## ACT Growth Modeling Resources

Growth modeling based on assessments of college and career readiness can be used to measure progress—both for individual students and school systems.

• Growth modeling tells students how far they need to progress to reach their readiness goals.
• Growth modeling is also used for educational research and evaluation. Measures of student growth can be used as one component of teacher, school, or district evaluation and can help diagnose areas of strength and weakness.

To help individuals and school systems implement growth models based on ACT assessments, ACT provides normative growth data for various assessment combinations and grade levels.

In a Growth to Standards model, student progress is monitored with respect to an external criterion—in our case, the ACT College Readiness Benchmarks. The Growth to Standards model directly addresses the question “Has the student gained enough?”

In the graph below, the Growth to Standards model is applied to a fictitious 4th-grade student (John) who took ACT Aspire in grades 3 and 4. His score is below the 4th-grade ACT Readiness Benchmark in mathematics, and his goal is to become on target for college readiness by 7th grade. At each future grade level, one can determine if he is growing enough to reach his goal. The ACT Readiness Benchmarks for each grade level are represented by the points on the red line, John’s scores are represented by the solid black squares, and John’s goals are represented by the dashed black line. The ACT College Readiness Benchmark for Mathematics is 22 and is represented by the black X.

Note: For illustration, this graph shows ACT Aspire scores on one vertical axis and ACT scores on the other vertical axis. However, the two scales are not interchangeable.

ACT Aspire supports Growth to Standard Models by reporting student progress over time with respect to the ACT Readiness Benchmarks. Sample reports can be viewed here.

The ACT Readiness Benchmarks for ACT Aspire grades 3 through 10 and the ACT College Readiness Benchmarks for ACT Explore® (grades 8 and 9), ACT Plan® (grade 10), and the ACT® test (grades 11 and 12) are given in the table below. Shaded rows represent grade levels where the two scales overlap.

 Asessment Grade Level Subject Area English Reading Mathematics Science Writing ACT Readiness Benchmark ACT Aspire 3 413 415 413 418 428 4 417 417 416 420 428 5 419 420 418 422 428 6 420 421 420 423 428 7 421 423 422 425 428 8 422 424 425 427 428 9 426 425 428 430 428 10 428 428 432 432 428 ACT College Readiness Benchmark ACT Explore 8 13 16 17 18 9 14 17 18 19 ACT Plan 10 15 18 19 20 ACT 11/12 18 22 22 23

Growth can be described in a normative fashion by considering the average of test score 2 for each value of test score 1. These averages are known as conditional score averages. If students exceed the conditional score average, they performed better on test 2 than their peers with the same score on test 1. The conditional score averages are useful for predicting scores in a future grade and for measuring student growth relative to peers with the same prior test scores.

Below, we provide conditional score averages for numerous pairs of assessments. Find the assessment pair and select the growth period you are interested in to download the conditional score averages and 50% score prediction intervals.

Test 1 Test 2 Growth Period
ACT Explore English ACT QualityCore English 9 6–12 months
ACT Explore Mathematics ACT QualityCore Algebra I 6–12 months
ACT Explore Mathematics ACT QualityCore Geometry 6–12 months
ACT Explore Science ACT QualityCore Biology 6–12 months
ACT Explore English ACT QualityCore English 10 18–24 months
ACT Explore Mathematics ACT QualityCore Geometry 18–24 months
ACT Explore Science ACT QualityCore Biology 18–24 months
ACT Plan English ACT QualityCore English 10 6–12 months
ACT Plan Mathematics ACT QualityCore Geometry 6–12 months
ACT Plan Mathematics ACT QualityCore Algebra II 6–12 months
ACT Plan Science ACT QualityCore Biology 6–12 months
ACT Plan Reading ACT QualityCore US History 6–12 months
ACT Plan English ACT QualityCore English 11 18–24 months
ACT Plan Mathematics ACT QualityCore Geometry 18–24 months
ACT Plan Mathematics ACT QualityCore Algebra II 18–24 months
ACT Plan Mathematics ACT QualityCore Pre-Calculus 18–24 months
ACT Plan Reading ACT QualityCore U.S. History 18–24 months
ACT Plan Science ACT QualityCore Chemistry 18–24 months
ACT QualityCore English 9 ACT QualityCore English 10 10–14 months
ACT QualityCore English 10 ACT QualityCore English 11 10–14 months
ACT QualityCore English 11 ACT QualityCore English 12 10–14 months
ACT QualityCore Algebra I ACT QualityCore Algebra II 22–26 months
ACT English ACT Compass Writing Skills 10–14 months
ACT Mathematics ACT Compass Pre-Algebra 10–14 months
ACT Mathematics ACT Compass Algebra 10–14 months
ACT Mathematics ACT Compass College Algebra 10–14 months

### How to Apply the Conditional Score Averages

In this example, 124 students took the ACT Explore assessment in 9th grade and then took the ACT Plan assessment in 10th grade, 12 months later. Students’ predicted ACT Plan scores are determined by their ACT Explore score in the same subject area using the Conditional Score Average model.

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

The worksheet titled “Conditional Score Averages” is obtained from the ACT Explore/ACT Plan/Grade 9 to grade 10 (10–14 months) row in the table above.

Projection models are used to predict scores in a future grade and are meant to answer the question “Given this student’s observed past scores and based on patterns of scores in the past, where is she likely to score in the future?”

The projection model is a variant of linear regression where an equation is established that relates students’ past scores to their future scores. The projection model is flexible in that multiple past scores, as well as other measures, can be used to predict a single future score.

For example, a grade 10 ACT Plan Mathematics score can be predicted based on grade 9 ACT Explore scores in all four subject areas (English, mathematics, reading, and science) and on the number of months between the two assessments:

• ACT Plan Mathematics Score= β0 + β1 × ACT Explore English Score + β2 × ACT Explore Mathematics Score + β3× ACT Explore Reading Score + β4 × ACT Explore Science Score + β5 × Months Elapsed

In this model, the β values are weights relating each input variable to the future test score. We refer to these weights as projection parameters.

The projection model we employ is different from the conditional score average model because, instead of conditioning on a single past test score, we are conditioning on multiple past test scores. Generally, score predictions from the projection model are more accurate than score predictions from the conditional score average model because it uses more information for predicting future test scores.

Below, we provide projection parameters for several pairs of assessments. Find the assessment pair and select the growth period you are interested in to download the projection parameters.

Test 1 Test 2 Growth Period
ACT Explore ACT QualityCore English 9 6–12 months
ACT Explore ACT QualityCore Algebra I 6–12 months
ACT Explore ACT QualityCore Geometry 6–12 months
ACT Explore ACT QualityCore Biology 6–12 months
ACT Explore ACT QualityCore English 10 18–24 months
ACT Explore ACT QualityCore Geometry 18–24 months
ACT Explore ACT QualityCore Biology 18–24 months
ACT Plan ACT QualityCore English 10 6–12 months
ACT Plan ACT QualityCore Geometry 6–12 months
ACT Plan ACT QualityCore Algebra II 6–12 months
ACT Plan ACT QualityCore Biology 6–12 months
ACT Plan ACT QualityCore U.S. History 6–12 months
ACT Plan ACT QualityCore English 11 18–24 months
ACT Plan ACT QualityCore Geometry 18–24 months
ACT Plan ACT QualityCore Algebra II 18–24 months
ACT Plan ACT QualityCore US History 18–24 months
ACT Plan ACT QualityCore Chemistry 18–24 months
ACT Plan ACT QualityCore Pre-Calculus 18–24 months
ACT ACT Compass Writing Skills 10–14 months
ACT ACT Compass Pre-Algebra 10–14 months
ACT ACT Compass Algebra 10–14 months
ACT ACT Compass College Algebra 10–14 months
ACT ACT Compass Reading Skills 10–14 months

### How to Apply the Projection Model

In this example, 131 students took the ACT Plan assessment in 10th grade and then took the ACT test in 11th grade (11 or 12 months later). Students’ predicted ACT scores are determined by their ACT Plan scores in all four subject areas, as well as the number of months elapsed between the ACT Plan and ACT tests.

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

The worksheet named “Projection Model Parameters” is obtained from the ACT Plan/ACT/Grade 10 to grade 11 (10–14 months) row in the table above.

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. Also included are SGP lookup tables for grade 10 ACT Aspire to the grade 11 ACT test. 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 59 (as shown in the table below, which is an excerpt from the grade 4–5 SGP lookup table).

version current_grade subject prior_score current_score growth_percentile
2016F 5 Mathematics 411 411 16
2016F 5 Mathematics 411 412 24
2016F 5 Mathematics 411 413 35
2016F 5 Mathematics 411 414 47
2016F 5 Mathematics 411 415 59
2016F 5 Mathematics 411 416 73
2016F 5 Mathematics 411 417 81

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 below.

Test 1 Test 2 Growth Period Reference Group
ACT Aspire ACT Aspire Grade 3 to grade 4 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire ACT Aspire Grade 4 to grade 5 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire ACT Aspire Grade 5 to grade 6 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire ACT Aspire Grade 6 to grade 7 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire ACT Aspire Grade 7 to grade 8 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire ACT Aspire Grade 8 to grade 9 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire ACT Aspire Grade 9 to grade 10 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire The ACT Grade 10 to grade 11 (1 year) Examinees who tested in consecutive years from spring 2013 through spring 2016
ACT Aspire PreACT Grade 9 to grade 10 (1 year) Examinees who tested in fall 2015 (grade 9) and fall 2016 (grade 10)
ACT Explore ACT Plan Grade 9 to grade 10 (1 year) Examinees who tested in consecutive years from 2006 through 2016
ACT Plan The ACT Grade 10 to grade 11 (1.5 years) Examinees who tested in consecutive years from 2006 through 2016
The ACT The ACT Grade 11 to grade 12 (6 months) Examinees who tested in consecutive years from 2013 through 2016

### 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. Formulas are used in the Excel spreadsheet to look up the SGP value based on the ACT Aspire score and ACT test 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.

### Earlier Versions of ACT Aspire SGP Lookup Tables

The lookup tables below were developed in 2015 and are not the most current lookup tables available.

Test 1 Test 2 Growth Period Reference Group
ACT Aspire ACT Aspire Grade 3 to grade 4 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT Aspire ACT Aspire Grade 4 to grade 5 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT Aspire ACT Aspire Grade 5 to grade 6 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT Aspire ACT Aspire Grade 6 to grade 7 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT Aspire ACT Aspire Grade 7 to grade 8 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT Aspire ACT Aspire Grade 8 to grade 9 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT Aspire ACT Aspire Grade 9 to grade 10 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015
ACT Aspire The ACT Grade 10 to grade 11 (1 year) Examinees who tested in spring 2013 and spring 2014, or spring 2014 and spring 2015

The lookup tables below were developed in 2014 and are not the most current lookup tables available.

Test 1 Test 2 Growth Period Reference Group
ACT Aspire ACT Aspire Grade 3 to grade 4 (1 year) Examinees who tested in spring 2013 and spring 2014
ACT Aspire ACT Aspire Grade 4 to grade 5 (1 year) Examinees who tested in spring 2013 and spring 2014
ACT Aspire ACT Aspire Grade 5 to grade 6 (1 year) Examinees who tested in spring 2013 and spring 2014
ACT Aspire ACT Aspire Grade 6 to grade 7 (1 year) Examinees who tested in spring 2013 and spring 2014
ACT Aspire ACT Aspire Grade 7 to grade 8 (1 year) Examinees who tested in spring 2013 and spring 2014
ACT Aspire ACT Aspire Grade 8 to grade 9 (1 year) ACT Explore examinees tested in academic years 2008–2009
and 2010–2011 (grade 9). The ACT Explore/Plan-to-ACT
Aspire concordance was applied to estimate SGPs on the
ACT Aspire scale.
ACT Aspire ACT Aspire Grade 9 to grade 10 (1 year) ACT Explore and ACT Plan examinees tested in academic
2010–2011 (grade 9) and 2011–2012 (grade 10). The ACT Explore/Plan-to-ACT Aspire concordance was applied to
estimate SGPs on the ACT Aspire scale.
ACT Aspire The ACT Grade 10 to grade 11 (1 year) Examinees who tested in spring 2013 and spring 2014

Student growth measures can be used within systems for evaluating teachers, schools, and districts. Several methods attempt to estimate the distinct effects of teachers and schools on student growth. These methods are intended to support value-added interpretations.

### The Multivariate Model

The Multivariate model is designed for the primary purpose of supporting value-added inferences for teachers and schools. By simultaneously considering multiple years of student scores across subject areas, the Multivariate model attempts to attribute student performance to individual teachers and schools. A well-known example of the Multivariate model is the Education Value-Added Assessment System (EVAAS). Because of its technical complexity and extensive data requirements, the Multivariate model is not supported here.

### Value-Added Interpretations from Other Models

With proper attribution of student growth measures, value-added interpretations can be made from simpler models, including the Conditional Score Averages, Projection, and Student Growth Percentile models.

Note that the Conditional Score Averages and Projection models both produce predicted scores. For a group of students, a normative measure of aggregate growth can be constructed by averaging the residual scores—the difference between actual and predicted scores. If the mean residual score is significantly greater than 0, then the group of students performed better than predicted, on average. If the mean residual score is significantly less than 0, then the group of students performed worse than predicted, on average. Simple statistical tests can be used to determine if the mean residual score is greater or less than 0.

For the Student Growth Percentile (SGP) model, the mean (or median) SGP is a normative measure of aggregate growth. If the mean SGP is significantly greater than 50, then the group of students performed better than predicted, on average. If the mean SGP is significantly less than 50, then the group of students performed worse than predicted, on average. Simple statistical tests can be used to determine if the mean SGP is greater or less than 50.

Value-added interpretations of teachers and schools are better supported when individual student performance can be attributed directly to the teacher and school. Factors that negatively affect confidence in attribution include:

• Misalignment of timing of assessments and timing of instruction
• Misalignment of assessment content coverage to instructional content coverage
• Team teaching, multidisciplinary instruction, or other situations where multiple teachers affect student learning
• Student migration, absenteeism, and other personal events that affect academic performance

Generally, attribution is difficult because many forces act upon student performance, and it is difficult to disentangle them. Because of difficulties with attribution and year-to-year inconsistency in estimates of teacher and school effects, many experts suggest that teacher and school effect estimates should supplement, not replace, other sources of information for evaluation.

In some cases, it may be unreasonable to attribute student performance to a single teacher. In other cases, it may be more reasonable to assign weights to student growth measures representing the level of attribution to individual teachers.

### Examples

In the first two examples below, students’ predicted scores are compared to their actual scores to obtain a residual score. If the mean residual score is significantly greater than 0, then the group of students performed better than predicted, on average. If the mean residual score is significantly less than 0, then the group of students performed worse than predicted, on average. A simple statistical test known as the one-sample t-test is used to determine if the mean residual score is significantly greater or less than 0. If it is significantly greater than 0, the aggregate growth is classified as “Above Expected”; if it is significantly less than 0, the aggregate growth is classified as “Below Expected.” Otherwise, the aggregate growth is classified as “Expected.” In the third example, a statistical test is used to determine if the mean SGP is significantly greater or less than 50.

#### Example 1

In this example, 124 students took the ACT Explore assessment in 9th grade and then took the ACT Plan assessment in 10th grade, 12 months later. Students’ predicted ACT Plan scores are determined by their ACT Explore score in the same subject area using the Conditional Score Averages model. Predicted ACT Plan scores can be compared to actual ACT Plan scores to obtain residual scores that measure growth relative to peers. The predicted values and residual scores are highlighted in the spreadsheet.The worksheet named “Conditional Score Averages” is obtained from theConditional ACT Explore grade 9 to ACT Plan grade 10 (10 to 14 months) file.

The mean residual scores are calculated for each subject area. Each of the mean residual scores is greater than 0, and the t-test p-values (<0.05) indicate that the means are significantly greater than 0. Therefore, the growth in each subject area is classified as “Above Expected.”

#### Example 2

In this example, 131 students took the ACT Plan assessment in 10th grade and then took the ACT in 11th grade (11 or 12 months later). Students’ predicted ACT scores are determined by their ACT Plan scores in all four subject areas, as well as the number of months elapsed between the ACT Plan and ACT tests. Predicted ACT scores can be compared to actual ACT scores to obtain residual scores that measure growth relative to peers. The predicted values and residual scores are highlighted in the spreadsheet. The worksheet named “Projection Model Parameters” is obtained from theProjection ACT Plan grade 10 to ACT grade 11 (10–14 months) file.

The mean residual scores are calculated for each subject area. For English, reading, and science, the mean of the residual scores is less than 0, and the t-test p-values (<0.05) indicate that the means are significantly less than 0. Therefore, the growth in English, reading, and science is classified as “Below Expected.” For mathematics, the mean of the residual scores is less than 0, but the t-test p-value (0.269) indicates that the mean is not significantly less than 0. Therefore, the growth in mathematics is classified as “Expected.”

#### Example 3

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.

The mean SGP values are calculated for each subject area. The mean SGP values range from 50.60 for science to 56.70 for Reading. For each subject area, the t-test p-value is greater than 0.05, so there is not enough evidence to conclude that the mean SGP is significantly different from 50 in any subject area. Therefore, the growth is classified as “Expected” for each subject area.