MKinfer (version 1.4)

hsu.t.test: Hsu Two-Sample t-Test

Description

Performs Hsu two sample t-tests on vectors of data.

Usage

hsu.t.test(x, ...)
# S3 method for default
hsu.t.test(x, y,
       alternative = c("two.sided", "less", "greater"),
       mu = 0, conf.level = 0.95, ...)
# S3 method for formula
hsu.t.test(formula, data, subset, na.action, ...)

Value

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

statistic

the value of the t-statistic.

parameter

the degrees of freedom for the t-statistic.

p.value

the p-value for the test.

conf.int

a confidence interval for the mean appropriate to the specified alternative hypothesis.

estimate

the estimated means and standard deviations.

null.value

the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test.

stderr

the standard error of the difference in means, used as denominator in the t-statistic formula.

alternative

a character string describing the alternative hypothesis.

method

a character string indicating what type of t-test was performed.

data.name

a character string giving the name(s) of the data.

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". You can specify just the initial letter.

mu

a number indicating the true value of the mean (or difference in means if you are performing a two sample test).

conf.level

confidence level of the interval.

formula

a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs a factor with two levels giving the corresponding groups.

data

an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

...

further arguments to be passed to or from methods.

Details

The function and its documentation was adapted from t.test.

alternative = "greater" is the alternative that x has a larger mean than y.

If the input data are effectively constant (compared to the larger of the two means) an error is generated.

Following the recommendation of Section 6.8.3 and 7.4.4.2 of Hedderich and Sachs (2018), one should at least have six observations per group to apply the test.

The test is conservative, but is a valid alternative when the sample sizes are very small in one group and larger in the second group as considered in Adusah and Brooks (2011).

References

A.K. Adusah, G.P. Brooks (2011). Type I Error Inflation of the Separate-Variances Welch t test with Very Small Sample Sizes when Assumptions Are Met. Journal of Modern Applied Statistical Methods 10, 362-372.

J. Hedderich, L. Sachs. Angewandte Statistik: Methodensammlung mit R. Springer 2018.

P. Hsu (1938). Contribution to the theory of ``student's'' t-test as applied to the problem of two samples. Statistical Research Memoirs 2, 1-24.

See Also

t.test

Examples

## Examples taken and adapted from function t.test
t.test(1:10, y = c(7:20))      # P = .00001855
t.test(1:10, y = c(7:20, 200)) # P = .1245    -- NOT significant anymore
hsu.t.test(1:10, y = c(7:20))
hsu.t.test(1:10, y = c(7:20, 200))

## Traditional interface
with(mtcars, t.test(mpg[am == 0], mpg[am == 1]))
with(mtcars, hsu.t.test(mpg[am == 0], mpg[am == 1]))
## Formula interface
t.test(mpg ~ am, data = mtcars)
hsu.t.test(mpg ~ am, data = mtcars)