RCT and "Mathematical Embellishment"

[R_cubed]

@llynn

Perhaps it would be useful to categorize clinical measurements on a 0-10 scale from highly applicable to statistical formulae to not applicable. We know the many measurements of the Apnea Hypopnea Index (AHI) would be close to 0 but for most measurements it is not at all clear.

Are there any thoughts about how this could be accomplished?

I’d be looking at the mathematical area known as measurement theory for the tools to answer your question.

Joel Michell is a scholar on the issue of measurement in psychology and psychometrics. He coined the term “pathological science” that seems to describe too much of the “peer reviewed” published literature.

David Hand is a statistician who wrote a relatively recent textbook on modern measurement theory (Measurement Theory and Practice: The World Through Quantification) that might be closer to your immediate needs. His old 1996 paper Statistics an the Theory of Measurement is worth study.

An undervalued application of measurement theory can be found here:

Article: Robustness of statistical methods when measure is affected by ceiling and/or floor effect

I was following up on citations to a paper @f2harrell cited in a number of threads supporting his preference for ordinal methods in applied problems: The following PLOS paper approaches the problem from a formal measurement theory perspective. I’m still digesting the paper, but their reference section is an excellent historical review of the simulation studies and the longstanding argument that compares the performance of textbook parametric and nonparametric methods on ordinal data. Th…