Larroulet Philippi, Cristian (2022) Against Prohibition (Or, When Using Ordinal Scales to Compare Groups Is OK). [Preprint]
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Abstract
There is a widely held view on measurement inferences, that goes back to Stevens’s theory of measurement scales and ‘permissible statistics’. This view defends the following prohibition: you should not make inferences from averages taken with ordinal scales (versus quantitative scales: interval or ratio). This prohibition is general—it applies to all ordinal scales—and it is sometimes endorsed without qualification. Adhering to it dramatically limits the research that the social and biomedical sciences can conduct. I provide a Bayesian analysis of this inferential problem, determining when measurements from ordinal scales can be used to confirm hypotheses about relative group averages. The prohibition, I conclude, cannot be upheld, even in a qualified sense. The beliefs needed to make average comparisons are less demanding than those appropriate for quantitative scales. I illustrate with the alleged paradigm ordinal scale, the Mohs scale of mineral hardness, arguing that the literature has mischaracterized it.
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| Item Type: | Preprint | ||||||
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| Additional Information: | Accepted for publication in The British Journal of Philosophy of Science | ||||||
| Keywords: | measurement; ordinal scales; hardness; Bayesianism | ||||||
| Subjects: | Specific Sciences > Economics General Issues > Evidence Specific Sciences > Psychology General Issues > Theory/Observation |
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| Depositing User: | Cristian Larroulet Philippi | ||||||
| Date Deposited: | 20 Aug 2023 12:37 | ||||||
| Last Modified: | 20 Aug 2023 12:37 | ||||||
| Item ID: | 22438 | ||||||
| Official URL: | https://doi.org/10.1086/721759 | ||||||
| DOI or Unique Handle: | https://doi.org/10.1086/721759 | ||||||
| Subjects: | Specific Sciences > Economics General Issues > Evidence Specific Sciences > Psychology General Issues > Theory/Observation |
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| Date: | 2022 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/22438 |
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