Glossary of Rasch Measurement Terminology

Glossary of Rasch Measurement Terminology
Glosario Español www.rasch.org/rmt/glosario.htm
Ability	the level of successful performance of the objects of measurement on the variable.
Agent of Measurement	the tool (items, questions, etc.) used to define a variable and position objects or persons along that variable.
Anchor	the process of using anchor values to insure that different analyses produce directly comparable results.
Anchor Value	a pre-set logit value assigned to a particular object, agent or step to be used as a reference value for determining the measurements or calibrations of other objects, agents or steps.
Anchor Table	the table of Anchor Values used during Rasch analysis of an Input Grid and so included in the Results Table produced. The Anchor Table has the same format as the Results Table.
Best Test Design	Wright, B.D. & Stone, M.H., Best Test Design: Rasch Measurement. Chicago: Mesa Press, 1979
Bias	A change in logit values based on the particular agents or objects measured.
BOTTOM	The value shown in the Results Table for an agent on which all objects were successful, (so it was of bottom difficulty), or for an object which had no success on any agent (so it was of bottom ability)
Bottom Category	the response category at which no level of successful performance has been manifested.
Calibration	a difficulty measure in logits used to position the agents of measurement along the variable.
Categories	levels of performance on an observational or response format.
Cell	Location of data in the spreadsheet, given by a column letter designation and row number designation e.g. B7
Common Scale	a scale of measurement on which all agents and objects can be represented.
Column	Vertical line of data in the Spreadsheet data, usually representing in an Input Grid all responses to a particular item, or in a Results Table, all statisitics measuring the same attribute of agents or objects.
Construct Construct Validity	What we want to measure. It is usually defined by a theory, the construct theory, and oeprationalized by the items in the test/instrument. The construct theory predicts the difficulty ordering (hierarchy) of the items. If the theoretical and empirical orderings of the items agree, then Construct Validity is confirmed.
Content	the subject area evoked and defined by an agent.
Convergence	the point at which further improvement of the item and person estimates makes no useful difference in the results. Rasch calculation ends at this point.
Dichotomous Response	a response format of two categories such as correct-incorrect, yes-no, agree-disagree.
Difficulty	the level of resistance to successful performance of the agents of measurement on the variable.
Discrepancy	one or more unexpected responses.
Disturbance	one or more unexpected responses.
Diverging	the estimated calibrations at the end of an iteration are further from convergence than at the end of the previous iteration.
Expected Response	the predicted response by an object to an agent, according to the Rasch model analysis.
Fit Statistic	a summary of the discrepancies between what is observed and what we expect to observe.
Heading	an identifier or title for use on tables, maps and plots.
Independent	Not dependent on which particular agents and objects are included in the analysis. Rasch analysis is independent of agent or object population as long as the measures are used to compare objects or agents which are of a reasonably similar nature.
Infit	an information weighted fit statistic that focuses on the overall performance of an item or person, i.e, the information-weighted average of the squared standardized deviation of observed performance from expected performance. The statistic plotted and tabled by Rasch is this mean square normalized.
Interval scale	Scale of measurement on which equal intervals represent equal amounts of the vairable being measured.
Item	agent of measurement, not necessarily a test question, e.g., a product rating.
Iteration	one run through the data by the Rasch calculation program, done to improve estimates by minimizing residuals.
Knox Cube Test	a tapping pattern test requiring the application of visual attention and short term memory.
Link	Relating the measures derived from one test with those from another test, so that the measures can be directly compared.
Logit	the unit of measure used by Rasch for calibrating items and measuring persons. A log_e odds transformation of the probability of a correct response.
Map	a bar chart showing the frequency and spread of agents and objects along the variable.
Matrix	a rectangle of responses with rows (or columns) defined by objects and columns (or rows) defined by agents.
Measure Measurement	the process of quantifying the amount of a variable, or the result of the process. Rasch measurements are locations (usually in logits) on the latent variable. The Rasch measure for persons is the person ability. The Rasch measure for items is the item difficulty.
Normal	a random distribution, graphically represented as a "bell" curve which has a mean value of 0 and a standard deviation of 1.
Normalized	the transformation of the actual statistics obtained so that they are theoretically part of a normal distribution.
Object of Measurement	people, products, sites, to be measured or positioned along the variable.
Observed Response	the actual response by an object to an agent.
Outfit	an outlier sensitive fit statistic that picks up rare events that have occurred in an unexpected way. It is the average of the squared standardized deviations of the observed performance from the expected performance. Rasch plots and tables use the normalized unweighted mean squares so that the graphs are symmetrically centered on zero.
Outliers	unexpected responses usually produced by agents and objects far from one another in location along the variable.
Person	the object of measurement, not necessarily human, e.g., a product.
Plot	an x-y graph used by Rasch to show the fit statistics for agents and objects.
Point Labels	the placing on plots of the identifier for each point next to the point as it is displayed.
Poisson Counting	a method of scoring tests based on the number of occurences or non-occurences of an event, e.g. spelling mistakes in a pice of dictation.
Process	the psychological quality, i.e.,the ability, skill, attitude, etc., being measured by an item.
PROX	the normal approximation estimation formula, used by some Rasch programs for the first part of the iteration process.
Rasch, Georg	Danish Mathematician (1906-1980), who first propounded the application of the statistical approach used by Rasch.
Rasch Model	a mathematical formula for the relationship between the probability of success (P) and the difference between an individual's ability (B) and an item's difficulty (D). P=exp(B-D)/(1+exp(B-D)) or log_e [P/(1-P)] = B - D
Rating Scale	A format for observing responses wherein the categories increase in the level of the variable they define, and this increase is uniform for all agents of measurement.
Rating Scale Analysis	Wright, B.D. & Masters, G.N., Rating Scale Analysis: Rasch Measurement. Chicago: Mesa Press, 1982.
Reliability	the ratio of sample or test variance, corrected for estimation error, to the total variance observed.
Residuals	the difference between data observed and values expected.
Response	The value indicating degree of success by an object on an agent, and entered into the appropriate cell of an Input Grid.
Results Table	a report of Rasch calculations.
Rigidity	when agents, objects and steps are all anchored, this is the logit inconsistency between the anchoring values, and is reported on the Iteration Screen and Results Table. 0 represents no inconsistency.
Row	a horizontal line of data on a Spreadsheet, usually used, in the Input Grid, to represent all responses by a particular object. The top row of each spreadsheet is reserved for Rasch control information.
Scale	1. the quantitive representation of a variable (e.g., a weight scale) 2. ordinal representation of a variable (e.g., a rating scale)
Score points	the numerical values assigned to responses when summed to produce a score for an agent or object.
Separation	the ratio of sample or test standard deviation, corrected for estimation error, to the average estimation error.
Standard Deviation	the root mean square of the differences between the calculated logits and their mean.
Standard Error	an estimated quantity which, when added to and subtracted from a logit measure or calibration, gives the least distance required before a difference becomes meaningful.
Steps	the transitions between adjacent categories ordered by the definition of the variable.
Template	a specially formatted input file.
TOP	The value shown in the Results Table for an agent on which no objects were successful, (so it was of top difficulty), or for an object which succeeded on every agent (so it was of top ability)
Top Category	the response category at which maximum performance is manifested.
UCON	the unconditional (or "joint" JMLE) maximum likelihood estimation formula, used by some Rasch programs for the second part of the iteration process.
UNSURE	Rasch was unable to calibrate this data and treated it as missing.
Unweighted	the situation in which all residuals are given equal significance in fit analysis, regardless of the amount of the information contained in them.
Variable	the idea of what we want to measure. A Rasch variable is defined by the items or agents of measurement used to elicit its manifestations or responses.
Weighted	the adjustment of a residual for fit analysis, according to the amount of information contained in it.

Glosario Español www.rasch.org/rmt/glosario.htm

Ability

the level of successful performance of the objects of measurement on the variable.

Agent of Measurement

the tool (items, questions, etc.) used to define a variable and position objects or persons along that variable.

Anchor

the process of using anchor values to insure that different analyses produce directly comparable results.

Anchor Value

a pre-set logit value assigned to a particular object, agent or step to be used as a reference value for determining the measurements or calibrations of other objects, agents or steps.

Anchor Table

the table of Anchor Values used during Rasch analysis of an Input Grid and so included in the Results Table produced. The Anchor Table has the same format as the Results Table.

Best Test Design

Wright, B.D. & Stone, M.H., Best Test Design: Rasch Measurement. Chicago: Mesa Press, 1979

Bias

A change in logit values based on the particular agents or objects measured.

BOTTOM

The value shown in the Results Table for an agent on which all objects were successful, (so it was of bottom difficulty), or for an object which had no success on any agent (so it was of bottom ability)

Bottom Category

the response category at which no level of successful performance has been manifested.

Calibration

a difficulty measure in logits used to position the agents of measurement along the variable.

Categories

levels of performance on an observational or response format.

Cell

Location of data in the spreadsheet, given by a column letter designation and row number designation e.g. B7

Common Scale

a scale of measurement on which all agents and objects can be represented.

Column

Vertical line of data in the Spreadsheet data, usually representing in an Input Grid all responses to a particular item, or in a Results Table, all statisitics measuring the same attribute of agents or objects.

Construct
Construct Validity

What we want to measure. It is usually defined by a theory, the construct theory, and oeprationalized by the items in the test/instrument. The construct theory predicts the difficulty ordering (hierarchy) of the items. If the theoretical and empirical orderings of the items agree, then Construct Validity is confirmed.

Content

the subject area evoked and defined by an agent.

Convergence

the point at which further improvement of the item and person estimates makes no useful difference in the results. Rasch calculation ends at this point.

Dichotomous Response

a response format of two categories such as correct-incorrect, yes-no, agree-disagree.

Difficulty

the level of resistance to successful performance of the agents of measurement on the variable.

Discrepancy

one or more unexpected responses.

Disturbance

one or more unexpected responses.

Diverging

the estimated calibrations at the end of an iteration are further from convergence than at the end of the previous iteration.

Expected Response

the predicted response by an object to an agent, according to the Rasch model analysis.

Fit Statistic

a summary of the discrepancies between what is observed and what we expect to observe.

Heading

an identifier or title for use on tables, maps and plots.

Independent

Not dependent on which particular agents and objects are included in the analysis. Rasch analysis is independent of agent or object population as long as the measures are used to compare objects or agents which are of a reasonably similar nature.

Infit

an information weighted fit statistic that focuses on the overall performance of an item or person, i.e, the information-weighted average of the squared standardized deviation of observed performance from expected performance. The statistic plotted and tabled by Rasch is this mean square normalized.

Interval scale

Scale of measurement on which equal intervals represent equal amounts of the vairable being measured.

Item

agent of measurement, not necessarily a test question, e.g., a product rating.

Iteration

one run through the data by the Rasch calculation program, done to improve estimates by minimizing residuals.

Knox Cube Test

a tapping pattern test requiring the application of visual attention and short term memory.

Link

Relating the measures derived from one test with those from another test, so that the measures can be directly compared.

Logit

the unit of measure used by Rasch for calibrating items and measuring persons. A log_e odds transformation of the probability of a correct response.

Map

a bar chart showing the frequency and spread of agents and objects along the variable.

Matrix

a rectangle of responses with rows (or columns) defined by objects and columns (or rows) defined by agents.

Measure
Measurement

the process of quantifying the amount of a variable, or the result of the process. Rasch measurements are locations (usually in logits) on the latent variable. The Rasch measure for persons is the person ability. The Rasch measure for items is the item difficulty.

Normal

a random distribution, graphically represented as a "bell" curve which has a mean value of 0 and a standard deviation of 1.

Normalized

the transformation of the actual statistics obtained so that they are theoretically part of a normal distribution.

Object of Measurement

people, products, sites, to be measured or positioned along the variable.

Observed Response

the actual response by an object to an agent.

Outfit

an outlier sensitive fit statistic that picks up rare events that have occurred in an unexpected way. It is the average of the squared standardized deviations of the observed performance from the expected performance. Rasch plots and tables use the normalized unweighted mean squares so that the graphs are symmetrically centered on zero.

Outliers

unexpected responses usually produced by agents and objects far from one another in location along the variable.

Person

the object of measurement, not necessarily human, e.g., a product.

Plot

an x-y graph used by Rasch to show the fit statistics for agents and objects.

Point Labels

the placing on plots of the identifier for each point next to the point as it is displayed.

Poisson Counting

a method of scoring tests based on the number of occurences or non-occurences of an event, e.g. spelling mistakes in a pice of dictation.

Process

the psychological quality, i.e.,the ability, skill, attitude, etc., being measured by an item.

PROX

the normal approximation estimation formula, used by some Rasch programs for the first part of the iteration process.

Rasch, Georg

Danish Mathematician (1906-1980), who first propounded the application of the statistical approach used by Rasch.

Rasch Model

a mathematical formula for the relationship between the probability of success (P) and the difference between an individual's ability (B) and an item's difficulty (D). P=exp(B-D)/(1+exp(B-D)) or log_e [P/(1-P)] = B - D

Rating Scale

A format for observing responses wherein the categories increase in the level of the variable they define, and this increase is uniform for all agents of measurement.

Rating Scale Analysis

Wright, B.D. & Masters, G.N., Rating Scale Analysis: Rasch Measurement. Chicago: Mesa Press, 1982.

Reliability

the ratio of sample or test variance, corrected for estimation error, to the total variance observed.

Residuals

the difference between data observed and values expected.

Response

The value indicating degree of success by an object on an agent, and entered into the appropriate cell of an Input Grid.

Results Table

a report of Rasch calculations.

Rigidity

when agents, objects and steps are all anchored, this is the logit inconsistency between the anchoring values, and is reported on the Iteration Screen and Results Table. 0 represents no inconsistency.

Row

a horizontal line of data on a Spreadsheet, usually used, in the Input Grid, to represent all responses by a particular object. The top row of each spreadsheet is reserved for Rasch control information.

Scale

1. the quantitive representation of a variable (e.g., a weight scale)
2. ordinal representation of a variable (e.g., a rating scale)

Score points

the numerical values assigned to responses when summed to produce a score for an agent or object.

Separation

the ratio of sample or test standard deviation, corrected for estimation error, to the average estimation error.

Standard Deviation

the root mean square of the differences between the calculated logits and their mean.

Standard Error

an estimated quantity which, when added to and subtracted from a logit measure or calibration, gives the least distance required before a difference becomes meaningful.

Steps

the transitions between adjacent categories ordered by the definition of the variable.

Template

a specially formatted input file.

TOP

The value shown in the Results Table for an agent on which no objects were successful, (so it was of top difficulty), or for an object which succeeded on every agent (so it was of top ability)

Top Category

the response category at which maximum performance is manifested.

UCON

the unconditional (or "joint" JMLE) maximum likelihood estimation formula, used by some Rasch programs for the second part of the iteration process.

UNSURE

Rasch was unable to calibrate this data and treated it as missing.

Unweighted

the situation in which all residuals are given equal significance in fit analysis, regardless of the amount of the information contained in them.

Variable

the idea of what we want to measure. A Rasch variable is defined by the items or agents of measurement used to elicit its manifestations or responses.

Weighted

the adjustment of a residual for fit analysis, according to the amount of information contained in it.

Based on: Wright, B.D. & Linacre J.M. (1985) Microscale Manual. Westport, Conn.: Mediax Interactive Technologies, Inc.

Rasch publications in Spanish - Español
www.rasch.org/rmt/glosario.htm	Rasch Anàlisis - Glosario Español - Spanish Glossary - Español-Inglés del diccionario - Spanish-English Dictionary - Dr. Agustín Tristàn Lòpez
www.rasch.org/diseno.htm	Spanish language introduction to Diseño de Mejores Pruebas (Best Test Design)
Book PDF	Diseño de Mejores Pruebas - Spanish-language translation of Best Test Design (Wright & Stone, 1979)

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

Rasch Books and Publications

Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang

Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene

Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver

Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone

Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale

Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes

Statistical Analyses for Language Testers (Facets), Rita Green

Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind

Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M

Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland

Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind

Rasch Measurement: Applications, Khine

Winsteps Tutorials - free
Facets Tutorials - free

Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre

Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

Other Rasch-Related Resources: Rasch Measurement YouTube Channel

Rasch Measurement Transactions & Rasch Measurement research papers - free

An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse

Rasch Measurement Theory Analysis in R, Wind, Hua

Applying the Rasch Model in Social Sciences Using R, Lamprianou

El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.

Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar

Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch

Rasch Models for Measurement, David Andrich

Constructing Measures, Mark Wilson

Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters

Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias

Diseño de Mejores Pruebas - free, Spanish Best Test Design

A Course in Rasch Measurement Theory, Andrich, Marais

Rasch Models in Health, Christensen, Kreiner, Mesba

Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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
Apr. 21 - 22, 2025, Mon.-Tue.	International Objective Measurement Workshop (IOMW) - Boulder, CO, www.iomw.net
Jan. 17 - Feb. 21, 2025, Fri.-Fri.	On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Feb. - June, 2025	On-line course: Introduction to Classical Test and Rasch Measurement Theories (D. Andrich, I. Marais, RUMM2030), University of Western Australia
Feb. - June, 2025	On-line course: Advanced Course in Rasch Measurement Theory (D. Andrich, I. Marais, RUMM2030), University of Western Australia
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