cor.test {ctest}R Documentation

Test for Zero Correlation

Description

cor.test tests the null that x and y are uncorrelated (independent).

Usage

cor.test(x, y, alternative = "two.sided", method = "pearson",
         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. Must be one of "pearson", "kendall", or "spearman". Only the first character is necessary.
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𤭫.


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