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Psychometrika

, Volume 28, Issue 3, pp 221–238 | Cite as

The statistical theory of stepped-up reliability coefficients when a test has been divided into several equivalent parts

  • Walter Kristof
Article

Abstract

This paper is a presentation of the statistical sampling theory of stepped-up reliability coefficients when a test has been divided into any number of equivalent parts. Maximum-likelihood estimators of the reliability are obtained and shown to be biased. Their sampling distributions are derived and form the basis of the definition of new unbiased estimators with known sampling distributions. These unbiased estimators have a smaller sampling variance than the maximum-likelihood estimators and are, because of this and some other favorable properties, recommended for general use. On the basis of the variances of the unbiased estimators the gain in accuracy in estimating reliability connected with further division of a test can be expressed explicitly. The limits of these variances and thus the limits of accuracy of estimation are derived. Finally, statistical small sample tests of the reliability coefficient are outlined. This paper also covers the sampling distribution of Cronbach's coefficient alpha.

Keywords

Sample Test Public Policy Statistical Sampling Statistical Theory Estimate Reliability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Psychometric Society 1963

Authors and Affiliations

  • Walter Kristof
    • 1
  1. 1.Educational Testing Service and University of Marburg/LahnGermany

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