trimmed_test: Two-sample trimmed t-test (Yuen's t-Test)

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

Two-sample trimmed t-test (Yuen's t-Test)

Description

trimmed_test performs the two-sample trimmed t-test.

Usage

trimmed_test(
  x,
  y,
  gamma = 0.2,
  alternative = c("two.sided", "less", "greater"),
  method = c("asymptotic", "permutation", "randomization"),
  delta = ifelse(scale.test, 1, 0),
  n.rep = 1000,
  na.rm = FALSE,
  scale.test = FALSE,
  wobble.seed = NULL
)

Arguments

x	a (non-empty) numeric vector of data values.
y	a (non-empty) numeric vector of data values.
gamma	a numeric value in [0, 0.5] specifying the fraction of observations to be trimmed from each end of the sample before calculating the mean. The default value is 0.2.
alternative	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater", or "less".
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.
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.
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.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 function performs Yuen's t-test based on the trimmed mean and winsorized variance \insertCiteYueDix73apprrobnptests. The amount of trimming/winsorization is set in gamma and defaults to 0.2, i.e. 20% of the values are removed/replaced. In addition to the asymptotic distribution a permutation and a randomization version of the test are implemented.

When computing a randomization distribution based on randomly drawn splits with replacement, the function permp \insertCitePhiSmy10permrobnptests is used to calculate the p-value.

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 because of zeros when scale.test = 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.
parameter	the degrees of freedom for the test statistic.
p.value	the p-value for the test.
estimate	the trimmed means of x and y (if scale.test = FALSE) or of log(x^2) and log(y^2) (if scale.test = TRUE).
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

YueDix73apprrobnptests

\insertRef

Yue74trimrobnptests

\insertRef

Fri12onlirobnptests

Examples

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

# Trimmed t-test
trimmed_test(x, y, gamma = 0.1)

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