Range-Preserving Confidence Intervals and Significance Tests for Scalability Coefficients in Mokken Scale Analysis

Mokken’s scalability coefficients take values on the interval (−∞, 1]. The sampling distribution of scalability coefficients is skewed near the boundary, so Wald-based confidence intervals and significance tests may be biased. We introduce a transformation of the scalability coefficients and their standard errors, which can be used to construct range-preserving confidence intervals and significance tests. We demonstrated that for scalability coefficients away from the boundary, the properties of this range-preserving method are similar to the properties of the Wald-based method, but the range-preserving method outperforms the Wald-based method when the coefficient is close to unity. The range-preserving method can be applied to all types of scalability coefficients. Its implementation in software is discussed.