wPerm (version 1.0.1)

perm.relation: Permutation Test for a Relationship

Description

Performs a permutation (randomization) test for a relationship (correlation, association) for two quantitative variables, using Pearson's r (product moment correlation coefficient), Spearman's rho (rank correlation coefficient), or Kendall's tau as the test statistic.

Usage

perm.relation(x, y, method = c("pearson", "kendall", "spearman"),
              alternative = c("two.sided", "less", "greater"),
              R = 9999)

Arguments

x

a numeric vector of data values representing the first variable.

y

a numeric vector of data values representing the second variable.

method

a character string indicating which method is to be used for the test; one of "pearson" (default), "kendall", or "spearman".

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.two.var" containing the following components:
• Perm.values
  the values of the test statistic obtained from the permutations.
• Header
  the main title for the output.
• Variable.1
  the name of the first variable.
• Variable.2
  the name of the second variable.
• n
  the sample size.
• Statistic
  the test statistic.
• Observed
  the observed value of the test statistic.
• Null
  the null hypothesis; here, always no relation.
• 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
• correlation test
• association test
• tests for a relationship
• Pearson's r
• Spearman's rho
• Kendall's tau

Details

The null hypothesis is that there is no relationship between the variables. The possible alternative hypotheses are: Two tailed ("two.sided"): There is a relationship between the variables---"relation". Left tailed ("less"): There is a negative relationship between the variables---"neg.relation". Right tailed ("greater"): There is a positive relationship between the variables---"pos.relation".

Examples

# Prices, in euros, of a 50cl bottle of water and distances, in meters,
# of convenience stores from the Contemporary Art Museum in El Raval,
# Barcelona.
data("water")
str(water)
attach(water)

# Permutation test to decide whether a negative relationship exists
# between price and distance, using Pearson's r as the test statistic.
perm.relation(PRICE, DISTANCE, alternative = "less")

# Permutation test to decide whether a negative relationship exists
# between price and distance, using Kendall's tau as the test statistic.
perm.relation(PRICE, DISTANCE, "kendall", "less")

# Permutation test to decide whether a negative relationship exists
# between price and distance, using Spearman's rho as the test statistic.
perm.relation(PRICE, DISTANCE, "spearman", "less")

detach(water)  # clean up.