The Discrimination Index Calculator is a tool used in educational assessment and psychological testing to measure the effectiveness of a test in distinguishing between high-performing and low-performing individuals. The discrimination index (DI) is a statistical measure that evaluates how well a test differentiates between groups of individuals who perform at different levels. It is typically used to assess the quality of test items, ensuring that they are effective at distinguishing between those who have mastered the content and those who have not.
The discrimination index is particularly useful in evaluating standardized tests, surveys, and any assessments where understanding the difference in performance between different groups is critical. A high discrimination index indicates that the test items are effective in differentiating between high and low performers, while a low discrimination index suggests that the test items may need to be revised or improved.
Formula of Discrimination Index Calculator
Discrimination Index (DI)
The formula to calculate the Discrimination Index (DI) is:
DI = (Proportion of Correct Answers for High Performers – Proportion of Correct Answers for Low Performers)
Where:
- Proportion of Correct Answers for High Performers is the percentage of correct responses given by the highest-performing group, typically the top 27% of participants (also called the upper group).
- Proportion of Correct Answers for Low Performers is the percentage of correct responses given by the lowest-performing group, typically the bottom 27% of participants (also called the lower group).
Key Points:
- The high-performing group consists of the top 27% of participants based on overall performance in the assessment.
- The low-performing group consists of the bottom 27% of participants.
- The result is a value between -1 and 1, where a higher positive value indicates that the test is better at distinguishing between high and low performers, while a value near 0 suggests that the test items may not be effective at distinguishing between groups.
General Terms for Discrimination Index Calculation
To help users understand the concepts involved in calculating the Discrimination Index, here is a table of general terms commonly searched when using the calculator:
| Term | Description |
|---|---|
| Discrimination Index (DI) | A measure of how well a test differentiates between high and low performers. |
| High Performers (Upper Group) | The top 27% of participants based on overall test performance. |
| Low Performers (Lower Group) | The bottom 27% of participants based on overall test performance. |
| Proportion of Correct Answers | The percentage of correct responses given by each group (high or low performers). |
| Test Item Discrimination | The ability of a test item to distinguish between high and low-performing individuals. |
| Reliability of the Test | The consistency and stability of test results over time or across different groups. |
This table provides a helpful overview of the key concepts involved in calculating and interpreting the discrimination index.
Example of Discrimination Index Calculator
Let’s go through an example to demonstrate how the Discrimination Index Calculator works.
Example 1: Calculating the Discrimination Index for a Test
Suppose we have the following information for a particular test:
- Proportion of Correct Answers for High Performers (Top 27%): 85% (0.85)
- Proportion of Correct Answers for Low Performers (Bottom 27%): 50% (0.50)
Now, using the formula:
DI = (Proportion of Correct Answers for High Performers – Proportion of Correct Answers for Low Performers)
DI = 0.85 – 0.50 = 0.35
In this case, the Discrimination Index (DI) is 0.35, which indicates a moderate ability of the test to differentiate between high and low performers.
Example 2: Low Discrimination Index
If the proportions for high and low performers were closer together, such as:
- Proportion of Correct Answers for High Performers (Top 27%): 70% (0.70)
- Proportion of Correct Answers for Low Performers (Bottom 27%): 60% (0.60)
Now, using the formula:
DI = (Proportion of Correct Answers for High Performers – Proportion of Correct Answers for Low Performers)
DI = 0.70 – 0.60 = 0.10
In this case, the Discrimination Index (DI) is 0.10, suggesting that the test does not do a good job of differentiating between high and low performers. The test items may need to be reviewed or modified to improve their effectiveness.
Most Common FAQs
A high discrimination index (closer to 1) indicates that the test items are effective in distinguishing between individuals who perform well and those who perform poorly. This means the test is good at identifying the level of knowledge or skill of the test takers.
A low discrimination index (close to 0 or negative) suggests that the test items are not distinguishing well between high and low performers. This could mean that the test items are too easy or too difficult for all participants, or that they are not aligned with the skills or knowledge being assessed.