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Unit 13 : Interpretation of Test Scores : Qualitative and Quantitative

toward the extremes. Inspection of the curve shows, for instance, that the distance on the base Notes
line (representing scores) between percentiles 50 and 6o and the distance between 50 and 40
(these being at the center and equal) are smaller than that between any other intervals of ten
percentile points. What this means in the practical interpretation of test results is that at, and
close to, the median, differences in scores between percentile ratings are smaller in the measured
characteristic than they are between the same percentile differences elsewhere on the curve. See,
for example, the spread of the base line between 50-60, and that between 80-90, or 90-100. Yet
each of these represents ten percentile points.

0 10 20 30 40 50 60 70 80 90 100
Figure 2 : Equal distances between points on the base line of a rectangle by
successive 10-percent divisions (deciles) of its area
The percentile technique has the advantage of being easily calculated, easily understood, and of
making no assumptions with regard to the characteristics of the tolal distribution. It answers the
question : “Where does an individual’s score rank him in his group ?” Or : “Where does an
individual’s score rank him in another group whose members have taken the same test ?”
13.1.2 Decile Rank
The decile rank is the same in principle as the percentile; but instead of designating the one-
hundredth part of a distribution, it designates the one-tenth part of the group (N/10) in which
any tested person is placed by his score. The term “decile” is used to mean a dividing point.
“Decile rank” signifies a range of scores between two dividing points. Thus a testee who has a
decile rank of 10 (D ) is located in the highest 10 percent of the group; one whose decile rank is
10
9 (D ) is in the second highest 10 percent; one whose decile rank is 1 (D ), is in the lowest 10
1
9
percent of the group.
When the number of scores in a distribution is small, percentiles are not used, because there is
little or no significance in making fine distinctions in rank. The decile-ranking method may be
used instead.
13.1.3 Mental Age
This concept was introduced by Alfred Binet in 1908 in conjunction with the first revision of his
scale. In this scale and in its later revision, items are grouped according to age levels. For
example, selected items, passed by a specified percentage of five-year-old children in the
standardization sample are placed at the five-year level; items passed by a specified percentage
of six-year-old children are placed at the six-year level.
To determine mental age, in the 1908 scale, Binet adopted the following rule : the child was
credited with the mental age of the highest year level in which he passed all test items, or all but
one. To this basic level an additional year in mental age was added for every five items he passed
in higher levels; but no fractional years were added for fewer than five items passed. The defect
of this method was recognized, so that in his 1911 scale, Binet modified his procedure in order to
permit the addition of a fraction of a year for items passed. In the Stanford-Binet revisions, the

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