A function to compare correlations between studies. This function is intended to be used to compare the compatibility of original studies with replication studies (lower p-values indicating lower compatibility).

```
compare_cor(
r1,
df1,
r2,
df2,
method = c("fisher", "kraatz"),
alternative = c("two.sided", "less", "greater", "equivalence", "minimal.effect"),
null = 0
)
```

## Arguments

- r1
Correlation study 1.

- df1
Degrees of freedom from study 1 (if a simple correlation the df is N-2).

- r2
Correlation study 2.

- df2
Degrees of freedom from study 2 (if a simple correlation the df is N-2).

- method
Method for determining differences. Default, "z", will use Fisher's transformation, while "Kraatz" will use the Kraatz method.

- 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.

- null
a number indicating the null hypothesis. For TOST, this would be equivalence bound.

## Details

This function tests for differences between correlations.
@return A list with class "htest" containing the following components:

"statistic": z-score

"p.value": numeric scalar containing the p-value for the test under the null hypothesis.

"estimate": difference in SMD between studies.

"null.value": the specified hypothesized value for the null hypothesis.

"alternative": character string indicating the alternative hypothesis (the value of the input argument alternative). Possible values are "greater", "less", or "two-sided".

"method": Type of SMD.

"data.name": "Summary Statistics" to denote summary statistics were utilized to obtain results.

"cor": Correlation input for the function.

"call": the matched call.

## References

Counsell, A., & Cribbie, R. A. (2015). Equivalence tests for comparing correlation and regression coefficients. The British journal of mathematical and statistical psychology, 68(2), 292–309. https://doi.org/10.1111/bmsp.12045

Anderson, S., & Hauck, W. W. (1983). A new procedure for testing equivalence in comparative bioavailability and other clinical trials. Communications in Statistics-Theory and Methods, 12(23), 2663-2692.