## Glossary of Rasch Measurement Terminology

Spanish Glossary: 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: Using pre-set measure values so that different analyses produce directly comparable results.

Anchor Value: a pre-set measure 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.

Bias: a change in measures based on the particular agents or objects measured.

BOTTOM: The measure corresponding to 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). An estimate of this value requires information or assertions beyond the current data.

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

Calibration: a difficulty measure used to position the agents of measurement along the variable.

Categories: levels of observed performance by an object on an agent.

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

Column: vertical line of data, usually representing all responses to a particular item, or in an output table, all statistics relating to the same attribute.

Construct: the variable as represented by the hierarchy of the agents.

Content: the subject area evoked and defined by an agent.

Convergence: the point at which further refinement of the item and person measure estimates makes no useful difference in the results.

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

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.

Displacement: when agents, objects or steps are anchored, this is an estimate of the difference between the anchored measure and the measure which would accord with the current data set.

Disturbance: the effect of one or more unexpected responses.

Diverging: the estimated calibrations at the end of an estimation 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.

Fit Statistic: a summary of the discrepancies between the observations and what is expected to be observed.

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

Independence, local: not dependent on which particular agents and objects are included in the analysis. Rasch analysis is independent of the distribution of agent or object samples so long as the objects or agents which are of a reasonably similar nature.

Infit: a fit statistic that focuses on the central performance of an item or person, the information-weighted average of the squared standardized deviations of observations from their expectations.

Interval scale: scale of measurement on which equal intervals represent equal amounts of the variable.

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

Iteration: one run through the data by the estimation program, done in order to improve the estimates.

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

Logit: the "natural" unit of measure used by Rasch for calibrating items and measuring persons. A log-odds transformation of the probability of a response.

Map: a picture showing the frequency and spread of agents and objects along the variable.

Mean-square: a chi-square statistic divided by its degrees of freedom, so that it has an expectation of 1. Values less than 1 indicate overfit. Values greater than 1 indicate unpredictability.

Measure: the performance level in logits, or their linear transformations, used to position objects and agents of measurement along the variable.

Normal: a random distribution, graphically represented as a "bell" curve. The Unit Normal distribution 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 unit 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.

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

Partial Credit: a format for observing responses wherein the categories increase in the level of the variable they define, and this increase is unique to each agent of measurement.

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

Peirce, Charles Sanders: first recorded expression (1878) of the formulation of the Rasch model.

Plot: an x-y graph used to show measures or 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 occurrences or non-occurrences of a "rare" event, e.g., spelling mistakes in a piece 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 to obtain measure estimates quickly or by hand.

Rasch, Georg: Danish mathematician (1901-1980), who first propounded the practical conversion of qualitative observations into linear measures.

Rasch Model: a family of mathematical formulae for the relationship between the probability of being observed in a particular category, and the difference between an individual's ability and an item's difficulty.

Rating Scale: a format for observing responses wherein the categories increase in the level of the variable they define, and this increase is uniform across all relevant agents of measurement.

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 observation indicating degree of success by an object on an agent.

Results: a report of Rasch measures and fit statistics.

Row: a horizontal line of data representing all responses by a particular object.

Scale: the quantitative representation of a variable.

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 statistically averaged measure standard error.

Standard Deviation: the root mean square of the differences between the values 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 statistically meaningful.

Standardized: transformed to accord with a unit normal distribution.

Standardized fit statistic: the probability that the data fit the model (perfectly) expressed as a unit normal deviate.

Standardized residual: the difference between an observation and its expected value (according to the measures) divided by the square-root of its model variance.

Steps: the transitions between adjacent categories on an agent ordered by the definition of the variable.

TOP: The value corresponding to 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). An estimate of this value requires information or assertions beyond the current data.

Top Category: the response category at which maximum performance on an agent is manifested.

UCON: the unconditional (or joint JMLE) maximum likelihood estimation formula.

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 is to be measured. A 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, or the adjustment of the influence of a person or item on the estimation of measures.

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

For a more comprehensive glossary, see:
Bond T.G. & Fox C.M (2001) Applying the Rasch Model: Fundamental Measurement in the Human Sciences. Mahwah NJ: Lawrence Erlbaum Assoc.

Glossary of Rasch Measurement Terminology Wright B.D., Linacre J.M. … Rasch Measurement Transactions, 2001, 15:2 p. 824-5

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

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