Biserial Estimators in the Presence of Guessing

Daniel Ashler

Journal of Educational and Behavioral Statistics, 1979, vol. 4, issue 4, 325-355

Abstract: As estimators of correlation of a criterion variable with the continuous latent variable that underlies a dichotomous test item score, both the biserial correlation coefficient, r b , and Brogden’s coefficient of selective efficiency, S * , are severely depressed (negatively biased) by guessing, regardless of sample size or true latent correlation. Formulas and charts are given for computing better estimates, r̂ and Ŝ * , free of guessing bias, based on observed proportions of right, wrong, and omitted answers. In Monte Carlo studies both r̂ and Ŝ * had smaller mean square errors in the presence of guessing than r b and S * , and Ŝ * stayed on target even when the latent and criterion variable were given (the same) rectangular, bimodal, or chi square distribution.

Keywords: Latent Correlation; Guessing; Biserial Correlation; Selective Efficiency; Topastic (search for similar items in EconPapers)
Date: 1979
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:4:y:1979:i:4:p:325-355

DOI: 10.3102/10769986004004325

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