confband: Confidence Bands

In smirnov: Exact Smirnov Two-sample Test and Q-Q Confidence Bands

Description

Computes confidence bands for functions defined by a model. There is a method for objects inheriting from class "ks.test".

Usage

confband(object, level = 0.95, ...)

Arguments

object	a fitted model object.
level	the confidence level required.
...	additional argument(s) for methods.

Details

confband is a generic function.

For objects of class "ks.test" a confidence band for the treatment function in two-sample parallel designs is computed following Switzer (1976). This function is also known as quantile-quantile plot.

Value

A matrix with columns giving the estimated function ("Estimate") as well as lower ("lwr") and upper ("upr") confidence limits for each function argument ("x"). Confidence bands control the coverage probability ("level") for all intervals simultaneously.

References

Paul Switzer (1976). Confidence Procedures for Two-sample Problems. Biometrika 63(1), 13–25. doi: 10.1093/biomet/63.1.13.

See Also

ks.test

Examples

# data from Switzer (1976)
angle <- c(-31, -30, -25, -25, -23, -23, -22, -20, -20, -18,
           -18, -18, -16, -15, -15, -14, -13, -11, -10, - 9,
           - 8, - 7, - 7, - 7, - 6, - 6, - 4, - 4, - 3, - 2,
           - 2, - 1,   1,   1,   4,   5,  11,  12,  16,  34,
           -31, -20, -18, -16, -16, -16, -15, -14, -14, -14,
           -14, -13, -13, -11, -11, -10, - 9, - 9, - 8, - 7,
           - 7, - 6, - 6,  -5, - 5, - 5, - 4, - 2, - 2, - 2,
             0,   0,   1,   1,   2,   4,   5,   5,   6,  17)
sex <- gl(2, 40, labels = c("Female", "Male"))

(sk <- ks.test(angle ~ sex))
cb <- confband(sk, level = .945)
plot(cb) # => no indication of deviation from the null because 
         # diagonal is covered by the confidence band

set.seed(29)
# artificial example
grp <- rep(gl(2, 1, labels = c("Group A", "Group B")), c(40, 60))
# shift model
x1 <- rnorm(length(grp), mean = c(1, 2)[grp], sd = 1)
# shift/scale model
x2 <- rnorm(length(grp), mean = c(1, 2)[grp], sd = c(1, .5)[grp])
layout(matrix(1:4, nrow = 2))
# treatment function is parallel to diagonal, `significant' 
# deviation from the null of both distributions being equal
# because diagonal not covered by confidence band
plot(confband(ks.test(x1 ~ grp)), main = "Shift model")
# true treatment function in blue
lines(-3:3, -3:3 + 1, col = "blue")
boxplot(x1 ~ grp)
# shift model not appropriate because treatment function
# is nonlinear, also `significant' deviation from null
plot(confband(ks.test(x2 ~ grp)), main = "Shift/scale model")
# true treatment function
lines(-3:3, qnorm(pnorm(-3:3, mean = 1, sd = 1), mean = 2, sd = .5), 
      col = "blue")
boxplot(x2 ~ grp)

smirnov documentation built on Sept. 5, 2021, 3 p.m.