Estimation of Cronbach's alpha coefficient in the context of item response theory

Kojiro Shojima*, Hideki Toyoda

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Cronbach's alpha coefficient is an index of reliability for the total score of a set of measurements. The alpha takes a value of 1.0 when the total score variance is perfectly attributable to the common factors running through the test items. In this research, a method of estimating Cronbach's coefficient alpha is proposed for the case where the parameters of dichotomous item response model arc known and the ability distribution of subjects is given. In addition, the case of polytomous response model where the item parameters are estimated by graded response model (Samejima, 1969) is also considered, and a method of estimating the alpha coefficient is proposed for that case.

Original languageEnglish
Pages (from-to)227-233
Number of pages7
JournalShinrigaku Kenkyu
Issue number3
Publication statusPublished - 2002


  • Cronbach's alpha coefficient
  • Graded response model
  • Item response theory
  • Reliability

ASJC Scopus subject areas

  • Psychology(all)

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