"Are the sub-tests and the total test shown in the Table reliable
enough to support interpretations about the achievement of
individual students? And of groups of students at classroom,
school, district, and state levels? How many performance levels do
|Group size for|
Test "reliability", R, is a cryptic index because it amalgamates the distribution of the sample and the measurement characteristics of the test into one correlation reporting repeatability (not quality) of a local combination of the test and the sample. We are actually interested in two statistics: (i) the student standard deviation with measurement error removed; (ii) the average precisions of student measures. The ratio of the sample error-adjusted S.D. to the average measure S.E. is the "separation". It is easy to compute here because it is sqrt[R/(1-R)].
The total test has reliability 0.88, and so a student separation of 2.7. If the sample is normally distributed, there are about 3 measurably different levels of performance in this sample. But none of the sub-tests sustains even two measurably different levels.
If we are prepared to consider that all students within a group (classroom, school, district, ...) are randomly equivalent, then we can compute separations for group means. These are (student separation) * sqrt(number of students in group), i.e., for a separation of 3, group size = 3².(1-R)/R.
Of course, high separation of group-means does not stop group
distributions from overlapping considerably. Men are usually
taller than women, but not all men are taller than all women.
There is sufficient overlap that any serious study of men's and
women's heights (or any commercial clothing business) has to
consider more than just the group averages.
Benjamin D. Wright
Wright B.D. (1998) Interpreting Reliabilities. Rasch Measurement Transactions 11:4 p. 602.
Interpreting Reliabilities. Wright B.D. Rasch Measurement Transactions, 1998, 11:4 p. 602.
|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|
|June 23 - July 21, 2023, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|Aug. 11 - Sept. 8, 2023, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt114j.htm