What is Information?

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 Publications
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

To be emailed about new material on www.rasch.org
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Rasch.org

www.rasch.org welcomes your comments:

Your email address (if you want us to reply):

 

ForumRasch 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
May 17 - June 21, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024
June 21 - July 19, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 5 - Aug. 6, 2024, Fri.-Fri. 2024 Inaugural Conference of the Society for the Study of Measurement (Berkeley, CA), Call for Proposals
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 4 - Nov. 8, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
May 16 - June 20, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 20 - July 18, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com
Oct. 3 - Nov. 7, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

The URL of this page is www.rasch.org/rmt/rmt42h.htm

Website: www.rasch.org/rmt/contents.htm