The immediate quantification of precision is the standard error (SE) of estimation. The calculation of an estimate and its SE are specified by the estimation model and use the same data. This SE estimates the standard deviation of innumerable independent replications of this data collecting process when the only disturbances encountered are those modelled.
The convenience of the SE is that it is in the units of the estimate and can be used directly to specify regions of confidence, 2 SE's, or margins of error, 1 SE.
The inconvenience of the SE is that, when several pieces of independent data bearing on a common quantity are brought together to form a "better" estimate or when improvement of "precision" is tracked during data collecting, the SE's are not additive. R A Fisher devised a cure for this inconvenience in 1920. While the SE's of independently obtained but commonly bearing estimates are not additive, their inverse squares are. Fisher called 1/SE^2 the "information" (I) in an estimate.
When estimating a measure from a sample of independent observations, the information obtained from each observation (1/SE^2) combine to give the same information as the standard error of the estimated measure (SEM): sum(1/SE^2) = I = 1/SEM^2. For Rasch-modelled dichotomous data, the maximum possible information in one observation, 4, is obtained when a person encounters a perfectly targeted item. This means that 4/SEM^2 is the minimum number of perfectly targeted items it would take to produce the SEM estimated from the data. We will call units of (4/SEM^2), "EQUITS", (EQUivalent on-target ITemS).
The algebraic definition of SE for one Rasch modelled dichotomous datum is SE^2 = 1/[P(1-P)], where P = exp(b-d)/[1+exp(b-d)], the probability of a right answer. For a test, 1/SEM^2 = sum[P(1-P)]. When an item is perfectly targeted, P = 1/2 and P(1-P) = 1/4, so that 4 * sum[P(1-P)] = 4/SEM^2 is the number of perfectly targeted responses necessary to obtain this SEM. We can compare the information values of measures by calculating the EQUITS of information in each one.
The relative information in any pair of measures can be determined by the "Relative Efficiency" (RE) of one measure with respect to the other. The inverse ratio of their error variances, RE21 = SE1^2/SE2^2, gives the "information" provided by the second measure, b2, in units of the "information" provided by the first, b1.
What is Information?, B Wright Rasch Measurement Transactions, 1990, 4:2 p. 109
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
|in Spanish:||Análisis de Rasch para todos, Agustín Tristán||Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez|
|Forum||Rasch Measurement Forum to discuss any Rasch-related topic|
Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement
Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.
|Coming Rasch-related Events|
|Aug. 14 - 16, 2019. Wed.-Fri.||An Introduction to Rasch Measurement: Theory and Applications (workshop led by Richard M. Smith) https://www.hkr.se/pmhealth2019rs|
|August 25-30, 2019, Sun.-Fri.||Pacific Rim Objective Measurement Society (PROMS) 2019, Surabaya, Indonesia https://proms.promsociety.org/2019/|
|Oct. 11 - Nov. 8, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Nov. 3 - Nov. 4, 2019, Sun.-Mon.||International Outcome Measurement Conference, Chicago, IL,http://jampress.org/iomc2019.htm|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt42h.htm