Certiverse calculates item-writing assignments using a blueprint with weighted topics, exam parameters, and a margin to ensure sufficient items for independent forms and alignment with the blueprint's structure.
Certiverse calculates item-writing assignments based on a blueprint. A blueprint serves as a weighted outline of the exam content, with all weights adding up to 100%. It incorporates the following parameters:
- Number of Forms: Typically two or three forms are desired.
- Number of Scored Items: The total items that count toward the exam score.
- Margin: A buffer to account for item loss during reviews or beta testing. This ensures extra items are available for pretesting and other purposes. Programs that do not beta test or pretest items may prefer a margin of 0%.
Assignment Calculation Process
For each weighted topic or subtopic, the Certiverse system calculates item assignments using these blueprint parameters. When fractional assignments arise, the system rounds up to the nearest whole number to help ensure sufficient items. Additionally, it ensures the total number of assignments is at least equal to the number of forms. This increases the likelihood of building independent exam forms, even when some items are lost during reviews or testing.
Example Calculation
Imagine the following scenario:
- Topic 1 has a 9% weight.
- Subtopic 1.1 constitutes 33% of Topic 1’s weight (i.e., 3% of the exam total).
- For a 75-item exam, the calculation is:
75×0.03=2.2575 \times 0.03 = 2.2575×0.03=2.25 items for Subtopic 1.1.
After rounding, this would initially yield 2 items. However, to better align with the blueprint weight of 3%, the system generates 3 items. If all 3 items are operational, some forms will use 2 items, while others will use 3. On average, the number of items across all forms will match the target weight.
System Formula
Certiverse uses the following formula to calculate the number of item assignments for each topic or subtopic:
For a 75-item exam, consider Topic 1 with a 9% weight, and its subtopic, Topic 1.1, representing 33% of that weight (equivalent to 3% of the total exam). This calculation results in 75×0.03=2.2575 \times 0.03 = 2.2575×0.03=2.25 items for Topic 1.1. While rounding this down to 2 items would reduce the weight to 2.25%, the system instead generates 3 items to better align with the target 3% weight. If all 3 items are operational, 75% of the exam forms will use 2 items from Topic 1.1, and 25% will use 3 items, achieving an average of 2.25 items per form across the exam.
This is the actual calculation made by the system:
Number of assignments for a weighted topic/subtopic = max( trunc( 0.9999 + K*N*WEIGHT*(1+MARGIN)), K*trunc( 0.9999 + N*WEIGHT) )
Where:
- K = Number of forms (default: 3).
- N = Exam length, i.e., total scored items (default: 50).
- WEIGHT = Blueprint weight as a proportion of the total exam (e.g., 9% = 0.09).
- MARGIN = Default margin of 30% (0.3).
- max() = Returns the larger of two values.
- trunc() = Removes the decimal portion of a value.
- trunc(0.9999+X) rounds X up; for example, trunc(0.9999+2.25)=3
Key Points
- The system rounds up fractional item counts.
- Assignments are adjusted to align closely with blueprint weights.
- Ensuring enough items per form helps build independent exam forms, even with item losses.
Contact Us
If you have any questions or need additional assistance, please contact us by either emailing support@certiverse.com or by submitting a ticket from this article.