Test for Association/Correlation Between Paired Samples

[Stable]

Test for association between paired samples, using one of Pearson's product moment correlation coefficient, Kendall's \(\tau\) (tau) or Spearman's \(\rho\) (rho). Unlike the stats version of cor.test, this function allows users to set the null to a value other than zero.

z_cor_test(
  x,
  y,
  alternative = c("two.sided", "less", "greater", "equivalence", "minimal.effect"),
  method = c("pearson", "kendall", "spearman"),
  alpha = 0.05,
  null = 0
)

Arguments

x, y

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

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater", "less", "equivalence" (TOST), or "minimal.effect" (TOST). 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.

alpha

alpha level (default = 0.05)

null

a number indicating the null hypothesis. Default is a correlation of zero.

Value

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

  • "p.value": the p-value of the test.

  • "estimate": the estimated measure of association, with name "pb", "wincor", "cor", "tau", or "rho" corresponding to the method employed.

  • "null.value": the value of the association measure under the null hypothesis.

  • "alternative": character string indicating the alternative hypothesis (the value of the input argument alternative).

  • "method": a character string indicating how the association was measured.

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

  • "call": the matched call.

Details

This function uses Fisher's z transformation for the correlations, but uses Fieller's correction of the standard error for Spearman's \(\rho\) and Kendall's \(\tau\). See vignette("correlations") for more details.

References

Goertzen, J. R., & Cribbie, R. A. (2010). Detecting a lack of association: An equivalence testing approach. British Journal of Mathematical and Statistical Psychology, 63(3), 527-537. https://doi.org/10.1348/000711009X475853, formula page 531.

See also

Other Correlations: boot_cor_test(), corsum_test(), plot_cor(), power_z_cor()

Examples

# example code
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)
# Sig test
z_cor_test(x, y, method = "kendall", alternative = "t", null = 0)
#> 
#> 	Kendall's rank correlation tau
#> 
#> data:  x and y
#> z = 1.616, N = 9, p-value = 0.1061
#> alternative hypothesis: true tau is not equal to 0
#> 95 percent confidence interval:
#>  -0.1013291  0.7845858
#> sample estimates:
#>       tau 
#> 0.4444444 
#> 
# MET test
z_cor_test(x, y, method = "kendall", alternative = "min", null = .2)
#> 
#> 	Kendall's rank correlation tau
#> 
#> data:  x and y
#> z = 0.93028, N = 9, p-value = 0.1761
#> alternative hypothesis: minimal.effect
#> null values:
#>  tau  tau 
#>  0.2 -0.2 
#> 90 percent confidence interval:
#>  -0.008520225  0.746069903
#> sample estimates:
#>       tau 
#> 0.4444444 
#>