bws_stat {BWStest} | R Documentation |

## Compute the test statistic of the Baumgartner-Weiss-Schindler test.

### Description

Compute the Baumgartner-Weiss-Schindler test statistic.

### Usage

bws_stat(x, y)

### Arguments

### Details

Given vectors *X* and *Y*, computes *B_X* and *B_Y* as
described by Baumgartner *et al.*, returning their average, *B*.
The test statistic approximates the variance-weighted square norm of the
difference in CDFs of the two distributions. For sufficiently large sample
sizes (more than 20, say), under the null the test statistic approaches the asymptotic
value computed in `bws_cdf`

.

The test value is an approximation of

*\tilde{B} = \frac{mn}{m+n} \int_0^1 \frac{1}{z(1-z)} ≤ft(F_X(z) - F_Y(z)\right)^2 \mathrm{dz},*

where *m* (*n*) is the number of elements in *X* (*Y*), and
*F_X(z)* (*F_Y(z)*) is the CDF of *X* (*Y*).

The test statistic is based only on the ranks of the input. If the same
monotonic transform is applied to both vectors, the result should be unchanged.
Moreover, the test is inherently two-sided, so swapping *X* and *Y*
should also leave the test statistic unchanged.

### Value

The BWS test statistic, *B*.

### Author(s)

Steven E. Pav shabbychef@gmail.com

### 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.
http://doai.io/10.2307/2533862

### See Also

`bws_cdf`

, `bws_test`

### Examples

set.seed(1234)
x <- runif(1000)
y <- runif(100)
bval <- bws_stat(x,y)
# check a monotonic transform:
ftrans <- function(x) { log(1 + x) }
bval2 <- bws_stat(ftrans(x),ftrans(y))
stopifnot(all.equal(bval,bval2))
# check commutivity
bval3 <- bws_stat(y,x)
stopifnot(all.equal(bval,bval3))

[Package

*BWStest* version 0.2.2

Index]