MCQ Distractor Efficiency Calculator
Enter one multiple-choice item’s response counts to identify distractors that students use and that attract the lower group more than the upper group.
Distractor efficiency100%
- Functioning distractors
- 3
- Effective option count
- 4
- Item facility
- 55%
- Item discrimination index
- 0.55
- Chance-adjusted target facility
- 62.5%
- Revision summary
- All distractors meet the 5% frequency rule and attract the lower group more often than the upper group.
Option diagnostic table
| Option | Overall rate | Upper rate | Lower rate | Discrimination | Assessment |
|---|---|---|---|---|---|
| A | 20% | 9.09% | 36.36% | -0.27 | Functioning distractor |
| B | 55% | 81.82% | 27.27% | 0.55 | Keyed answer |
| C | 20% | 9.09% | 27.27% | -0.18 | Functioning distractor |
| D | 5% | 0% | 9.09% | -0.09 | Functioning distractor |
A functioning distractor is selected by at least 5% of examinees and has negative upper-minus-lower discrimination.
Upper and lower groups must be separate groups whose option totals match their stated sizes.
How to use this calculator
- Choose the number of answer options and select the keyed answer.
- Enter the total response count for each active option; the counts must add to the number of examinees.
- Enter the corresponding option counts for equally defined upper and lower groups.
- Review the option table and revision summary before changing the item.
How distractor efficiency is calculated
A distractor is an incorrect option intended to appeal to examinees who have not yet mastered the material. This calculator treats a distractor as functioning only when it meets two checks: at least 5% of all examinees selected it, and the lower group selected it at a higher rate than the upper group.
For each option j, the overall selection rate is qj = nj ÷ N. Its option discrimination is dj = uj ÷ U − lj ÷ L, where n is the all-examinee count and u and l are the upper- and lower-group counts. An incorrect option functions when qj ≥ 0.05 and dj < 0.
With m active options, there are m − 1 distractors. If F of them function, then distractor efficiency = 100 × F ÷ (m − 1). The effective option count is 1 + F: one keyed answer plus the distractors that actually contribute to the item.
Reading the item statistics
Item facility is the proportion selecting the keyed answer: p = nk ÷ N. The item discrimination index here is the keyed option’s upper-group rate minus its lower-group rate. A positive value means the upper group chose the key more often, which is the expected direction. The chance-adjusted target facility is (1 + 1 ÷ m) ÷ 2, the midpoint between random guessing and perfect performance. It is a reference point, not a required score.
- A distractor below 5% may be implausible, too obviously wrong, or simply based on too few responses.
- A distractor with zero or positive discrimination attracts the upper group as much as, or more than, the lower group.
- A keyed answer with weak or negative discrimination calls for a review of the key, wording, scoring, and the skill being measured.
What this calculation does not decide
The 5% rule is a useful convention, not evidence that an option is valid. This tool does not measure content validity, accessibility, fairness, alignment with objectives, or the point-biserial correlation with total test score. It also assumes the supplied groups are separate and were formed consistently, often from the upper and lower 27% of total scores.
Small groups make each response influential, and omitted responses need a documented treatment before the option totals can be analyzed. Use the results as a prompt to inspect student reasoning and the item’s purpose, rather than as an automatic instruction to delete an option.
Worked example
Consider a four-option item answered by 40 examinees, keyed B. The total counts are A = 8, B = 22, C = 8, and D = 2. In upper and lower groups of 11, B is chosen by 9 upper-group and 3 lower-group examinees. A is chosen by 1 upper-group and 4 lower-group examinees; C by 1 and 3; and D by 0 and 1.
A and C each have a 20% overall rate and negative discrimination, so both function. D has negative discrimination but only a 5% rate, which still meets the threshold. The result is three functioning distractors, 100% distractor efficiency, an effective option count of four, 55% item facility, and an item discrimination index of 0.55. The chance-adjusted target for four options is 62.5%.
Common questions
What is a non-functioning distractor?
A non-functioning distractor is an incorrect option that does not contribute useful separation between stronger and weaker examinees. In this calculator, it is selected by fewer than 5% of examinees, or it is selected at least as often by the upper group as by the lower group.
Why use a 5% distractor frequency threshold?
The 5% threshold is a common item-analysis convention for identifying options that few examinees considered plausible. It is a screening rule rather than a universal standard, especially when the sample is small or the item measures a rare but important misconception.
Why should a distractor have negative option discrimination?
A useful incorrect option should appeal more often to the lower-scoring group than to the upper-scoring group. Negative upper-minus-lower discrimination shows that pattern; a zero or positive value can indicate ambiguity, a miscued key, or an option that rewards an unintended strategy.
How do I form upper and lower 27% groups?
Rank examinees by their total test score using a scoring rule that is independent of the item under review when practical. Take the highest and lowest roughly 27% using the same rounding rule, and enter their option counts; do not overlap the groups.
What does 100% distractor efficiency mean?
It means every incorrect option meets this calculator’s frequency and direction rules in this sample. It does not prove that the item is fair, aligned, or appropriate for its learning objective, so the wording and content still need expert review.