Error In Proportional Reduction Statistics
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PRE
Pre Statistics
measures. Proportional Reduction of Error (PRE) The proportional reduction in error lambda concept that underlies the definition and interpretation of several measures
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of association, PRE measures are derived by comparing the errors made in predicting the dependent while ignoring the proportional reduction in error definition independent variable with errors made when making predictions that use information about the independent variable. E1 = errors of prediction made when the independent variable is ignored E2 = errors of prediction made when the prediction proportional reduction in error formula is based on the independent variable "All PRE measures are based on comparing predictive error levels that result from each of two methods of prediction" (Frankfort-Nachmias and Leon-Guerrero 2011:366). Table 12.1 on page 366 of the textbook helps us to understand this. The independent variable is number of children; the dependent variable is support for abortion. Content on this page requires a newer version of Adobe Flash Player. Two of the most commonly used PRE measures of association are lambda (λ) and gamma (γ). Two PRE Measures: Lambda and Gamma Lambda λ Appropriate for: Nominal Variables Gamma γ Appropriate for: Ordinal and Dichotomous Nominal Variables
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
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about the intended quantity compared with not having those observations. Proportional reduction in proportional reduction of error example error is a more restrictive framework widely used in statistics, in which the general loss function is replaced
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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 of proportional reduction in loss https://learn.bu.edu/bbcswebdav/pid-826908-dt-content-rid-2073693_1/courses/13sprgmetcj702_ol/week05/metcj702_W05S03T02_proportional.html 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 reliability of qualitative data. For example, this framework provides https://en.wikipedia.org/wiki/Proportional_reduction_in_loss 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 Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More Search Navig
PRE, proportional reduction of errorPRE, proportional reduction of error having a mental medical condition financial status relatively bad relatively good total yes 390 (97,5 %) 10 (2,5 %) 400 (100 %) no 40 (6,7 %) 560 (93,3 %) 600 (100 %) total http://www.tankonyvtar.hu/en/tartalom/tamop425/0010_2A_21_Nemeth_Renata-Simon_David_Tarsadalomstatisztika_magyar_es_angol_nyelven_eng/ch08s02.html 430 (43 %) 570 (57 %) 1000 (100 %) Using one of the illustrations from the previous lecture (where we considered mental health to be the independent variable and financial status to be the dependent variable), let’s guess the financial status of the individual respondents based on our knowledge of the distribution: 57% have relatively good, 43% have relatively worse financial status.Let’s imagine that the respondents turn up one by one and we have to guess their financial status proportional reduction as accurately as possible. What’s the best way to do that? having a mental medical condition financial status relatively bad relatively good total yes 390 (97,5 %) 10 (2,5 %) 400 (100 %) no 40 (6,7 %) 560 (93,3 %) 600 (100 %) total 430 (43 %) 570 (57 %) 1000 (100 %) Declareing each respondent to have a relatively good financial status is the safest way: thus we are wrong in 430 cases out of 1000.How does reduction in error the situation change if we already know Table 1 and we can ask each respondent whether or not they have a mental medical condition?In this case we can improve the chances of our guesswork by categorizing everyone with a mental problem as having worse financial status, while those without mental problems as having better financial status. Thus the number of mistakes we make is down to 50.In other words, the guessing error characterizes the relationship of the two variables. Associational indices that work on this principle are called ’proportional reduction of error’ (PRE) indices.Calculating (λ) to get the connection of two nominal variables:8.1. egyenlet - Where:E1 is the number of categorising mistakes made without considering the independent variableE2 is the number of categorising mistakes made considering the independent variable having a mental medical condition financial status relatively bad relatively good total yes 390 (97,5 %) 10 (2,5 %) 400 (100 %) no 40 (6,7 %) 560 (93,3 %) 600 (100 %) total 430 (43 %) 570 (57 %) 1000 (100 %) in this specific case:8.2. egyenlet - Lambda’s characteristicsLet’s assume that mental health is the dependent variable and financial status is the independent one (also assuming that being rich drives you crazy). In this case lambda is calculated thus:8.3. egyenlet - That is, lambda depends on which variable is the dependent and which the independent one. These associational indices are called assymmetric indice