mean2.ttest {SHT}

Two-sample Student's t-test for Univariate Means

Description

Given two univariate samples x and y, it tests

H_0 : \mu_x^2 \left\lbrace =,\geq,\leq \right\rbrace \mu_y^2\quad vs\quad H_1 : \mu_x^2 \left\lbrace \neq,<,>\right\rbrace \mu_y^2

using the procedure by Student (1908) and Welch (1947).

Usage

mean2.ttest(
  x,
  y,
  alternative = c("two.sided", "less", "greater"),
  paired = FALSE,
  var.equal = FALSE
)

Arguments

x

a length-n data vector.

y

a length-m data vector.

alternative

specifying the alternative hypothesis.

paired

a logical; whether consider two samples as paired.

var.equal

a logical; if FALSE, use Welch's correction.

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

p-value under H_0.

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

References

Student (1908). “The Probable Error of a Mean.” Biometrika, 6(1), 1. ISSN 00063444.

Student (1908). “Probable Error of a Correlation Coefficient.” Biometrika, 6(2-3), 302–310. ISSN 0006-3444, 1464-3510.

Welch BL (1947). “The Generalization of ‘Student’s' Problem when Several Different Population Variances are Involved.” Biometrika, 34(1/2), 28. ISSN 00063444.

Examples

## empirical Type 1 error 
niter   = 1000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  x = rnorm(57)  # sample x from N(0,1)
  y = rnorm(89)  # sample y from N(0,1)
  
  counter[i] = ifelse(mean2.ttest(x,y)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'mean2.ttest'\n","*\n",
"* number of rejections   : ", sum(counter),"\n",
"* total number of trials : ", niter,"\n",
"* empirical Type 1 error : ",round(sum(counter/niter),5),"\n",sep=""))