User Guide for the TIMSS International Database.pdf - TIMSS and ...

C H A P T E R 6 A C H I E V E M E N T S C O R E S
ASMSTDR Standardized mathematics raw score – Population 1
ASSSTDR Standardized science raw score – Population 1
BSMSTDR Standardized mathematics raw score – Population 2
BSSSTDR Standardized science raw score – Population 2
Because of the difficulty in making any comparisons across the test booklets using only
the number of raw score points obtained on a set of items, raw scores were standardized
by booklet to provide a simple score which could be used in comparisons across booklets
in preliminary analyses. The standardized score was computed so that the weighted mean
score within each booklet was equal to 50, and the weighted standard deviation was equal
to 10.
These standardized raw scores were used in the initial item analysis for computing the
discrimination coefficients for each of the items in the test. This initial item analysis was
conducted prior to scaling the test items. The standardized raw scores can be found in the
Student Background data files and in the Written Assessment data files.
ASMNRSC National Rasch Mathematics Score (ML) – Population 1
ASSNRSC National Rasch Science Score (ML) – Population 1
BSMNRSC National Rasch Mathematics Score (ML) – Population 2
BSSNRSC National Rasch Science Score (ML) – Population 2
The national Rasch scores were also designed for preliminary analyses. These provided a
basic Rasch score for preliminary analyses within countries, but could not be used for
international comparisons since each country has been assigned the same mean score.
The national Rasch scores were computed by standardizing mathematics and science logit
scores to have a weighted mean of 150 and a standard deviation of 10 within each
country. The logit scores were computed using the Quest Rasch analysis software; Quest
provides maximum likelihood (ML) estimates of a scaled score, based on the Rasch
model, for the performance of the students on a set of items. The computation took into
account the varying difficulty of the items across test booklets, and the performance and
ability of the students responding to each set of items. These logit scores were obtained
using item difficulties that were computed for each country using all available item
responses for the country and centering the item difficulty around zero. When computing
the item difficulties, responses marked as "not reached" were treated as items that were not
administered. This avoids giving inflated item difficulties to the items located at the end
of the test in cases where students systematically do not reach the end of the test. These
item difficulties were then used to compute logit scores for each student.
When computing the student logit scores the responses marked as “not reached” were
treated as incorrect responses. This avoided unfairly favoring students who started
answering the test and stopped as soon as they did not know the answer to a question.
Logit scores for the students generally ranged between -4 and +4. Since it is not possible
to obtain finite logit scores for those students who correctly answered all or none of the
items, scores for these students were set to +5 and -5 logits, respectively. These logit scores
were then standardized to have a weighted mean of 150 and a standard deviation of 10.
6 - 2 T I M S S D A T A B A S E U S E R G U I D E