Proportional Reduction Error Statistics
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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) proportional reduction in error lambda of the uncertainty about the intended quantity compared with not having those
The Proportionate Reduction In Error Is A Measure Of The Quizlet
observations. Proportional reduction in error is a more restrictive framework widely used in statistics, in which the general
Proportionate Reduction In Error Symbol
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.[1] The concept
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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 Ben J. Winer (1971). It also provides a general way of developing measures for the proportional reduction in error stata 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). References[edit] ^ Upton G., Cook, I. (2006) Oxford Dictionary of Statistics, OUP. ISBN 978-0-19-954145-4 Cooil, B., and Rust, R. T. (1994), "Reliability and Expected Loss: A Unifying Principle," Psychometrika, 59, 203-216. (available here) Cooil, B., and Rust, R. T. (1995), "General Estimators for the Reliability of Qualitative Data," Psychometrika, 60, 199-220. (available here) Rust, R. T., and Cooil, B. (1994), "Reliability Measures for Qualitative Data: Theory and Implications," Journal of Marketing Research, 31(1), 1-14. (available here) Winer, B.J. (1971), Statistical Principles in Experimental Design. New York: McGraw-Hill. Perreault, W.D. and Leigh, L.E. (1989), “Reliability of Nominal Data Based on Qualitative Judgments,” Journal of Marketing Research, 26, 135-148 Retrieved from "https://en.wikipedia.org/w/index.php?title=Proportional_reduction_in_loss&oldid=735653331" Categories: Comparison of assessments Navigation menu Personal tools
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one another? We need a summary measure; we can't just reproduce the table in our articles and reports. General principle of PRE measures: does knowing the value of a case on one variable help you to predict its value on the http://www.d.umn.edu/~schilton/2700/LectureNotes/PREsynopsis.html other, that is, help you as compared to not knowing its value? General PRE Formula: (error before - error after) / (error before) So: each specific PRE formula has three elements: How shall we measure error in prediction https://www.ibm.com/support/knowledgecenter/SSLVMB_21.0.0/com.ibm.spss.statistics.help/alg_crosstabs_measures.htm for each case, or what will count as an error? How shall we predict the dependent variable before knowing the independent variable? In general, we use the prediction method which minimizes our total error (subject perhaps to reduction in side constraints). How shall we predict the dependent variable after knowing the independent variable? Notice that this measure always varies between 0 and 1. 0 occurs when error before = error after, in other words, when knowing the independent variable doesn't help us predict. In other words, 0 means no association. 1 occurs when error after = 0, i.e., when knowing the independent variable enables us to make a perfect prediction of the dependent reduction in error variable. In other words, 1 means perfect association. Can there ever be a negative measure? No, because you can't predict worse than by not knowing anything. Can there ever be a measure greater than 100%? No, because that would mean errors after would have to be negative, and there's no such thing as a negative error. We're going to study three measures: Lambda for nominal, Pearson's r-squared for interval, and gamma for ordinal. LAMBDA: A PRE MEASURE FOR NOMINAL VARIABLES For the specific example of nominal variables, the elements of this formula come out as follows: How shall we measure error in prediction, or what will count as an error? Answer: Having our prediction wrong counts as one error. Having it right counts as no errors. For nominal variables, that's the only possible definition of an error. How shall we predict the dependent variable before knowing the independent variable? Answer: We use the mode, which is the prediction method which minimizes the error. How shall we predict the dependent variable after knowing the independent variable? Answer: We use the mode for each category of the independent variable. This measure is called lambda. There are other (and better) measures of association for nominal variables, but this is the simplest. Let's apply this to the table I showed last time: Parents lean: Democrat Repu