Test Analysis
Assessment analysis
Item Discrimination Index Calculator
Compare correct-response rates in equal-sized upper and lower groups.
Enter upper- and lower-group results
From inputs to result
Interpretation: The two groups may differ in size, so their rates are calculated before subtraction.
Selection and fairness questions remain
An item can distinguish performance groups because it measures intended knowledge, reading load, background familiarity, or another factor. The index alone cannot tell which explanation is correct.
Combine statistical review with expert content and accessibility review.
Upper and lower response groups
Twenty-four of 30 upper-group students and 11 of 30 lower-group students answer correctly. The discrimination index is 0.43, a 43.3-point rate gap.
Group construction changes the statistic
Define the upper and lower groups from the same total-score basis and administration.
Different cut proportions can yield different indices.
A companion calculation can pair discrimination with overall facility.
Negative values require investigation
A negative index can reflect a wrong key, ambiguous wording, multidimensional content, or sampling noise.
It is a diagnostic signal rather than automatic proof that an item is defective.
The work can also summarize correctness without group comparison.
Make the grouping reproducible
Save the total-score variable, ranking rules, group cut points, exclusions, and counts. Without them, another analyst may create different upper and lower populations.
If the analyzed item contributes to the total used for grouping, note that part-whole relationship.
Small groups produce unstable differences; report both correct counts and rates rather than the index alone.
Check subgroup fairness and content alignment separately, because a positive aggregate index does not establish unbiased functioning.
When upper and lower groups are based on a total containing the item, the relationship is partly mechanical. Analysts sometimes calculate a corrected relationship that excludes the item from the ranking score.
A low index for universally mastered essential content may be expected. Removal should depend on the blueprint and intended decision, not a universal numeric cutoff.
Compare the index with the item's facility and content role. Extremely easy or difficult items have limited room to distinguish groups, while a moderate facility can support a larger difference. This relationship helps explain a result but does not provide a universal accept-or-reject rule.
Questions about the result
Must the groups be the same size?
Equal sizes are common, but the rate calculation supports different valid group sizes.
Can the index exceed one?
No. With valid counts it ranges from −1 to 1.
Does a larger value always mean a better item?
No. Assessment purpose and essential content still govern interpretation.
Construct both performance groups
- Define the ranking score.
- Select nonoverlapping groups.
- Reconcile correct counts in each group.
- Review anomalous items with content evidence.