cor.test                package:ctest                R Documentation

_T_e_s_t _f_o_r _Z_e_r_o _C_o_r_r_e_l_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

    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 character string indicating which correlation coefficient
          is to be  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.

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

     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 character string indicating how the correlation was
          estimated.

data.name: a character string giving the names of the data.

_R_e_f_e_r_e_n_c_e_s:

     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).

_E_x_a_m_p_l_e_s:

     ## 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")

