Facility vs Discrimination by question number
This scatter plot visualises the relationship between question facility and discrimination for a given test. The plot allows for the identification of trends and outliers in question difficulty, and the detection of poorly discriminating questions, which may signal issues with answer keys or question design. On hover, you can view the facility and discrimination values, along with the question number.
Metrics
- Facility (x-axis): Represents the difficulty of a question, ranging from 0 to 1. A lower value indicates a more difficult question. It's calculated as the proportion of correct responses to total attempts, normalised to 1.
- Discrimination (y-axis): Indicates how effectively a question differentiates between high-performing and low-performing students, ranging from -1 to +1. A value of 0 suggests no differentiation, while negative values indicate that higher-performing students are more likely to answer incorrectly (potentially due to an error in the answer key). For more information, please refer to the point-biserial correlation coefficient.
Interpreting the Quadrants:
- Upper Right: Questions that are relatively easy and effectively differentiate between students.
- Upper Left: Questions that are challenging but still provide valuable discrimination.
- Lower Right: Questions that are easy but offer limited differentiation.
- Lower Left: Questions that are difficult and poorly discriminating, indicating potential problems.
- Negative Discrimination: Raises a red flag and warrants immediate investigation.
Important Note: While this graph is not currently showing very easy questions, it is important to remember that both very easy and very difficult questions often exhibit low discrimination. This is due to the inherent nature of these questions: most students will either answer them correctly (very easy) or incorrectly (very difficult), resulting in limited differentiation.
Facility by question number
As explained earlier, facility represents the difficulty of a question, ranging from 0 to 1. A lower value indicates a more difficult question. This graph plots the facility of all the questions in the selected assessment, giving us information about the sequential trend of difficulty in the assessment.
Discrimination by question number
Discrimination indicates how effectively a question differentiates between high-performing and low-performing students, ranging from -1 to +1. A value of 0 suggests no differentiation, while negative values indicate that higher-performing students are more likely to answer incorrectly.
This graph represents the sequential trend of discrimination in the selected assessment.