Student Growth Percentile Model

The Student Growth Percentile (SGP) model answers the question “What is the percentile rank of a student’s current score compared to students with similar score histories?” The model describes how well a student performed, relative to peers with similar score histories.

Similar to the Projection model and the Conditional Score Average model, the SGP model can be used to predict how much students will grow and describes the level of growth that occurred. The SGP model is flexible because multiple prior test scores can be used as inputs. The model lets users examine how much future performance varies for different percentile levels. Many states and school systems use the SGP model for describing student growth, predicting future test scores, and as the basis for examining differences in growth across student groups.

ACT Aspire reports SGPs for students tested in consecutive years for grade levels 3 through 10. For students tested in grade 10 with ACT Aspire and grade 11 with the ACT, an SGP lookup table for grade 10 ACT Aspire to grade 11 ACT is provided. The lookup table provides an estimate of the SGP for each possible combination of grade 10 ACT Aspire score and grade 11 ACT score. SGPs are provided for four subject areas: English, Mathematics, Reading, and Science. This set of SGPs was estimated using quantile regression methods (Koenker, 2005) by the SGP R package (Betebenner, VanIwaarden, Domingue, Shang, 2014). When interpreting SGPs, the reference group used to estimate the model should always be considered. In this case, the reference group consists of students tested with ACT Aspire in 10th grade in spring 2013 and tested with the ACT in 11th grade in 2014. For an example set of grade 10 ACT Aspire and grade 11 ACT scores with SGPs appended, please see Example 1 below.

For ACT assessments other than ACT Aspire, SGP models supported below can be used to predict student’s future scores, at specific percentile levels, relative to their peers with similar score histories. The percentile levels we include are the 10th, 25th, 50th, 75th, and 90th. For example, suppose a student took the ACT Plan assessment in the fall of 10th grade and will take the ACT QualityCore Algebra 2 end-of-course test in spring of 10th grade (8 months after the ACT Plan test). The student’s ACT Plan scores were 16 (English), 17 (Mathematics), 15 (Reading), and 19 (Science). His predicted ACT QualityCore Algebra 2 scores are:

  • 141 if he performs at the 10th percentile relative to students with similar ACT Plan scores
  • 144 if he performs at the 25th percentile relative to students with similar ACT Plan scores
  • 146 if he performs at the 50th percentile relative to students with similar ACT Plan scores
  • 148 if he performs at the 75th percentile relative to students with similar ACT Plan scores
  • 150 if he performs at the 90th percentile relative to students with similar ACT Plan scores

Below, we provide parameters needed for predicting various percentile levels of test scores for several pairs of assessments (not including ACT Aspire). Find the assessment pair and select the growth period you are interested in to download the parameters.

Test 1Test 2Growth Period
ACT ExploreACT ExploreGrade 8 to grade 9 (10–14 months)
ACT ExploreACT PlanGrade 8 to grade 10
ACT ExploreACTGrade 8 to grade 11
ACT ExploreACT PlanGrade 9 to grade 10 (10–14 months)
ACT ExploreACT QualityCore English 96–12 months
ACT ExploreACT QualityCore Algebra I6–12 months
ACT ExploreACT QualityCore Geometry6–12 months
ACT ExploreACT QualityCore Biology6–12 months
ACT ExploreACT QualityCore English 1018–24 months
ACT ExploreACT QualityCore Geometry18–24 months
ACT ExploreACT QualityCore Biology18–24 months
ACT PlanACT PlanGrade 9 to grade 10 (10–14 months)
ACT PlanACTGrade 10 to grade 11 (10–14 months)
ACT PlanACTFall grade 10 to spring grade 11
ACT PlanACT QualityCore English 106–12 months
ACT PlanACT QualityCore Geometry6–12 months
ACT PlanACT QualityCore Algebra II6–12 months
ACT PlanACT QualityCore Biology6–12 months
ACT PlanACT QualityCore US History6–12 months
ACT PlanACT QualityCore English 1118–24 months
ACT PlanACT QualityCore Geometry18–24 months
ACT PlanACT QualityCore Algebra II18–24 months
ACT PlanACT QualityCore US History18–24 months
ACT PlanACT QualityCore Chemistry18–24 months
ACT PlanACT QualityCore Pre-Calculus18–24 months
ACTACT Compass Writing Skills10–14 months
ACTACT Compass Pre-Algebra10–14 months
ACTACT Compass Algebra10–14 months
ACTACT Compass College Algebra10–14 months
ACTACT Compass Reading Skills10–14 months

How to Apply the Student Growth Percentile Model

In this example, 50 students took ACT Aspire in spring grade 10 and then took the ACT in spring grade 11. Each student was tested in four subject areas (English, Mathematics, Reading, and Science). The spreadsheet displays each student’s ACT Aspire and ACT scores, as well as their SGP in each subject area. SGP values are highlighted. Note that the SGP lookup table is needed to obtain each SGP value, based on the subject area tested, ACT Aspire score, and ACT score.

In this example, 85 students took the ACT Plan assessment in the fall and then took the ACT QualityCore Algebra 2 end-of-course test in the spring. For each student, ACT QualityCore Algebra 2 score predictions are made for different percentile levels of growth: 10th, 25th, 50th, 75th, and 90th. Students’ predicted scores are determined by their ACT Plan scores in all four subject areas.

The predicted values are highlighted in the spreadsheet. Predicted ACT QualityCore Algebra 2 scores can be compared to actual ACT QualityCore Algebra 2 scores to obtain residual scores that measure growth relative to peers.

The worksheet named “SGP Parameters” is obtained from the ACT Plan/ACT QualityCore Algebra II/6–12 months row in the table above.

References

Betebenner, D.W., VanIwaarden, A., Domingue, B., and Shang, Y (2014). SGP: An R Package for the Calculation and Visualization of Student Growth Percentiles & Percentile Growth Trajectories. R package version 1.2-0.0. URL.

Koenker, R. (2005). Quantile Regression. New York, NY: Cambridge University Press.