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Convert a Correlation Coefficient (r) Into the Scale of Fisher's Z

Source: R/convert_r_Z.R
convert_r_Z.Rd

This function converts a correlation coefficient into the scale of Fisher's Z, the variance-stabilizing transformation of a correlation. Many authors call this map the z-prime transform and write the transformed value as z'. The capital Z is meaningful: Fisher's Z is not a z-score (it is not a standardized variate, that is, an observation centered and divided by a standard deviation). It is the transform \(Z = \mathrm{atanh}(r)\) of a correlation coefficient, applied because the sampling distribution of Z is approximately normal with a variance that does not depend on the population correlation, which makes Z convenient for forming confidence intervals.

Usage

convert_r_Z(r)

Arguments

r

Correlation coefficient (between two variables)

Value

A 1-row data.frame with columns term and value. The term is "Z_from_r" and value is Fisher's Z corresponding to the supplied correlation coefficient. The inverse direction is convert_Z_r.

Details

This function is typically used in the context of forming a confidence interval for a population correlation coefficient. Note that, in that situation, the two variables are assumed to follow a bivariate normal distribution (e.g., Hays, 1994).

References

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24. doi:10.18637/jss.v020.i08

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

See also

convert_Z_r, ci_r

Other parameterization conversions: convert_F_chisq(), convert_R2, convert_Z_r(), convert_cor_cov(), convert_d_or(), convert_d_r(), convert_t_smd, convert_z_normal()

Author

Ken Kelley kkelley@nd.edu

Examples

# From Hays (1994, pp. 649--650)
convert_r_Z(.35)
#>  term     value
#>  Z_from_r 0.365