Proportional reduction in loss
Encyclopedia
Proportional reduction in loss (PRL) refers to 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. Examples are the coefficient of determination
and Goodman and Kruskal's lambda
.
The concept of proportional reduction in loss was proposed by Bruce Cooil and Roland T. Rust in their 1994 paper. 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 B.J. Winer (1971). 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 (Cooil and Rust, 1995). Measures of this latter type have been proposed by several researchers, including Perrault and Leigh (1989).
Reliability (statistics)
In statistics, reliability is the consistency of a set of measurements or of a measuring instrument, often used to describe a test. Reliability is inversely related to random error.-Types:There are several general classes of reliability estimates:...
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. Examples are the coefficient of determination
Coefficient of determination
In statistics, the coefficient of determination R2 is used in the context of statistical models whose main purpose is the prediction of future outcomes on the basis of other related information. It is the proportion of variability in a data set that is accounted for by the statistical model...
and Goodman and Kruskal's lambda
Goodman and Kruskal's lambda
In probability theory and statistics, Goodman & Kruskal's lambda is a measure of proportional reduction in error in cross tabulation analysis...
.
The concept of proportional reduction in loss was proposed by Bruce Cooil and Roland T. Rust in their 1994 paper. 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 B.J. Winer (1971). 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 (Cooil and Rust, 1995). Measures of this latter type have been proposed by several researchers, including Perrault and Leigh (1989).