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selected reference database by adjusting the reference database to more closely resemble a
normal (i.e., bell shaped curve) distribution of scores. By using this transformation, the usual
distribution of scores relative to the mean apply. Specifically, it can be expected that 68% of
healthy individuals will score within one standard deviation of the mean (green boxes), 95% of
healthy individuals will score within two standard deviations of the mean (blue and yellow
boxes), and 99% of healthy individuals will score within three standard deviations of the mean
(purple and orange boxes).
BACKGROUND
Interpretation of an individual’s score with respect to reference (i.e., normative) data is a
common challenge faced by many practitioners. One approach to interpreting an individual’s
score is to consider the distance of the scores from the mean in standard deviation units. A
prerequisite to using this approach is that the reference database must be normally distributed
(i.e., bell shaped curve). When the reference database is normally distributed, it is possible to
take advantage of certain probability ranges within the distribution of the reference database.
68% of the scores will be within one standard deviation, 95% of the scores will be within two
standard deviations, and 99% of the scores will be within three standard deviations. If
practitioners consider individuals scoring beyond (i.e., outside) 95% of the reference database
as reflective of pathology, they would seek individuals demonstrating scores that exceed two
standard deviations from the reference database mean for intervention or more extensive
evaluation. In the case of balance testing, higher scores of center of pressure movement (i.e.,
Sway Index) are considered to reflect a deficiency in balance ability. Thus, the practitioner
would be prudent to consider an individual with a Sway Index greater than two standard
deviations from the mean as indicative of postural instability.
Many metrics of human performance used by practitioners have minimum or maximum scores.
Center of pressure movement is one such measure. Maintaining balance with very little
corrective action and body sway would produce Sway Indices that would approach zero. In
contrast, individuals demonstrating postural instability would demonstrate sway indices that
could become extremely large. The effect of this characteristic on reference databases is to
produce reference distributions that deviate from being normally distributed. Specifically in the
case of Sway Indices, the reference distributions become positively skewed. Because of the
skewness, the probability ranges of the normal distribution cannot be immediately applied. In
these circumstances, a data transformation becomes necessary prior to standardizing the
scores. Common transformations to improve normality include square root or logarithmic (e.g.,
base 10, natural log). Specific to logarithm transformations, is the useful feature that it moves
large values closer together while moving small values farther apart. As a result, positively
skewed distributions become closer to a normal distribution.
METHODOLOGY AND RESULTS
A review of several large databases of Clinical Test of Sensory Integration and Balance (CTSIB)
testing conducted on the Biodex Balance Systems revealed, similar to other human performance
measures that have a minimum value, the existence of slight to moderate positive skewness.
The purpose of this section is to describe the process of deciding upon the natural logarithm
transformation and standardization method that is used to interpret an individual’s
performance on each of the CTSIB conditions.
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