SHT (version 0.1.9)

mean1.ttest: One-sample Student's t-test for Univariate Mean

Description

Given an univariate sample \(x\), it tests $$H_0 : \mu_x = \mu_0\quad vs\quad H_1 : \mu_x \neq \mu_0$$ using the procedure by Student (1908).

Usage

mean1.ttest(x, mu0 = 0, alternative = c("two.sided", "less", "greater"))

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.

Arguments

x

a length-\(n\) data vector.

mu0

hypothesized mean \(\mu_0\).

alternative

specifying the alternative hypothesis.

References

student_probable_1908SHT

student_probable_1908aSHT

Examples

## empirical Type 1 error 
niter   = 1000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  x = rnorm(10)         # sample from N(0,1)
  counter[i] = ifelse(mean1.ttest(x)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'mean1.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=""))