Abstract
For over 40 years now the relationship between measurement scales and statistical procedures has been debated, with some theoreticians arguing that parametric statistics require interval or ratio data, as opposed to nominal or ordinal data. This debate has occurred simultaneously but independently in the univariate and factor-analytic literatures. It is argued in this paper that subinterval data are amenable to factor analysis when correlation matrices are based on product-moment coefficients (rho, point-biserial, phi). This is demonstrated with data of known factor structure. Data were transformed by downgrading and mixing scale properties, and skewing and mixing distributions. Despite increasingly tenuous variable interdependence, factor structures remained highly robust across scales, distributions, and populations. The findings offer further support for the thesis that measurement scales are irrelevant in statistical analysis.
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Atkinson, L. The measurement-statistics controversy: Factor analysis and subinterval data. Bull. Psychon. Soc. 26, 361–364 (1988). https://doi.org/10.3758/BF03337683
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DOI: https://doi.org/10.3758/BF03337683