1 2 | ```
proportion_distractors_less_than_given_proportion(exam,
numchoicesperitem = NULL, givenproportion = 0.05, check_format = TRUE)
``` |

`exam` |
A data.frame object containing a test that follows the formatting of a typical Scantron file. |

`numchoicesperitem` |
A vector which has the same length as the number of questions on the test, where each element in the vector corresponds to the number of choices there were for each of the questions on the test. For example, if your test had 35 questions which each had 5 options, numchoicesperitem = rep(5, 35). |

`givenproportion` |
The proportion for which you would like to calculate the proportion of the test's distractors that are less than this value. For example, one definition of a non-functional distractor is a distractor which less than 5 \itemcheck_formata logical value (default = TRUE) indicating whether the "exam" object should be tested for correct formatting. |

Returns a numerical value from 0 to 1 corresponding to the proportion of distractors on the test for which less than "givenproportion" of students chose the distractor. For example, if givenproportion = 0.05, and there were 200 total distractors on the test, and 30 of these distractors were chosen by less than 5 function would return 0.15 (which is 30/200). Finds the proportion of the test's distractors which were selected by less than a given proportion of the students. The argument "exam" must be in the format of a typical Scantron results file. Column 1 should correspond to ID (e.g., student number); column 2 should correspond to DEPT (e.g., MATH); column 3 should correspond to COURSE CODE (e.g., 1051); the remaining columns should each correspond to one of the questions on the test. The header of the data frame should contain the column names, and row 1 of the data frame should contain the answer key for the test. For example, if you had an exam with 25 students and 40 questions, the data.frame object should have 26 rows and 43 columns.

The "check_format" argument defaults to null. If this is left as null, the function will call
the `num_choices_per_item`

function, which will do its best to guess the number of options
for each question. This is done by looking at the student answers and finding the
"largest" answer for each question. For example, if at least one student answered "E", but no students
answered "F", the function would guess that there were 5 options for that question.

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