Convert between estimates, z-values, p-values, and confidence intervals

ci2se(lower, upper, conf.level = 0.95, ratio = FALSE)

ci2estimate(lower, upper, ratio = FALSE, antilog = FALSE)

ci2z(lower, upper, conf.level = 0.95, ratio = FALSE)

ci2p(lower, upper, conf.level = 0.95, ratio = FALSE, alternative = "two.sided")

z2p(z, alternative = "two.sided")

p2z(p, alternative = "two.sided")

p2ci(p, estimate, conf.level = 0.95, ratio = FALSE, alternative = "two.sided")

Arguments

lower: Numeric vector of lower confidence interval bounds.
upper: Numeric vector of upper confidence interval bounds.
conf.level: The confidence level of the confidence intervals. Default is 0.95.
ratio: Indicates whether the confidence interval is for a ratio, e.g. an odds ratio, relative risk or hazard ratio. If TRUE, the standard error of the log ratio is computed. Defaults to FALSE.
antilog: Indicates whether the estimate is reported on the ratio scale. Only applies if ratio = TRUE. Defaults to FALSE.
alternative: Direction of the alternative of the p-value. Either "two.sided" (default), "one.sided", "less", or "greater". If "one.sided" or "two.sided" is specified, the z-value is assumed to be positive.
z: Numeric vector of z-values.
p: Numeric vector of p-values.
estimate: Numeric vector of parameter estimates.

Value

ci2se returns a numeric vector of standard errors.

ci2estimate returns a numeric vector of parameter estimates.

ci2z returns a numeric vector of z-values.

ci2p returns a numeric vector of p-values.

z2p returns a numeric vector of p-values. The dimension of the output depends on the input. In general, the output will be an array of dimension c(nrow(z), ncol(z), length(alternative)). If any of these dimensions is 1, it will be dropped.

p2z returns a numeric vector of z-values. The dimension of the output depends on the input. In general, the output will be an array of dimension c(nrow(p), ncol(p), length(alternative)). If any of these dimensions is 1, it will be dropped.

p2ci returns a named numeric vector with the lower and upper bound of the confidence interval, or a matrix with columns lower and upper if p has length greater than 1.

Details

z2p is vectorized over all arguments.

p2z is vectorized over all arguments.

p2ci is the inverse of ci2p.

Examples

ci2se(lower = 1, upper = 3)
#> [1] 0.5102135
ci2se(lower = 1, upper = 3, ratio = TRUE)
#> [1] 0.2802634
ci2se(lower = 1, upper = 3, conf.level = 0.9)
#> [1] 0.6079568

ci2estimate(lower = 1, upper = 3)
#> [1] 2
ci2estimate(lower = 1, upper = 3, ratio = TRUE)
#> [1] 0.5493061
ci2estimate(lower = 1, upper = 3, ratio = TRUE, antilog = TRUE)
#> [1] 1.732051

ci2z(lower = 1, upper = 3)
#> [1] 3.919928
ci2z(lower = 1, upper = 3, ratio = TRUE)
#> [1] 1.959964
ci2z(lower = 1, upper = 3, conf.level = 0.9)
#> [1] 3.289707

ci2p(lower = 1, upper = 3)
#> [1] 8.857544e-05
ci2p(lower = 1, upper = 3, alternative = "one.sided")
#> [1] 4.428772e-05

z2p(z = c(1, 2, 5))
#> [1] 3.173105e-01 4.550026e-02 5.733031e-07
z2p(z = c(1, 2, 5), alternative = "less")
#> [1] 0.8413447 0.9772499 0.9999997
z2p(z = c(1, 2, 5), alternative = "greater")
#> [1] 1.586553e-01 2.275013e-02 2.866516e-07
z <- seq(-3, 3, by = 0.01)
plot(z, z2p(z), type = "l", xlab = "z", ylab = "p", ylim = c(0, 1))
lines(z, z2p(z, alternative = "greater"), lty = 2)
legend("topright", c("two-sided", "greater"), lty = c(1, 2), bty = "n")


p2z(p = c(0.005, 0.01, 0.05))
#> [1] 2.807034 2.575829 1.959964
p2z(p = c(0.005, 0.01, 0.05), alternative = "greater")
#> [1] 2.575829 2.326348 1.644854
p2z(p = c(0.005, 0.01, 0.05), alternative = "less")
#> [1] -2.575829 -2.326348 -1.644854
p <- seq(0.001, 0.05, 0.0001)
plot(p, p2z(p), type = "l", ylim = c(0, 3.5), ylab = "z")
lines(p, p2z(p, alternative = "greater"), lty = 2)
legend("bottomleft", c("two-sided", "greater"), lty = c(1, 2), bty = "n")

p2ci(p = 0.03, estimate = 0.5)
#>     lower     upper 
#> 0.0484142 0.9515858 
p2ci(p = 0.04, estimate = 2, ratio = TRUE)
#>    lower    upper 
#> 1.032159 3.875372 
p2ci(p = 0.03, estimate = 0.5, conf.level = 0.9)
#>     lower     upper 
#> 0.1210173 0.8789827 
p2ci(p = 0.015, estimate = 0.5, alternative = "greater")
#>     lower     upper 
#> 0.0484142 0.9515858