PSAE Scores in Reading, Mathematics, and Science
PSAE scores in mathematics and reading are based on the ACT and WorkKeys tests, and both of
these tests weigh equally in computing the overall PSAE scores. Similarly, the PSAE science
score is determined equally by the ACT and the ISBE developed science test.
How PSAE Scores are NOT computed. PSAE scores do NOT directly use the ACT’s 1
through 36 scale scores, the WorkKeys’ levels (i.e., 0, 3, 4, 5, 6, or 7), or the ISBE science test
scores (40-100). Although the 1 through 36 and the 0, 3, …, 7 are used by the ACT company
and they are reported back to schools and students, these values are not used to compute PSAE
scores. Thus, the PSAE scores cannot be derived directly from the ACT’s 1 thru 36 and the
WorkKeys’s 3, …, 7 because a different approach is used. Similarly, the PSAE science score
cannot directly be computed from the ACT and the ISBE science scores (i.e., 40-100).
How are PSAE scores computed? Rather than using the ACT, WorkKey, and ISBE test scores,
the PSAE scores in mathematics and reading are based on the equated (i.e., “difficulty
adjusted”) raw scores on these tests. Such “equating” is necessary because portions of the ACT,
ISBE science, and the WorkKeys questions’ are changed yearly, and this introduces variation is
the tests’ overall difficulties. By “weighting” questions’ according to their difficulty, students
who get the same scale scores in, say, 2001 and 2004, can be expected to have the same level of
knowledge. At the same time, these students might well have answered a different number of
items correctly on their respective test forms. For proprietary reasons, ACT and ISBE do not
release the relation between students’ equated and un-equated raw scores.
Procedure. In the PSAE’s first year (2001), the following conversions were established for
reading and mathematics separately:
1. Illinois students’ equated raw scores on the ACT were converted to z-scores (i.e., a
variable with mean 0 and standard deviation 1).
2. Reading and Math: Illinois students’ equated raw scores on WorkKeys were converted
to z-scores (i.e., a variable with mean 0 and standard deviation 1).
3. Science: Students’ equated scores on the ISBE science test were similarly converted to
z-scores.
4. The two z-scores were added (i.e., ACT and WK for Reading and Math, and ACT and
ISBE test for science), and the result was given a mean of 160 and a standard deviation of
15.
5. All transformations involved in the above procedures were kept and applied to the data of
all following years, including the current year.
The preceding thus produces PSAE scores that rise or fall with increases or decreases in student
performance, but NOT with the easiness or difficulty of the questions contained in a particular
form of the ACT, ISBE test or WorkKeys. Also, since the cutoff scores for meeting or exceeding
the Illinois Learning Standards remain fixed on the PSAE score dimension, the same levels of
content knowledge are required to meet or exceed these Standards over time.
In summary, adding two z-scores gives equal weights to the two components that make up the
Reading, Math, and Science scores as expressed in terms of equated raw scores.