wPerm (version 1.0.1)

perm.ind.spread: 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).

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.

concept

• permutation tests
• randomization tests
• tests for difference in spread
• independent-samples inferences

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".

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")