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A further difficulty in defining the desired population for the final-year

assessment is that many students drop out before the final year of any track.

Thus a TIMSS Coverage Index (TCI) was calculated that quantifies the

proportion of the entire school-leaving age cohort that is covered by the

TIMSS final-year sample in each country. The TCI was defined as follows:

TCI = Total Enrollment in TIMSS Grades 1995/(Total National Population Aged 15 -19 in 1995)

The numerator in this expression is the total enrollment in the grades tested by

TIMSS, estimated from the weighted sample data. This estimate corresponds to

the size of the population to which the TIMSS results generalize and makes

appropriate provision for student non-response. It does not include students

who are no longer attending school or students who were excluded from the

sample on grounds of physical or other disability. It also does not include

students who were repeating the final grade. Because some students repeat

the final year of a track, or take the final year in more than one track at

different times, they may be in the final year of a track without completing

their secondary education that year. On the one hand, students who are not

completing their education still have the potential to gain further knowledge

in additional years of schooling, and thus will not have attained their full yield

at the time of the TIMSS assessment. On the other hand, and of more serious

concern, the presence both of students who are repeating the final track and

of those who will repeat that track can contribute a substantial downward bias

to the estimated achievement of the population. Repeating students would be

represented twice in the population, and are likely to be lower-achieving on

average than those who do not repeat. The only practical way for TIMSS to

deal with this problem was to exclude students who were repeating the final

year. Thus, the population of final-year students is formally defined as those

students taking the final year of one track of the secondary system for the first


The denominator in the expression is an estimate of the school-leaving age

cohort size. Since the age at which students in upper-secondary school may

leave school varies, TIMSS estimated the size of the school-leaving age cohort

by taking the average of the size of the 1995 age cohorts for 15-, 16-, 17-, 18-,

and 19-year-olds in each country. (Although the estimate was generally based

on the 15-19 age group, there were exceptions; for example, in Germany it

was based on the 17-19 age group.) This information was provided by NRCs

from official population census figures in their countries. This approach

reflects the fact that students in the final year of secondary school are likely to

be almost entirely a subset of the population of 15- to 19-year-olds in most

countries. Table A.4 presents the computation of the TCI for each country.