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Reliability and Validity in Classical Test Theory

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A Course in Rasch Measurement Theory

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Abstract

In CTT, reliability is defined as the proportion of true score variance to total variance. It is most often estimated using the coefficient \( \alpha \). This index assumes the instrument is unidimensional and is not a test of unidimensionality. Construct validation addresses the substantive dimension of the variable assessed.

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References

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Further Reading

  • Andrich, D. (1988). Rasch models for measurement (pp. 84–86). Newbury Park, CA: Sage.

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  • Andrich, D. (2016). Components of variance of scales with a bi-factor structure from two calculations of coefficient alpha. Educational Measurement: Issues and Practice,35(4), 25–30.

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  • Roscoe, J. T. (1975). Fundamental research statistics for the behavioral sciences (2nd ed.). New York: Holt, Reinhart and Winston.

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Author information

Authors and Affiliations

  1. Graduate School of Education, The University of Western Australia, Crawley, WA, Australia

    David Andrich & Ida Marais

Authors
  1. David Andrich
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  2. Ida Marais
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Corresponding author

Correspondence to David Andrich .

Exercises

Exercises

In the Exercises of Chap. 3, you were given a table of person–item responses.

  1. 1.

    Calculate the variance of each of the eight items in the test and the total score and summarize them as below:

    A table has 9 columns and 2 rows. The upper row entries are as follows: s superscript 2 with subscripts from 1 through 8 and y. The lower row is empty.
  2. 2.

    Calculate the reliability of this test according to coefficient \( \alpha \). Show your working. Use the variances of the eight items and the variance of the total score that you calculated in question 1.

  3. 3.

    Comment on the size of the reliability.

  4. 4.

    Consider a test or examination with which you are familiar with. Describe the test and its purposes first, then comment on the reliability of the examination and the validity in terms of the various functions the examination is supposed to serve. How might these be investigated?

For further exercises, see Exercise 1: Interpretation of RUMM2030 printout in Appendix C.

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Andrich, D., Marais, I. (2019). Reliability and Validity in Classical Test Theory. In: A Course in Rasch Measurement Theory. Springer Texts in Education. Springer, Singapore. https://doi.org/10.1007/978-981-13-7496-8_4

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  • DOI: https://doi.org/10.1007/978-981-13-7496-8_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-7495-1

  • Online ISBN: 978-981-13-7496-8

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