bws_test {BWStest}

Perform the Baumgartner-Weiss-Schindler hypothesis test.

Description

Perform the Baumgartner-Weiss-Schindler hypothesis test.

Usage

bws_test(
  x,
  y,
  method = c("default", "BWS", "Neuhauser", "B1", "B2", "B3", "B4", "B5"),
  alternative = c("two.sided", "greater", "less")
)

Arguments

x

a vector of the first sample.

y

a vector of the second sample.

method

a character string specifying the test statistic to use. should be one of the following:

default

This is “Hobson's choice”, which uses the classical BWS test for two-sided alternative, but Neuhauser for one sided alternatives.

BWS

Use the classical BWS test.

Neuhauser

Use Neuhauser's test.

B1

Use Murakami's B_1 test.

B2

Use Murakami's B_2 test, which is exactly Neuhauser's test.

B3

Use Murakami's B_3 test.

B4

Use Murakami's B_4 test.

B5

Use Murakami's B_5 test.

Only Neuhauser's test supports one-sided alternatives.

alternative

a character string specifying the alternative hypothesis, must be one of “two.sided” (default), “greater” or “less”. You can specify just the initial letter. “greater” corresponds to testing whether the survival function of x is greater than that of y; equivalently one can think of this as x being ‘greater’ than y in the sense of first order stochastic dominance.

Value

Object of class htest, a list of the test statistic, the p-value, and the method noted.

Note

The code will happily compute Murakami's B_3 through B_5 for large sample sizes, even though nominal coverage is not achieved. A warning will be thrown. User assumes all risk relying on results from this function.

Author(s)

Steven E. Pav [e-mail]

References

W. Baumgartner, P. Weiss, H. Schindler, 'A nonparametric test for the general two-sample problem', Biometrics 54, no. 3 (Sep., 1998): pp. 1129-1135. doi:10.2307/2533862

See Also

bws_test, bws_stat, murakami_stat, murakami_cdf.

Examples

# under the null
set.seed(123)
x <- rnorm(100)
y <- rnorm(100)
hval <- bws_test(x,y)

# under the alternative
set.seed(123)
x <- rnorm(100)
y <- rnorm(100,mean=1.0)
hval <- bws_test(x,y)
show(hval)
stopifnot(hval$p.value < 0.05)

# under the alternative with a one sided test.
set.seed(123)
x <- rnorm(100)
y <- rnorm(100,mean=0.7)
hval <- bws_test(x,y,alternative='less')
show(hval)
stopifnot(hval$p.value < 0.01)

hval <- bws_test(x,y,alternative='greater')
stopifnot(hval$p.value > 0.99)

hval <- bws_test(x,y,alternative='two.sided')
stopifnot(hval$p.value < 0.05)