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ERIC Number: EJ1061264
Record Type: Journal
Publication Date: 2015-Jun
Pages: 24
Abstractor: As Provided
Reference Count: 40
ISSN: ISSN-0013-1644
Descriptive Statistics for Modern Test Score Distributions: Skewness, Kurtosis, Discreteness, and Ceiling Effects
Ho, Andrew D.; Yu, Carol C.
Educational and Psychological Measurement, v75 n3 p365-388 Jun 2015
Many statistical analyses benefit from the assumption that unconditional or conditional distributions are continuous and normal. More than 50 years ago in this journal, Lord and Cook chronicled departures from normality in educational tests, and Micerri similarly showed that the normality assumption is met rarely in educational and psychological practice. In this article, the authors extend these previous analyses to state-level educational test score distributions that are an increasingly common target of high-stakes analysis and interpretation. Among 504 scale-score and raw-score distributions from state testing programs from recent years, nonnormal distributions are common and are often associated with particular state programs. The authors explain how scaling procedures from item response theory lead to nonnormal distributions as well as unusual patterns of discreteness. The authors recommend that distributional descriptive statistics be calculated routinely to inform model selection for large-scale test score data, and they illustrate consequences of nonnormality using sensitivity studies that compare baseline results to those from normalized score scales.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: Institute of Education Sciences (ED)
Authoring Institution: N/A
IES Funded: Yes
Grant or Contract Numbers: R305D110018