Standard errors of two-level scalability coefficients

For the construction of tests and questionnaires that require multiple raters (e.g., a child behaviour checklist completed by both parents) a novel ordinal scaling technique is currently being further developed, called two‐level Mokken scale analysis. The technique uses within‐rater and between‐rater coefficients to assess the scalability of the test. These coefficients are generalizations of Mokken's scalability coefficients. In this paper we derived standard errors for the two‐level coefficients and for their ratios. The coefficients, the estimates, the estimated standard errors and the software implementation are discussed and illustrated using a real‐data example, and a small‐scale simulation study demonstrates the accuracy of the estimates.