hypothesis_latex {exams.forge}

Latex Hypothesis

Description

Creates a data frame for a test hypothesis with various columns:

• h0.left left value of the null hypothesis, usually ⁠\mu⁠ or ⁠\pi⁠

• h0.operator operator of the null hypothesis, one of the following: eq, ne, lt, le, gt, or ge

• h0.right right value of the null hypothesis, usually ⁠\mu_0⁠, ⁠\pi_0⁠, or a hypothetical value

• h1.left left value of the alternative hypothesis, usually ⁠\mu⁠ or ⁠\pi⁠

• h1.operator operator of the alternative hypothesis, one of the following: eq, ne, lt, le, gt, or ge

• h1.right right value of the alternative hypothesis, usually ⁠\mu_0⁠, ⁠\pi_0⁠, or a hypothetical value

• H0 latex representation of the null hypothesis

• H1 latex representation of the alternative hypothesis

• match.left do the left value in the null and the alternative hypothesis match?

• match.right do the right value in the null and the alternative hypothesis match?

• match.operator do the operators in the null and the alternative hypothesis cover all real numbers?

• match.right do the right value in the null and alternative hypothesis match?

• match.type either wrong, left.sided, right.sided, two.sided, greater, or less.

If null is not given then it is determined from alternative. Otherwise hypotheses pairs are generated by all combinations from alternative and null. Valid values for alternativeand null are two.sided, greater, less, eq, ne, lt, le, gt, or ge.

Usage

hypothesis_latex(
  left,
  alternative = NULL,
  null = NULL,
  right = paste0(left, "_0")
)

lhypo(left, alternative = NULL, null = NULL, right = paste0(left, "_0"))

Arguments

left

character: symbol, for example "\mu" or "\pi"

alternative

character: alternative hypotheses

null

character: null hypotheses (default: NULL)

right

character: a symbol (default: paste0(left, "_0"))

Value

A data frame with hypothesis pairs.

Examples

# Create one hypotheses pair
hypothesis_latex("\\mu")
hypothesis_latex("\\pi")
hypothesis_latex("\\mu", alternative="two.sided")
hypothesis_latex("\\mu", alternative="two.sided", null="lt")
hypothesis_latex("\\mu", alternative="ne", null="eq")
hypothesis_latex("\\mu", right=c(0,1))
hypothesis_latex("\\mu", alternative=c("eq", "ne", "lt", "le", "gt", "ge"))
hypothesis_latex("\\mu", alternative=c("eq", "ne", "lt", "le", "gt", "ge"), 
                         null=c("eq", "ne", "lt", "le", "gt", "ge"))