Understanding Measurement
Issues
The identification of learning
problems usually involves assessment or measurement. This measurement
process often involves determining two numbers: 1) an estimate of ability
or potential; and 2) an estimate of actual achievement in academic skills.
To understand measurement,
it is important to understand that we cannot measure anything exactly,
any more than we can know precisely how many ounces of cereal are in
a box. Any measurement is an estimate, and how good the estimate is
depends on how good the instrument of measurement is.
Just from experience, we
have found that measuring mental events is not that different from measuring
other biological events, such as height. That is, people only vary so
much, from the shortest to the tallest individual, with most people
clumping around the middle or average. The degree to which people are
dispersed (vary above and below the mean or average) is indicated by
the "standard deviation." In educational assessment, most of the instruments
we use have the same statistical qualities, so that we can calculate
"standard scores" which will be comparable between instruments. These
standard scores commonly have an average midpoint of 100 (at the 50th
percentile), and the same standard deviation of 15 points. This means
that the further someone is from the mean in 15 point units, or standard
deviations, the more notably he or she differs from the average. (There
is also another benchmark called the "standard error of measurement,"
but we aren't going to get into this here. Suffice it to say, this is
a way of recognizing that no test measures consistently what we want
it to and of assessing the probability that any student would have gotten
a different score on a different day.)
The measurement process becomes
more complicated when we are using two tests, and are then comparing
their standard scores. (Standard scores don't have to be expressed like
IQ's and can involve regularized scores such as a "z score" or a "T
score;" but in education we are usually talking about scores with a
mean of 100 and a standard deviation of 15). It is common when assessing
a learning disability to give an intellectual test (which yields an
IQ score) and a test of academic achievement or other skills (which
yields another standard score). Just as a rule of thumb, we can tolerate
a downward discrepancy between achievement or other skills of 15 points
below the IQ, because that is still within the average range. However,
as discrepancies get greater, we realize this may not be a random event,
but it actually means something! And what it means is this student is
having significant problems in the skills that have been assessed.
In estimating discrepancies
between ability and actual functioning in a particular skill, one can
quibble about which IQ score best represents a student's "ability."
Unless there is good reason to believe otherwise, we assume the child
is about average if he or she has an IQ of 100. This is usually the
Full Scale IQ (FSIQ) on an intelligence test like the Wechsler Intelligence
Scale for Children (WISC-III). Actually, a complex test like the WISC-III
does not yield just one, but several scores. However, we don't expect
these scores to vary much from the mean (or from each other). We also
don't expect the Verbal IQ (VIQ) and Performance IQ (PIQ) to differ
all that much.
Sometimes, however, the
child functions well above the mean (say at FSIQ 115, or one standard
deviation above the mean); or he or she has a significant discrepancy
between verbal and nonverbal ability (although his or her FSIQ is 115,
the PIQ is 130 and the VIQ is 100). In the first case, we would expect
academic functioning to also be much higher than average or roughly
equal to 115. In the second case, we could argue that academic functioning
should actually be closer to 130. In this second case, there may be
reasons why the child doesn't do well on certain subtests of the IQ
test (such as an impoverished or chaotic family environment or a psychiatric
diagnosis that causes him or her to do less well on certain subtests).
Whatever the reasons, it is important to determine if the child's actual
ability is uneven, what areas are affected, and whether the FSIQ may
actually be an underestimate of his or her true ability or potential.
There is a further complication. Some ability and achievement tests
are coordinated when they are first developed, so that we don't have
to use an arbitrary measurement of discrepancy such as the standard
deviation of 15 points or more (in California, for example, a discrepancy
of 22 points is required between ability and achievement in order for
a learning disability to be diagnosed). These tests are more highly
correlated with one another, and so we expect a better fit between ability
and achievement. In these cases, when looking at discrepancy in terms
of standard deviations, we might be looking at differences in units
of a lot less than 15 points. This becomes an issue in the area of advocacy,
when it is important to set as careful guidelines as possible for measuring
"learning disability."
