Convert a Standard Normal z Value to the Corresponding Value on a Normal Distribution

This function maps a value on the standard normal distribution (the z-distribution, with mean 0 and variance 1) to the equivalent point on a normal distribution with arbitrary mean and standard deviation, \(N(mean, sd^2)\).

Usage

convert_z_normal(z, mean = 0, sd = 1)

Arguments

z

A value on the standard normal distribution (with mean 0 and variance 1).

mean

The mean of the target normal distribution.

sd

The standard deviation of the target normal distribution.

Value

A 1-row data.frame with columns term and value. The term is "value_from_z" and value is the point on \(N(mean, sd^2)\) that lies at the same percentile as z does on the standard normal distribution.

Details

The conversion is value = mean + z * sd, which places the returned value at the same percentile of \(N(mean, sd^2)\) that z occupies on the standard normal distribution. Equivalently, value = qnorm(pnorm(z), mean, sd). With the defaults (mean = 0, sd = 1) the value is returned unchanged, since the target distribution is then the standard normal distribution itself.

See also

cv_z

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

Author

Ken Kelley kkelley@nd.edu

Examples

# A z value of 1.96 on the standard normal distribution maps to the
# corresponding point on a normal distribution with mean 100 and sd 15.
convert_z_normal(z = 1.96, mean = 100, sd = 15)
#>  term         value
#>  value_from_z 129  

# With the default standard normal target, the value is returned unchanged.
convert_z_normal(z = 1.96)
#>  term         value
#>  value_from_z 1.96