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NORM-REFERENCED, CRITERION-REFERENCED AND DOMAIN-REFERENCED TESTS 415
parameters of abilities are known. They assume the
following (Morrison 1993):
There is a normal curve of distribution of scores
in the population: the bell-shaped symmetry
of the Gaussian curve of distribution seen,
for example, in standardized scores of IQ or
the measurement of people’s height or the
distribution of achievement on reading tests in
the population as a whole.
There are continuous and equal intervals
between the test scores and, with tests
that have a true zero (see Chapter 24), the
opportunity for a score of, say, 80 per cent to be
double that of 40 per cent; this differs from the
ordinal scaling of rating scales discussed earlier
in connection with questionnaire design where
equal intervals between each score could not
be assumed.
Parametric tests will usually be published tests
which are commercially available and which have
been piloted and standardized on a large and
representative sample of the whole population.
They usually arrive complete with the backup
data on sampling, reliability and validity statistics
which have been computed in the devising of
the tests. Working with these tests enables the
researcher to use statistics applicable to interval
and ratio levels of data.
Non-parametric tests make few or no assumptions
about the distribution of the population (the
parameters of the scores) or the characteristics
of that population. The tests do not assume a
regular bell-shaped curve of distribution in the
wider population; indeed the wider population
is perhaps irrelevant as these tests are designed
for a given specific population – a class in school,
achemistrygroup,aprimaryschoolyeargroup.
Because they make no assumptions about the wider
population, the researcher must work with nonparametric
statistics appropriate to nominal and
ordinal levels of data. Parametric tests, with a
true zero and marks awarded, are the stock-intrade
of classroom teachers – the spelling test, the
mathematics test, the end-of-year examination,
the mock-examination.
The attraction of non-parametric statistics is
their utility for small samples because they do
not make any assumptions about how normal,
even and regular the distributions of scores
will be. Furthermore, computation of statistics
for non-parametric tests is less complicated
than that for parametric tests. Non-parametric
tests have the advantage of being tailored
to particular institutional, departmental and
individual circumstances. They offer teachers
a valuable opportunity for quick, relevant and
focused feedback on student performance.
Parametric tests are more powerful than nonparametric
tests because they not only derive
from standardized scores but also enable the
researcher to compare sub-populations with a
whole population (e.g. to compare the results of
one school or local education authority with the
whole country, for instance in comparing students’
performance in norm-referenced or criterionreferenced
tests against a national average score
in that same test). They enable the researcher
to use powerful statistics in data processing (see
Chapters 24–26), and to make inferences about
the results. Because non-parametric tests make no
assumptions about the wider population a different
set of statistics is available to the researcher (see
Chapter 24). These can be used in very specific
situations – one class of students, one year group,
one style of teaching, one curriculum area – and
hence are valuable to teachers.
Norm-referenced, criterion-referenced
and domain-referenced tests
A norm-referenced test compares students’ achievements
relative to other students’ achievements,
for example a national test of mathematical performance
or a test of intelligence which has been
standardized on a large and representative sample
of students between the ages of 6 and 16. A
criterion-referenced test does not compare student
with student but, rather, requires the student to
fulfil a given set of criteria, a predefined and absolute
standard or outcome (Cunningham 1998).
For example, a driving test is usually criterionreferenced
since to pass it requires the ability to
Chapter 19