Comparing single-level and multi-level regression models in analysing Rasch measures of numeracy

Date of Award


Degree Type


Degree Name

Master of Education


School of Education


Faculty of Education and Arts


This thesis describes a research study that investigated the empirical differences between two competing regression methods used to produce value-added performance indicator information for the monitoring of school effectiveness, and the practical consequences for schools when using this information for school improvement and accountability purposes. The two regression methods under review were single-level Means-on-Means regression and Multilevel Modelling. The study involved data from 24 government secondary schools with a total of 2862 students in 132 Year 8 classes in Western Australia. The dependent variable was a Rasch-created linear measure of Year 8 Numeracy from data of a Mathematics assessment, specially designed by the Department of Education. The main independent variable was a Rasch-created, linear measure of Year 7 Numeracy from student data of the Western Australian Literacy and Numeracy Assessment. Students' scored responses on items from both assessments were calibrated on a common Western Australian Monitoring Standards in Education linear scale which enabled: (1) the movement of a student's performance to be measured over time; and, (2) the application of subsequent statistical analyses from which valid inferences could be made. There were four other independent variables: (1) gender (male or fema1e); (2) ethnic group (Aborigina1 and Torres Strait Islander, or non-Aboriginal and Torres Strait Islander status); (3) language background (English or other than English); and the schoo1-level variable; and (4) school socioeconomic status.

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