num_to_schoice: Generate Single-Choice Question List from Numeric Solution

Description

A function for generating a single-choice question list for one correct numeric solution along with four wrong solutions.

Usage

num_to_schoice(correct, wrong = NULL, range = c(0.5, 1.5) * correct,
  delta = 1, digits = 2, method = c("runif", "delta"), sign = FALSE,
  verbose = getOption("num_to_choice_warnings"))

Value

num_to_schoice/num2schoice returns either NULL (if no suitable question list can be found) or a list with the following components:

solutions: a logical vector of length 5 indicating the correct solution,
questions: a character vector of length 5 with question list.

Arguments

correct: numeric vector of length 1 with correct solution.
wrong: numeric vector (optional) with wrong solutions.
range: numeric vector of length 2 with range of random wrong solutions.
delta: numeric. Minimal distance between solutions.
digits: integer. Digits that should be displayed.
method: character specifying method for generating random results.
sign: logical. Should the sign be changed randomly?
verbose: logical. Should warnings be issued if no suitable set of wrong solutions can be found?

Details

The function num_to_schoice (or equivalently num2schoice) can be used for generating a single-choice question list for a numeric correct solution. The question list always comprises five elements, one of which is the correct solution. The wrong solutions can be provided or are generated randomly. If wrong is provided only up to 2 elements of it are used in order to assure some random solutions.

Two methods can be used to generate the wrong solutions: Either simply runif or otherwise a full equi-distant grid for the range with step size delta is set up from which a discrete uniform sample is drawn. The former is preferred if the range is large enough while the latter performs better if the range is small (as compared to delta.

The function tries to avoid patterns in the question list that could be used for guessing the correct solution, e.g., situations where (almost) always the highest (or always the lowest) answer is the correct one. Therefore, internally num_to_schoice first randomly decides how many of the 4 wrong solutions should be to the left or to the right of the correct solution, respectively. And in a second step the sampling method is used to find these fixed numbers of wrong solutions to the left and right (if possible!).

Exercise templates using num_to_schoice should be thoroughly tested in order to avoid problems with too small ranges or almost identical correct and wrong answers! This can potentially cause problems, infinite loops, etc. See https://www.R-exams.org/tutorials/stresstest/ for some comments/hints regarding stress-testing of such exercise templates.

Examples

Run this code

set.seed(1)
## just a correct solution
num_to_schoice(123.45)

## or equivalently
set.seed(1)
num2schoice(123.45)

## just a correct integer solution
num_to_schoice(123, digits = 0)

## a correct solution with a wider range
num_to_schoice(123.45, range = c(0, 200))

## here, the defaults can't work...
## num_to_schoice(0.1234)

## alternatives could be
num_to_schoice(0.1234, range = c(0, 1), delta = 0.03, method = "delta")
num_to_schoice(0.1234, range = c(-5, 5), delta = 0.05)
num_to_schoice(0.1234, wrong = c(0.2749, 1.9723), delta = 0.05)
num_to_schoice(0.1234, wrong = c(0.2749, 1.9723), range = c(-5, 5), delta = 0.05)