Intervention for Dyslexia - The British Dyslexia Association

how well the screening device predicts the criterion across all possible cutting points of
the distributions whilst at the same time taking account of the common variance
between them. It therefore may be said to represent the predictive validity of the
screening instrument, since it covers the predictive efficacy of the test for the whole
group, including high and intermediate scorers as well as the low scorers who will
typically be of greatest practical interest. It is in the nature of correlational statistics that
if the sample size is large then relatively low correlation coefficients will achieve
statistical significance. Not all test users may appreciate this, and may believe that a
given test is more efficient than it really is.
By contrast, discriminant function analysis must also take into account the number of
incorrect categorisations of subjects, and hence gives a measure of predictive accuracy,
usually expressed as a percentage. When all the results are reported, this is generally an
extremely efficient way to judge the efficacy of a prediction or identification tool.
However, what often happens is that only overall identification rates are reported, and
these can be extremely high due to the fact that good identification of a large grouping
has occurred. This good identification of the large group (e.g. children without dyslexia)
may outweigh a poor identification rate of the smaller group (e.g. children with dyslexia)
and thus an overall high identification rate can be reported, which is misleading. Proper
identification of group membership (e.g. an ‘at risk’ group and a ‘not at risk’ group)
should include four reported rates for a proper evaluation to take place, i.e. true
positives (those who actually have dyslexia and were identified by the screening test as
having dyslexia); true negatives (those who do not have dyslexia and were identified by
the screening test as not having dyslexia); false positives (those who do not have
dyslexia but were identified by the screening test as having dyslexia); and false
negatives (those who do have dyslexia but were identified by the screening test as not
having dyslexia). This categorisation is depicted in Figure 4.
Dyslexic?
Yes No
Identified as
dyslexic by the
Yes True positive False positive
screening test? No False negative True negative
Figure 4. Categorisation of cases in order to determine predictive accuracy of a screening test
Jansky (1977) argues cogently that false negative and false positive rates in excess of
25% ought not to be acceptable in any screening instrument. It should be noted,
however, that a distinction must be drawn between incidence of false negatives and
false positives, and the real percentages of these measures, which must be calculated
not as a percentage of the overall sample (which would be misleading) but of the
appropriate sub-sample (for discussion see Carran and Scott, 1992; Kingslake, 1982). In
other words, of the children who actually have dyslexia, we must ask: what percentage
were identified by the screening test as having dyslexia? This statistic is known at the
sensitivity of the screening test and may be calculated by the formula TP/(TP+FN) ×100
(where TP = the number of true positive cases, FN = the number of false negative
cases). And of the children who do not have dyslexia, we must ask: what percentage
was identified by the screening test as not having dyslexia? This statistic is known as the
specificity of the screening test and may be calculated by the formula TN/(TN+FP) ×100
(where TN = the number of true negative cases, FP = the number of false positive
82 Intervention for Dyslexia