Kuder-Richardson Formula 20 (KR-20) Calculator
Welcome to the Kuder-Richardson Formula 20 (KR-20) Calculator! Follow the steps below to calculate KR-20 for your dichotomous data.
- Prepare Your Data: Arrange your data with one subject per row and one dichotomous item per column (e.g., 1 for correct/yes, 0 for incorrect/no). Supported formats include CSV, Excel (.xlsx), and JSON.
- Upload Your Data File: Drag and drop your file into the designated area below.
- Calculate KR-20: After uploading and parsing your data, click the "Calculate KR-20" button to obtain the result.
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KR-20 Formula
The Kuder-Richardson Formula 20 (KR-20) is a statistical measure used to evaluate the internal consistency of tests that contain dichotomous items, meaning items with two possible responses, such as true/false or yes/no. It was developed by Kuder and Richardson in 1937 and is widely applied in fields like educational and psychological testing (Kuder & Richardson, 1937).
Internal consistency refers to how well the items on a test measure the same underlying construct or trait. If the items are highly correlated, it suggests that they are reliably assessing the same characteristic. A higher KR-20 value indicates better internal consistency, meaning the items work well together to measure the intended construct.
The KR-20 formula is expressed as:
\[ KR_{20} = \frac{K}{K-1} \left(1 - \frac{\sum_{i=1}^{K} p_i q_i}{\sigma^2_X}\right) \]Where:
- \( K \) is the total number of items on the test.
- \( p_i \) represents the proportion of test-takers who answered item \( i \) correctly.
- \( q_i = 1 - p_i \) represents the proportion of test-takers who answered item \( i \) incorrectly.
- \( \sigma^2_X \) is the variance of the total test scores across all items.
KR-20 is particularly useful for tests with dichotomous items because it assumes that all items measure the same construct. While conceptually similar to Cronbach's Alpha, KR-20 is specifically tailored for binary items. A high KR-20 value indicates that the test items are consistently measuring the intended trait, suggesting the overall test is reliable. Conversely, a low KR-20 value may suggest that some items are poorly correlated with others, either because they do not effectively measure the intended construct or due to poor item design.
One of the key advantages of KR-20 is its ability to detect inconsistencies in tests with dichotomous items. Unlike Guttman's Lambda-6, which accounts for varying item variances, KR-20 is more sensitive to item homogeneity and the range of item difficulty. If a test contains items that are too easy or too difficult, the KR-20 value may be lower, even if the items are otherwise valid. Therefore, while KR-20 offers valuable insights into test reliability, it should be used alongside other measures of test quality, such as item analysis and content validity (Brennan, 2006).
References
Brennan, R. L. (Ed.). (2006). Educational measurement (4th ed.). American Council on Education/Praeger.
Kuder, G.F. & Richardson, M.W. (1937). The Theory of the Estimation of Test Reliability. Psychometrika, 2, 151-160. https://doi.org/10.1007/BF02288391