perm.ind.spread {wPerm}

Permutation Test for Difference in Spread

Description

Performs a permutation (randomization) test for difference in spread (variation) based on independent samples from two populations.

Usage

perm.ind.spread(x, y, parameter, stacked = TRUE, variable = NULL,
                alternative = c("two.sided", "less", "greater"),
                R = 9999)

Arguments

x

a numeric vector of observations of the variable (stacked case) or a numeric vector of data values representing the first of the two samples (unstacked case).

y

a vector of corresponding population identifiers (stacked case) or a numeric vector of data values representing the second of the two samples (unstacked case).

parameter

the spread parameter under consideration (e.g., sd, var).

stacked

a logical value (default TRUE) indicating whether the data are stacked.

variable

an optional character string that gives the name of the variable under consideration; ignored if stacked is TRUE.

alternative

a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "less", or "greater".

R

number of replications (default = 9999).

Details

The null hypothesis is that the distributions of the variable on the two populations are identical—"identical".

The possible alternative hypotheses are:

Two tailed ("two.sided"): The distribution of the variable on the first population has a different spread than that of the variable on the second population—"different.spread".

Left tailed ("less"): The distribution of the variable on the first population has a smaller spread than that of the variable on the second population—"smaller.spread".

Right tailed ("greater"): The distribution of the variable on the first population has a larger spread than that of the variable on the second population—"larger.spread".

Value

A list with class "perm.ts.ind" containing the following components:

Stacked

TRUE if the data are stacked, FALSE otherwise.

Perm.values

the values of the test statistic obtained from the permutations.

Header

the main title for the output.

Variable

the name of the variable under consideration or NULL.

Pop.1

the first population.

Pop.2

the second population.

n.1

the sample size for the first population.

n.2

the sample size for the second population.

Statistic

the test statistic.

Observed

the observed value of the test statistic.

Null

the null hypothesis; here, always identical.

Alternative

the alternative hypothesis.

P.value

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

p.value

the P-value.

Author(s)

Neil A. Weiss

Examples

# Manufacturers use the Elmendorf tear test to evaluate material
# strength for various manufactured products. 
#
# Elmendorf tear strength, in grams, of two different vinyl floor
# coverings, Brand A and Brand B.
data("elmendorf")
str(elmendorf)
# Note that the data are stacked.

# Permutation test to decide whether there is a difference in spread of
# tear strength for Brand A and Brand B vinyl floor coverings, using the
# standard deviation as the spread parameter.
attach(elmendorf)
perm.ind.spread(STRENGTH, BRAND, sd)

detach(elmendorf)  # clean up

# Final-exam scores (out of 40 possible) for two groups of algebra
# students. One group, called the control group, was taught the usual
# algebra course; the other group, called the experimental group, was
# taught by a new teaching method.
data("control")
str(control)
data("experimental")
str(experimental)

# Permutation test to decide whether the new teaching method reduces
# variation in final-exam scores, using the variance as the spread
# parameter.
perm.ind.spread(control, experimental, var, stacked = FALSE,
variable = "Score", alternative = "greater")