Proportional Reduction Of Error Pre

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Proportional Reduction In Error Lambda

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Not Found Show page numbers Download PDF Sections Menu Opener Search form icon-arrow-top icon-arrow-top Page Site Advanced 7 of 230 Not Found Opener Sections within this page Sections Proportional Reduction Of Error (PRE) In: The SAGE Encyclopedia of Social Science Research Methods Encyclopedia By: Scott Menard Edited by: Michael S. Lewis-Beck, Alan Bryman & Tim Futing Liao Published: 2004 DOI: http://dx.doi.org/10.4135/9781412950589.n765 +- LessMore information Print ISBN: 9780761923633 | Online ISBN: 9781412950589 Online Publication Date: January 1, 2011 Disciplines: Anthropology, Business and Management, Communication and Media Studies, Criminology and Criminal Justice, Economics, Education, Geography, Health, History, Marketing, Nursing, Political Science and International Relations, Psychology, Social Policy and Public Policy, Social Work, Sociology Buy in print Entry Reader’s Guide Entries A-Z Subject Index Search form Not Found Download PDF Show page numbers Looks like you do not have access to this content. Please login or find out how to gain access. Analysis of VarianceAnalysis of Covariance (ANCOVA)Analysis of Variance (ANOVA)Main EffectModel I ANOVAMod

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 proportionate reduction in error can be symbolized by intended quantity compared with not having those observations. Proportional reduction in error is proportional reduction in error interpretation a more restrictive framework widely used in statistics, in which the general loss function is replaced by a more

Proportional Reduction In Error Spss

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 of proportional reduction in loss was proposed by Bruce http://methods.sagepub.com/reference/the-sage-encyclopedia-of-social-science-research-methods/n765.xml 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 reliability of qualitative data. For example, this framework provides several possible measures that are https://en.wikipedia.org/wiki/Proportional_reduction_in_loss 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 Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main pageContentsFeatured contentCurrent eventsRandom articleDonate to WikipediaWikipedia store Interaction Hel

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 other, that is, help http://www.d.umn.edu/~schilton/2700/LectureNotes/PREsynopsis.html 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 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 side constraints). How shall we predict the proportional reduction 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 variable. In other words, 1 means perfect association. Can there ever reduction in error 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 Republican Total Children lean Democrat 11 (79%) 7 (26%) 18 (44%) Republican 3 (21% 20 (74%) 23 (56%) Total 14 (100%) 27