# Kuder-Richardson Formula 20 (KR-20) Calculator

Welcome to the KR-20 Calculator! Follow the steps below to calculate the KR-20 for your data.

**Download the example file:**Click here to download an example file and follow these steps to prepare your data:- Open your original dataset in Excel.
- Ensure that each item/response is in its own column, and each participant's responses are in a separate row.
- Save your file as a CSV (Comma delimited) (*.csv).
- Open the saved CSV file in Notepad to copy the comma-separated values.

**Paste Your Data:**After copying your comma-separated values, paste them into the textarea below.**Generate Table:**Click the "Generate Table" button to view your data in tabular form.**Calculate KR-20:**After generating the table, click the "Calculate KR-20" button to get the result.

## KR-20 Formula

The Kuder-Richardson Formula 20 (KR-20) is a statistical measure used to assess the internal consistency of assessments with dichotomous choices (i.e., items that have two possible responses, such as true/false or yes/no).

Internal consistency refers to the extent to which all the items in a test measure the same construct or trait. Higher internal consistency indicates that the items are well correlated with each other, suggesting that they are all measuring the same underlying characteristic.

The KR-20 formula (Kuder & Richardson, 1937) 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 number of items
- \( p_i \) is the proportion of participants that got item \( i \) correct
- \( q_i = 1 - p_i \) is the proportion of participants that got item \( i \) incorrect
- \( \sigma^2_X \) is the variance of the total scores

## 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