In common equipercentile equating methods such as the percentile-rank method or kernel equating (von Davier, Holland, & Thayer, 2004b), sample distributions of test scores are approximated by continuous distributions with positive density functions on intervals that include all possible scores. The use of continuous distributions with positive densities facilitates the equating process, for such distributions have continuous and strictly increasing distribution functions on intervals of interest, so conversion functions can be constructed based on the principles of equipercentile equating. When the density functions are also continuous, as is the case in kernel equating, the further gain is achieved that the conversion functions are differentiable. This gain permits derivation of normal approximations for the distribution of the conversion function, so estimated asymptotic standard deviations (EASDs) can be derived.
Normal Random Variable Quantile Function Conversion Function Continuous Random Variable Standard Normal Random Variable
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