Abstract
An empirical study of test scores shows the variance of the errors of measurement to be significantly associated with true score in each of four groups studied; it also shows the distribution of the errors of measurement to be significantly skewed in three of these four groups. The mathematical rationale underlying the statistical treatment is presented. Standard error formulas are given for making the necessary significance tests.
Similar content being viewed by others
References
Cook, M. B. Bi-variatek-statistics and cumulants of their joint sampling distribution.Biometrika, 1951,38, 179–195.
Cramér, H.Mathematical methods of statistics. Princeton: Princeton Univ. Press, 1946.
Gulliksen, H.Theory of mental tests. New York: Wiley, 1950.
Kendall, M. G.The advanced theory of statistics. (5th ed.) New York: Hafner, 1952. 2 vols.
Lord, F. M. The joint cumulants of true values and errors of measurement.Ann. math. Statist., 1959,30, 1000–1004.
Lord, F. M. Do tests of the same length have the same standard error of measurement?Educ. psychol. Measmt., 1957,17, 510–521.
Lord, F. M. Statistical inferences about true scores.Psychometrika, 1959,24, 1–18.
Author information
Authors and Affiliations
Additional information
This research was in part carried out under Contracts Nonr-2214(00) and Nonr-2752(00) with the Office of Naval Research, Department of the Navy.
Rights and permissions
About this article
Cite this article
Lord, F.M. An empirical study of the normality and independence of errors of measurement in test scores. Psychometrika 25, 91–104 (1960). https://doi.org/10.1007/BF02288936
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02288936