Test for association between paired samples, using one of Pearson's product moment correlation coefficient, Kendall's $$\tau$$ (tau) or Spearman's $$\rho$$ (rho). This is the updated version of the TOSTr function.

corsum_test(
r,
n,
alternative = c("two.sided", "less", "greater", "equivalence", "minimal.effect"),
method = c("pearson", "kendall", "spearman"),
alpha = 0.05,
null = 0
)

## Arguments

r

observed correlation

n

number of pairs of observations

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:

• "statistic": z-score.

• "p.value": the p-value of the test.

• "estimate": the estimated measure of association, with name "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 $$\tau$$.

## 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.

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