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A Scaling Method That Produces Scale Score Distributions With Specific Skewness and Kurtosis

Moses, Tim P.; Golub-Smith, Marna L.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Scaling, Equating Methods, Normal Distributions, Arcsine Transformations


A raw-to-scale transformation method that utilizes cubic functions is described for producing scale score distributions with a specified mean, standard deviation, skewness, and kurtosis. The method is demonstrated in four examples, two of which compare symmetric and skewed scaling results to those obtained from the traditional method based on normal distributions. A third example shows how the proposed raw-to-scale transformation method can be used to scale a test’s equated scores and standard errors of equating. A final example demonstrates how the proposed scaling method can be used to stabilize the conditional standard error of measurement when a hypothetical test distribution generated from an IRT model is scaled. The final discussion considers the flexibility of the proposed scaling method for developing raw-to-scale transformations that respond to multiple criteria.

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