Proportional reduction in loss

Proportional reduction in loss (PRL) is a general framework for developing and evaluating measures of the reliability of particular ways of making observations which are possibly subject to errors of all types. Such measures quantify how much having the observations available has reduced the loss (cost) of the uncertainty about the intended quantity compared with not having those observations.

Proportional reduction in error is a more restrictive framework widely used in statistics, in which the general loss function is replaced by a more direct measure of error such as the mean square error.^{[citation needed]} Examples are the coefficient of determination and Goodman and Kruskal's lambda.^[1]

The concept of proportional reduction in loss was proposed by Bruce Cooil and Roland T. Rust in their 1994 paper Reliability and Expected Loss: A Unifying Principle.^[2] Many commonly used reliability measures for quantitative data (such as continuous data in an experimental design) are PRL measures, including Cronbach's alpha and measures proposed by Ben J. Winer in 1971.^[3] It also provides a general way of developing measures for the reliability of qualitative data. For example, this framework provides several possible measures that are applicable when a researcher wants to assess the consensus between judges who are asked to code a number of items into mutually exclusive qualitative categories.^[4] Measures of this latter type have been proposed by several researchers, including Perrault and Leigh in 1989.^[5]

References

1. Upton, Graham J. G. (2008). A dictionary of statistics. Ian Cook (2nd ed., rev ed.). Oxford: Oxford University Press. ISBN 978-0-19-954145-4. OCLC 191929569.
2. Cooil, Bruce; Rust, Roland T. (1994-06-01). "Reliability and expected loss: A unifying principle". Psychometrika. 59 (2): 203–216. doi:10.1007/BF02295184. ISSN 1860-0980. S2CID 122165746.
3. Winer, B. J. (1962). "Statistical principles in experimental design". doi:10.1037/11774-000. hdl:2027/mdp.39015002001249. {{cite journal}}: Cite journal requires |journal= (help)
4. Cooil, Bruce; Rust, Roland T. (1995-06-01). "General estimators for the reliability of qualitative data". Psychometrika. 60 (2): 199–220. doi:10.1007/BF02301413. ISSN 1860-0980. S2CID 121776134.
5. Perreault, William D.; Leigh, Laurence E. (May 1989). "Reliability of Nominal Data Based on Qualitative Judgments". Journal of Marketing Research. 26 (2): 135–148. doi:10.1177/002224378902600201. ISSN 0022-2437. S2CID 144279197.

Further reading

• Cooil, Bruce; Rust, Roland T. (1994-06-01). "Reliability and expected loss: A unifying principle". Psychometrika. 59 (2): 203–216. doi:10.1007/BF02295184. ISSN 1860-0980. S2CID 122165746.
• Cooil, Bruce; Rust, Roland T. (1995-06-01). "General estimators for the reliability of qualitative data". Psychometrika. 60 (2): 199–220. doi:10.1007/BF02301413. ISSN 1860-0980. S2CID 121776134.
• Rust, Roland T.; Cooil, Bruce (February 1994). "Reliability Measures for Qualitative Data: Theory and Implications". Journal of Marketing Research. 31 (1): 1–14. doi:10.1177/002224379403100101. ISSN 0022-2437. S2CID 149884833.