# ci.cc: Confidence interval for the population correlation... In MBESS: The MBESS R Package

 ci.cc R Documentation

## Confidence interval for the population correlation coefficient

### Description

This function is used to form a confidence interval for the population correlation coefficient. Note that this appraoch assumes that the variables the sample correlation coefficient are based are assumed to be bivariate normally distributed (e.g., Hays, 1994, Chapter 14).

### Usage

ci.cc(r, n, conf.level = 0.95, alpha.lower = NULL, alpha.upper = NULL)

### Arguments

 r observed value of the correlation coefficient (specifically the zero-order Pearson product-moment correlation coefficient) n sample size conf.level desired confidence level, where the error rate is the same on each side alpha.lower the Type I error rate for the lower confidence interval limit alpha.upper the Type I error rate for the upper confidence interval limit

### Details

Note that this appraoch to confidence intervals does will not generally lead to a symmetric confidence interval. The function first transforms r into Z^\prime , forms a confidence interval for the population value (i.e., \zeta), and then transforms the confidence limits for \zeta into the scale of the correlation coefficient.

### Value

 Lower.Limit  lower limit of the confidence interval Estimated.Correlation  observed value of the correlation coefficient Upper.Limit  upper limit of the confidence interval

### Note

This confidence interval assumes that the two variables the correlation is based are bivariate normal. See Hays (2004, Chapter 14) for details.

### Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

### References

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24.

Hays, W. L. (1994). Statistics (5th ed). Fort Worth, TX: Harcourt Brace College Publishers)

transform_Z.r, transform_r.Z

### Examples

# Example, from Hayes. Suppose n=100 and r=.35.
ci.cc(r=.35, n=100, conf.level=.95)

# Here is another way to enter the above example.
ci.cc(r=.35, n=100, conf.level=NULL, alpha.lower=.025, alpha.upper=.025)

# Here are examples of one-sided confidence intervals.
ci.cc(r=.35, n=100, conf.level=NULL, alpha.lower=0, alpha.upper=.05)
ci.cc(r=.35, n=100, conf.level=NULL, alpha.lower=.05, alpha.upper=0)


MBESS documentation built on Oct. 26, 2023, 9:07 a.m.