R: Test for Zero Correlation

cor.test {ctest}

R Documentation

Test for Zero Correlation

Description

Tests whether two samples come from uncorrelated (independent) populations, using Pearson's product moment correlation coefficient, Kendall's tau, or Spearman's rho.

Usage

cor.test(x, y,
         alternative = c("two.sided", "less", "greater"),
         method = c("pearson", "kendall", "spearman"), exact = NULL)

Arguments

x, y

numeric vectors of data values. x and y must have the same length.

alternative

indicates the alternative hypothesis and must be one of "two.sided", "greater" or "less". You can specify just the initial letter.

method

a string indicating which correlation coefficient is used for the test. One of "pearson", "kendall", or "spearman", can be abbreviated.

exact

a logical indicating whether an exact p-value should be computed.

Details

If method is "pearson", the test statistic is based on Pearson's product moment correlation coefficient cor(x, y) and follows a t distribution with length(x)-2 degrees of freedom.

If method is "kendall" or "spearman", Kendall's tau or Spearman's rho, respectively, are used to estimate the correlation. These tests should be used if the data do not necessarily come from a bivariate normal distribution.

For Kendall's test, by default (if exact is not specified), an exact p-value is computed if both samples contain less than 50 finite values and there are no ties. Otherwise, the standardized estimate is used as the test statistic, and is approximately normally distributed.

For Spearman's test, p-values are computed using algorithm AS 89.

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

parameter

the degrees of freedom of the test statistic in the case that it follows a t distribution.

p.value

the p-value of the test.

estimate

the estimated correlation coefficient, with names attribute "cor", "tau", or "rho", correspoding to the method employed.

null.value

the value of the correlation coefficient under the null hypothesis, hence 0.

alternative

a character string describing the alternative hypothesis.

method

a string indicating how the correlation was estimated

data.name

a character string giving the names of the data.

References

D. J. Best & D. E. Roberts (1975), Algorithm AS 89: The Upper Tail Probabilities of Spearman's \rho. Applied Statistics, 24, 377–379.

Myles Hollander & Douglas A. Wolfe (1973), Nonparametric statistical inference. New York: John Wiley & Sons. Pages 185–194 (Kendall and Spearman tests).

Examples

## Hollander & Wolfe (1973), p. 187f.
## Assessment of tuna quality.  We compare the Hunter L measure of
##  lightness to the averages of consumer panel scores (recoded as
##  integer values from 1 to 6 and averaged over 80 such values) in
#   9 lots of canned tuna.
##  The null is that the Hunter L value is positively associated
##  with the panel score.
x <- c(44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1)
y <- c( 2.6,  3.1,  2.5,  5.0,  3.6,  4.0,  5.2,  2.8,  3.8)
cor.test(x, y, method = "kendall", alternative = "greater")
## => p=0.05972
##
cor.test(x, y, method = "kendall", alternative = "greater",
         exact = FALSE) # using large sample approximation
## => p=0.04765
## Compare this to
cor.test(x, y, method = "spearm", alternative = "g")
cor.test(x, y,                    alternative = "g")