Discrimination Index Calculator

The Discrimination Index is used to assess the quality of test items by determining how well a question differentiates between high-performing and low-performing test takers.

Historical Background

The Discrimination Index was developed as part of classical test theory to improve the reliability of standardized testing. It focuses on determining whether a test item is effective in distinguishing between students who have mastered the material and those who have not. It has been widely used in educational assessments and psychometrics to evaluate test performance.

Calculation Formula

The Discrimination Index is calculated using the following formula:

\[ D = \frac{\text{High Scorers Correct} - \text{Low Scorers Correct}}{\text{Total Group Size} \times 0.27} \]

Where:

• High Scorers Correct is the number of correct answers from the top 27% of scorers.
• Low Scorers Correct is the number of correct answers from the bottom 27% of scorers.
• Total Group Size is the total number of test takers.

Example Calculation

If you have 30 correct answers from the high scorers, 10 correct answers from the low scorers, and 100 total test takers:

\[ D = \frac{30 - 10}{100 \times 0.27} = \frac{20}{27} = 0.741 \]

The Discrimination Index for this test item is 0.741.

Importance and Usage Scenarios

The Discrimination Index helps educators and test designers identify which questions are effective at distinguishing between strong and weak students. A higher discrimination index indicates a well-functioning question, while a negative or low index may signal that the question is either too easy or ambiguous, requiring revision or removal.

Common FAQs

1. What is a good Discrimination Index value?

   • A good discrimination index typically falls between 0.30 and 0.50. Values above 0.50 are considered excellent, while values below 0.20 may suggest the item needs review.

2. What does a negative Discrimination Index mean?

   • A negative index means that lower-performing students answered the item correctly more often than higher-performing students. This indicates a problematic or misleading question.

3. How can I improve the Discrimination Index of a test item?

   • Review ambiguous questions, ensure that distractors (incorrect answer choices) are plausible, and adjust the difficulty to better align with the knowledge level being assessed.