hl2_test: Two-sample location tests based on two-sample Hodges-Lehmann...

In s-abbas/robTests: Robust Nonparametric Two-Sample Tests for Location/Scale

Two-sample location tests based on two-sample Hodges-Lehmann estimator.

Description

hl2_test performs a two-sample location test based on the two-sample Hodges-Lehmann estimator for shift.

Usage

hl2_test(
  x,
  y,
  alternative = c("two.sided", "greater", "less"),
  delta = ifelse(scale.test, 1, 0),
  method = c("asymptotic", "permutation", "randomization"),
  scale = c("S1", "S2"),
  n.rep = 10000,
  na.rm = FALSE,
  scale.test = FALSE,
  wobble = FALSE,
  wobble.seed = NULL
)

Arguments

x	a (non-empty) numeric vector of data values.
y	a (non-empty) numeric vector of data values.
alternative	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater", or "less".
delta	a numeric value indicating the true difference in the location or scale parameter, depending on whether the test should be performed for a difference in location or in scale. The default is delta = 0 for a location test and delta = 1 for a scale test. In case of scale.test = TRUE, delta represents the ratio of the squared scale parameters.
method	a character string specifying how the p-value is computed with possible values "asymptotic" for an asymptotic test based on a normal approximation, "permutation" for a permutation test, and "randomization" for a randomization test. The permutation test uses all splits of the joint sample into two samples of sizes m and n, while the randomization test draws n.rep random splits with replacement. The values m and n denote the sample sizes. If not specified explicitly, defaults to "permutation" if m < 30, n < 30 and n.rep >= choose(m + n, m), "randomization" if m < 30, n < 30 and n.rep < choose(m + n, m), and "asymptotic" if m >= 30 and n >= 30.
scale	a character string specifying the scale estimator used for standardization of the test statistic; must be one of "S1" and "S2". The default is "S1". Ignored if method = "asymptotic"; see details for the definition of the scale estimators.
n.rep	an integer value specifying the number of random splits used to calculate the randomization distribution if method = "randomization". This argument is ignored if method = "permutation" or method = "asymptotic". The default is n.rep = 10000.
na.rm	a logical value indicating whether NA values in x and y should be stripped before the computation proceeds. The default is na.rm = FALSE.
scale.test	a logical value to specify if the samples should be compared for a difference in scale. The default is scale.test = FALSE.
wobble	a logical value indicating whether the sample should be checked for duplicated values that can cause the scale estimate to be zero. If such values are present, uniform noise is added to the sample, see wobble. Only necessary for the permutation and randomization version of the test. The default is wobble = FALSE.
wobble.seed	an integer value used as a seed for the random number generation in case of wobble = TRUE or when scale.test = TRUE with one of the vectors x and y containing zeros. When no seed is specified, it is chosen randomly and printed in a message. The argument is ignored if scale.test = FALSE and/or wobble = FALSE.

Details

The test statistic for this test is based on the two-sample Hodges-Lehmann estimator of x and y, see hodges_lehmann_2sample. Three versions of the test are implemented: randomization, permutation, and asymptotic.

The test statistic for the permutation and randomization version of the test is standardized using a robust scale estimator, see \insertCiteFriDeh11roburobnptests.

With scale = "S1", the scale is estimated by

S = med(|x_i - x_j|: 1 ≤ i < j ≤ m, |y_i - y_j|, 1 ≤ i < j ≤ n),

whereas scale = "S2" uses

S = med(|z_i - z_j|: 1 ≤ i < j ≤ m + n).

Here, z = (z_1, ..., z_{m + n}) = (x_1 - med(x), ..., x_m - med(x), y_1 - med(y), ..., y_n - med(y)) is the median-corrected sample.

The randomization distribution is based on randomly drawn splits with replacement. The function permp \insertCitePhiSmy10permrobnptests is used to calculate the p-value. For the asymptotic test, a transformed version of the HL2-estimator, which asymptotically follows a normal distribution, is used. For more details on the asymptotic test, see \insertCiteFriDeh11robu;textualrobnptests.

For scale.test = TRUE, the test compares the two samples for a difference in scale. This is achieved by log-transforming the original squared observations, i.e. x is replaced by log(x^2) and y by log(y^2). A potential scale difference then appears as a location difference between the transformed samples, see \insertCiteFri12onli;textualrobnptests. Note that the samples need to have equal locations. The sample should not contain zeros to prevent problems with the necessary log-transformation. If it contains zeros, uniform noise is added to all variables in order to remove zeros and a message is printed.

If the sample has been modified (either because of zeros if scale.test = TRUE or wobble = TRUE), the modified samples can be retrieved using

set.seed(wobble.seed); wobble(x, y).

Both samples need to contain at least 5 non-missing values.

Value

A named list with class "htest" containing the following components:

statistic	the value of the test statistic.
p.value	the p-value for the test.
estimate	the estimated location difference between x and y (if scale.test = FALSE) or of log(x^2) and log(y^2) (if scale.test = TRUE) based on the two-sample Hodges-Lehmann estimator.
null.value	the specified hypothesized value of the mean difference/squared scale ratio.
alternative	a character string describing the alternative hypothesis.
method	a character string indicating how the p-value was computed.
data.name	a character string giving the names of the data.

References

\insertRef

PhiSmy10permrobnptests

\insertRef

FriDeh11roburobnptests

\insertRef

Fri12onlirobnptests

Examples

# Generate random samples
set.seed(108)
x <- rnorm(20); y <- rnorm(20)

# Asymptotic HL2 test
hl2_test(x, y, method = "asymptotic", scale = "S1")

## Not run: 
# HL22 test using randomization principle by drawing 1000 random permutations
# with replacement

hl2_test(x, y, method = "randomization", n.rep = 1000, scale = "S2")

## End(Not run)

s-abbas/robTests documentation built on Feb. 20, 2023, 10:14 a.m.