths for the circle. Sankhya, Series B 38 329--338.

See Also

CoverageObj

Examples

Out <- coverage(variable = bgrouse$distance,group = bgrouse$sex,number.perms = 10000,
save.test = TRUE)
summary(Out)