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.