Premium
Defining Score Scales in Relation to Measurement Error
Author(s) -
Kolen Michael J.
Publication year - 1988
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/j.1745-3984.1988.tb00295.x
Subject(s) - scale (ratio) , statistics , mathematics , variance (accounting) , rounding , nonlinear system , test score , confidence interval , transformation (genetics) , computer science , standardized test , biochemistry , physics , chemistry , accounting , quantum mechanics , business , gene , operating system
Scale scores for educational tests can be made more interpretable by incorporating score precision information at the time the score scale is established. Methods for incorporating this information are examined that are applicable to testing situations with number‐correct scoring. Both linear and nonlinear methods are described. These methods can be used to construct score scales that discourage the overinterpretation of small differences in scores. The application of the nonlinear methods also results in scale scores that have nearly equal error variability along the score scale and that possess the property that adding a specified number of points to and subtracting the same number of points from any examinee's scale score produces an approximate two‐sided confidence interval with a specified coverage. These nonlinear methods use an arcsine transformation to stabilize measurement error variance for transformed scores. The methods are compared through the use of illustrative examples. The effect of rounding on measurement error variability is also considered and illustrated using stanines