18
below the national average 50th percentile. When comparing performance across all subtests, it is noticeable that
the group performed lowest in Math.
A look at the frequency distribution (the bottom portion of the report) shows that on the Reading subtest, 2 students
(5%) earned a national percentile of 82–87, which in turn is equivalent to a national stanine of 7. By combining
selected data points, it can be determined that the Reading performance of 5 students (10%) fell within the upper 12%
of the national normative sample (88th–99th percentiles), which corresponds to the 8th and 9th national stanine band,
the high range of the national scales. From the data points shown for the Composite score, it may be determined that
the performance of 16 students (38%) fell within the Low/Below Average categories, 11 students (26%) fell within
the Average category, and 15 students (36%) fell within the Above Average/High categories.
Considerations:
Needless to say, the focus of this report is based upon the group rather than individuals. Hence, if one wishes to
identify the students who attained a national percentile of 99 for the composite score, it would be necessary to search
the list of individual student results to discover their names.
Caution must be used when interpreting group summary information when the group is based on small numbers.
Summary results are less precise for small groups and can be affected by extreme individual scores. For example, a
score that is extremely high or low may have a greater impact on the average scores of 10 students but will have less
effect on the average of say 100 student scores.
Number Tested, Standard Score Means, and Standard Deviations: The greatest value of the standard score scale
lies in its ability to function as a common denominator between various editions of the HSPT. Thus, it forms a bridge
between your current group and previous groups, and allows you to make direct comparisons of their respective
performance levels. The group summary standard score means also provide a comparison baseline for comparing
individual performance to the group average.
When comparing two groups, each consisting of 100 or more individuals, differences as small as 4 or 5 points
between standard score means are statistically significant; that is, one can conclude with reasonable confidence
that the observed difference stems from a true difference in test performance rather than the occurrence of chance
variations. As either the size of the groups or the magnitude of the difference increases, the same conclusion may
be drawn with even greater confidence. One must also recognize, however, that a difference which is statistically
significant does not always possess practical significance. While differences in the range of 5 to 40 standard score
points are statistically significant for groups of 100 or more, such differences are not large enough to warrant any
special concern other than noting their occurrence and the direction of the shift. In other words, the skill level of the
two groups—while measurably different—is sufficiently similar to be considered equivalent for all practical purposes.
Consequently, differences in this range lack practical significance.
As one might expect, observed differences in excess of 40 standard score points require more than a passing comment
on your part. Values in this range are indicative of substantial differences in test performance between groups, and
thus, signify major differences in their respective skill levels. When confronted by differences of this magnitude,
attention should be focused upon the curriculum related to the area in which the excessive difference was observed.
For example, if the standard score mean for Math of the current group were 45 to 50 points lower than that earned
by an earlier group, one would be well-advised to re-evaluate the math curriculum with respect to its suitability for
a group whose math skills are substantially weaker than those of previous students. A separate remedial program
might also be considered for those whose individual standard scores in Math are well below the mean of the current
group. Conversely, if the math performance of the current group were 45 or 50 points higher than earlier students, it
might be appropriate to increase the scope, pace, or depth of the curriculum to accommodate or even challenge their
higher level of math skills.
It should be noted that differences in excess of 40 points usually are not observed between groups whose testings are
separated only by a year or two. Typically, year-by-year comparisons yield differences well within the 5–40 range noted
earlier. However, if a given trend continues over an extended period, the accumulated differences (or the difference
between the initial and current groups) can reach proportions that merit serious attention. In other words, substantial
changes in performance are more likely to creep into view than burst dramatically upon the scene. Consequently, for
those who wish to monitor this aspect of the HSPT, it is vital to retain the data obtained from each testing for use in
subsequent analyses.