Use this article to choose between dichotomous and polytomous scoring for items that have more than one possible answer. The choice affects how Cirrus awards partial credit.
In one sentence each
- Dichotomous: all-or-nothing. The candidate gets the full score only if every part is correct; partial credit scores 0.
- Polytomous: partial credit. The candidate receives a proportional score based on how many parts are correct.
These rules apply only to auto-scored items where the candidate can give more than one answer. For example: Multiple response, Fill in the blank, Select from list, Order, Match, Extended match, Comprehensive integrated puzzle.
Order example
A four-item Order question with max score 4:
| Outcome | Dichotomous | Polytomous |
|---|---|---|
| No values correct | 0 | 0 |
| 1 value correct | 0 | 1 |
| 2 values correct | 0 | 2 |
| All 4 correct | 4 | 4 |
Multiple response (MR): two polytomous models
For Multiple response, the author also chooses between two polytomous models based on how many options the candidate can select. Set in the item's Options tab.
Model 1: number of selectable answers equals correct options
The candidate is told (implicitly) how many are correct because the system limits selections to that number. Each correct selection earns a fraction of the score.
Example, with 5 alternatives and 2 correct (Barcelona and Paris):
Select the 2 cities with most tourist visits in 2018: Barcelona, Paris, Amsterdam, New York, Moscow.
| Outcome | Score |
|---|---|
| 0 correct | 0 |
| 1 correct out of 2 | 0.5 × max |
| 2 correct out of 2 | max |
Model 2: number of selectable answers has no limit
The candidate can tick as many alternatives as they like. Wrong selections cancel correct ones, so the candidate must also know which to leave unchecked. Some implementations cap the final score at 0 (cannot go negative); others penalise wrong selections directly.
This model penalises uncertainty and is the better choice for high-stakes assessments where candidates should not be rewarded for ticking everything.
Taking chance score into account
Polytomous scoring can be combined with a chance-score adjustment in the item options. With chance score on:
- The candidate's raw polytomous score is reduced by the probability of getting that level of correctness by guessing.
- Useful for closed-question types with few alternatives, where guessing has a meaningful chance of being partially correct.
See Item statistics > Chance score for the definition.
Where to set the rule
Open the item's Options tab and choose Scoring type: dichotomous or polytomous. For Multiple response, the polytomous-model choice appears once polytomous is selected.
Defaults vary by item type:
- Multiple response, Match, Extended match, Order: dichotomous by default; polytomous available.
- Fill in the blank, Select from list, Comprehensive integrated puzzle: dichotomous by default; polytomous available.
Picking the right rule
- Dichotomous when correctness is binary: the question is right or wrong, and partial answers should not count.
- Polytomous when partial knowledge deserves credit, for example ordering tasks or matching pairs.
- Polytomous with chance-score adjustment when guessing is plausible and you want to discount it.