# 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 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 for examining differences in growth across student groups.

ACT Aspire reports SGPs for students tested in consecutive years for grade levels 3 through 10. This page includes SGP “lookup” tables for ACT Aspire. The tables can be used to find the SGP value (ranging from 1 to 100) associated with each combination of current-year test score and prior-year test score. For example, suppose a student scored 411 on the grade 4 ACT Aspire Mathematics test and 415 on the grade 5 ACT Aspire Mathematics test one year later. His SGP value (given by the “growth_percentile” column) would be 56 (as shown in the graphic, which is an excerpt from the grade 4–5 SGP lookup table).

The lookup tables provide an estimate of the SGP for each possible combination of same-subject test scores from consecutive years. SGPs are provided for five subject areas: English, mathematics, reading, science, and writing. The SGPs were estimated using quantile regression methods (Koenker, 2005) by the SGP R package (Betebenner, VanIwaarden, Domingue, Shang, 2014). The SGP model is flexible because multiple prior test scores can be used as inputs. The lookup tables provided below are based on a single prior-year score in the same subject area.

When interpreting SGPs, the reference group used to estimate the model should always be considered. The SGPs for ACT Aspire will be updated over time as larger and more diverse reference groups become available. Earlier versions of the SGP lookup tables are available here.

Test 1Test 2Growth PeriodReference Group
ACT AspireACT AspireGrade 3 to grade 4 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT AspireACT AspireGrade 4 to grade 5 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT AspireACT AspireGrade 5 to grade 6 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT AspireACT AspireGrade 6 to grade 7 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT AspireACT AspireGrade 7 to grade 8 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT AspireACT AspireGrade 8 to grade 9 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT AspireACT AspireGrade 9 to grade 10 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT AspireThe ACTGrade 10 to grade 11 (1 year)Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015

### 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 all five subject areas (English, mathematics, reading, science, and writing). 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.

#### 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.