What is the formula for calculating the reliability of a test with dichotomous items?

The Kuder Richardson 20 formula is specifically designed for measuring the reliability of tests that consist of dichotomous items, where responses are typically scored as 0 or 1 (e.g., true/false or yes/no questions). This formula calculates the internal consistency of the test, enabling evaluators to determine how reliably the test items measure the same underlying construct.

Dichotomous items present a unique set of challenges for reliability assessment, and the Kuder Richardson 20 is tailored for these kinds of items. It addresses the proportion of variance that can be attributed to true score variance, providing a means to estimate reliability in a way that is appropriate for this format.

In contrast, other formulas mentioned serve different purposes. For example, Cronbach's alpha measures internal consistency but is more suitable for items that are scored on a continuous scale or have multiple response formats, while Spearman rank-order is used for assessing correlation between ranked variables. Test-retest reliability focuses on measuring consistency over time but does not specifically cater to tests with dichotomous items. This specificity makes the Kuder Richardson 20 the most appropriate choice for scenarios involving dichotomous test items.