Test for Zero Correlation

DESCRIPTION:

Tests whether two vectors are uncorrelated using Pearson's product moment correlation coefficient, Kendall's tau-statistic, or Spearman's rank correlation.

USAGE:

cor.test(x, y, alternative="two.sided", method="pearson") 

REQUIRED ARGUMENTS:

x,y
numerical vectors. x and y must have the same length greater than 2. Missing values ( NAs) and +-Infs are allowed but ignored at calculation.

OPTIONAL ARGUMENTS:

alternative
a character string describing the alternative hypothesis for the test of correlation between x and y. "two.sided" (non-zero), "greater" (greater than 0), or "less" (less than 0).
method
the string "pearson", "kendall", or "spearman", depending on what coefficient of correlation should be used in the test statistic. Only the first character is necessary.

VALUE:

a list of class "htest", containing the following components:
statistic
the value of the test statistic, a t-statistic or a normalized z-statistic with names attribute.
parameters
the parameters of the null distribution of statistic containing its degrees of freedom when this is a t-distribution.
p.value
the p-value under the null hypothesis that the correlation between x and y is zero.
estimate
the value of the correlation coefficient with a names attribute which is either "tau" for Kendall's statistic, "cor" for Pearson's, or "rho" for Spearman's.
null.value
the hypothesized value for the correlation between x and y, coef=0.
alternative
the alternative hypothesis as entered, "two.sided", "greater", or "less" .
method
a string containing the name of the estimator used for the correlation coefficient: "Pearson\(aas product-moment correlation", "Kendall\(aas rank correlation tau", or "Spearman\(aas rank correlation".
data.name
a character string containing the actual names of the x and y vectors.

NULL HYPOTHESIS:

x and y are mutually uncorrelated.

TEST ASSUMPTIONS:

When method="pearson" the data are assumed to come from a bivariate Normal distribution. If this is not the case, the other two methods offer nonparametric alternatives.

DETAILS:

If method="pearson" the (usual) Pearson's product moment correlation coefficient ( r <- cor(x,y)) is computed, and divided by its standard error to produce a t-statistic with n-2 degrees of freedom, where n = length(x) = length(y). This statistic is given by t <- (sqrt(n-2)*r) / sqrt(1-r2).

If method="kendall" then Kendall's tau using ranks is computed.



If method="spearman" the rank correlation coefficient is used.

REFERENCES:

Conover, W. J. (1980). Practical Nonparametric Statistics. 2nd. ed. New York: Wiley.

SEE ALSO:

.

EXAMPLES:

murder <- state.x77[,"Murder"] 
illit <- state.x77[,"Illiteracy"] 
cor.test(murder,illit,method="k") 
# Transformations can be used 
cor.test(log(x),log(y),alt="gr")