trimmed_test {robnptests}

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 (Yuen and Dixon 1973). 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 (Phipson and Smyth 2010) 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 Fried (2012). 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

Yuen KK, Dixon WT (1973). “The approximate behaviour and performance of the two-sample trimmed t.” Biometrika, 60(2), 369–374. doi:10.2307/2334550.

Yuen KK (1974). “The two-sample trimmed t for unequal population variances.” Biometrika, 61(1), 165–170. doi:10.2307/2334299.

Fried R (2012). “On the online estimation of piecewise constant volatilities.” Computational Statistics & Data Analysis, 56(11), 3080–3090. doi:10.1016/j.csda.2011.02.012.

Examples

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

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