Implications of Dimensionality on Measurement Reliability
We study some topics of the reliability of measurement, especially certain implications of multidimensionality and unidimensionality. We consider these aspects within a measurement framework focusing on one hand on the dimensionality of the measurement model and on the other hand on the dimensionality of the measurement scale. Working through theorems and examples we compare two reliability estimators, namely Cronbach's alpha and Tarkkonen's rho. It seems that there is not much use for Cronbach's alpha. It is based on unidimensional models and scales, while the models and scales used in practice are multidimensional. Tarkko-nen's rho seems to work well in multidimensional studies, giving support to the real purpose of reliability estimation which seems to have been lost for a quite long time.
KeywordsMeasurement Model Measurement Scale True Score Test Theory Full Column Rank
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- 6.Heise, D.R., Bohrnstedt, G.W.: Validity, invalidity and reliability. In: Borgatta, E.F., Bohrnstedt, G.W. (eds.) Sociological Methodology, pp. 104–129. Jossey-Bass, San Francisco (1970)Google Scholar
- 8.Jöreskog, K.G.: Factor analysis and its extensions. In: Cudeck, R., MacCallum, R.C. (eds.) Factor Analysis at 100: Historical Developments and Future Directions, pp. 47–77. Lawrence Erlbaum, Mahwah, New Jersey (2007)Google Scholar
- 13.Mustonen, S.: SURVO MM: Computing environment for creative processing of text and numerical data. http://www.survo.fi/mm/english.html (2001)
- 15.Puntanen, S., Styan, G.P.H.: Matrix tricks for linear statistical models: our personal Top Thirteen. Research report A 345, Dept. of Mathematics, Statistics & Philosophy, University of Tampere, Tampere, Finland (2003)Google Scholar
- 16.Tarkkonen, L.: On Reliability of Composite Scales. No. 7 in Statistical Studies. Finnish Statistical Society, Helsinki, Finland (1987)Google Scholar
- 19.Vehkalahti, K.: Reliability of Measurement Scales. No. 17 in Statistical Research Reports. Finnish Statistical Society, Helsinki, Finland (2000)Google Scholar