Understanding and Using Student Growth
Percentiles
Damian Betebenner and Scott Marion
The National Center for the Improvement of Educational Assessment
Presentation to the Utah Technical Advisory Committee
May 19, 2025
This work is licensed under a
Creative Commons Attribution 4.0
International License.
Background
• The Utah Assessment and Accountability Directors
(assessment and accountability specialists in Utah school
districts) sent a request to USBE to have the state switch from
a cohort-referenced to a baseline-referenced SGP model.
• We want to consider the opportunities and tradeoffs
associated with their request.
Utah Growth Model Discussion (5/19/25) 2
According to UAAD….
• The Advantages of a Baseline-Referenced Model Are:
▪ Immediate Results: Growth calculations can be performed
immediately following assessments, allowing data to inform
instructional and programmatic decisions promptly…
▪ Stable and Consistent Comparison: Schools will have stable
reference points across years, allowing clearer longitudinal
analysis…
▪ Enhanced Utility for Planning: Immediate availability of actionable
data supports timely and strategic school improvement efforts...
• We will examine these and other claims.
Utah Growth Model Discussion (5/19/25) 3
Student Growth Percentile Basics
Utah Growth Model Discussion (5/19/25) 4
Student Growth Percentiles
• SGPs describe the relative location of a
student’s current score compared to
the current scores of students with
similar score histories.
• The location in this reference group of
“academic peers” is expressed as a
percentile rank. For example, a student
earning an SGP of 80 performed as well
as or better than 80 percent of her Norm- and Criterion-Referenced Student
academic peers. Growth (2009)
D. Betebenner
Utah Growth Model Discussion (5/19/25) 5
Graphic Representative of SGPs
Utah Growth Model Discussion (5/19/25) 6
SGPs and Key Questions from Castellano & Ho
1. What primary interpretation is best supported?
▪ Growth description—SGPs describe the relative performance of students by
comparing their current scores to those of a set of students with similar scores
on prior grade-level tests. The SGP metric expresses this relative status in
terms of percentile ranks.
▪ Growth projection—The SGP model is easily extended to describe the growth
necessary for students to reach important milestones (e.g., proficient, CCR).
2. What is the statistical foundation of the model?
▪ SGPs are calculated using quantile regression, which is a non-parametric
regression approach that can better fit non-linear data, especially for high and
low performers.
3. What are the required data features?
▪ SGPs require at least 5,000 students per grade/content area, which is
not a problem with any state. At least one prior score is required, but
two prior scores improves the accuracy substantially.
Utah Growth Model Discussion (5/19/25) 7
SGPs and Key Questions from Castellano & Ho
4. What kinds of group-level interpretations are best supported?
▪ SGPs are easily aggregated at the subgroup, school, district, and state levels using
medians or means. Medians describe the typical growth at the aggregate level,
while means describe the average growth.
5. Does the model set standards for expected or adequate growth?
▪ The 50th percentile is implicitly defined as typical growth, but some type of
standard-setting approach is necessary to define high, typical, low, and any other
level of growth (see next slide).
6. What are the common misinterpretations and unintended
consequences?
▪ Student Growth Percentiles are often incorrectly assumed to describe an absolute
amount of growth, but they are normative because “growth” is determined with
respect to other students in the model with a similar score history.
▪ As intuitive as SGPs seem to be, we often find confusion with things like percent
correct.
Utah Growth Model Discussion (5/19/25) 8
Types of SGPs
• Cohort-referenced SGPs: These are the typical SGPs that are normed
within each year such that the median SGP for each grade/content
area = 50 at the state level.
• Adequate Growth Percentiles (AGPs) represent the growth students
must make (in a percentile metric) each year to reach a specific score/
achievement target (e.g., proficiency) in a specified amount of time.
• Baseline-referenced SGPs: Unlike coherent-referenced SGPs, baseline-
referenced SGPs evaluate current growth against some baseline group
(e.g., student growth between 2018 and 2019). In this case, the entire
state can demonstrate higher or lower-than-average growth (e.g.,
what is the value of a dollar today in 2018 terms?).
Utah Growth Model Discussion (5/19/25) 9
Example of Adequate Growth Representation
Mathematics
Advanced
Achievement
Catch Up DEMO Mathematics
Target Scale Score
Catch Up
Target
Growth
Proficient Level Percentiles
Very High 81st − 99th
High 61st − 80th
Part Proficient
Typical 40th − 60th
Low 20th − 39th
Unsatisfactory Very Low 1st − 19th
Grade 3 Grade 4 Grade 5 Grade 6 Grade 7
Scale Score 314 378 399 396
Achievement Level
Achievement Target
Unsatisfactory Unsatisfactory Unsatisfactory
Proficient (472)
Unsatisfactory
Proficient (530)
Achievement
Growth Percentile 51 29 34
Growth Level
Growth Target
Typical Low Low
Catch Up (97) Catch Up (99)
Growth
Utah Growth Model Discussion (5/19/25) 10
Baseline Referenced SGPs
• Instead of re-norming growth from year-to-year, it is possible to use growth-
norms derived from a previous cohorts of students to calculate students’
SGPs.
• This approach has been utilized in Utah and more than a dozen other
states to investigate COVID-19 impact/recovery (learning deceleration/
acceleration).
• Adequate growth percentiles can be calculated with respect to baseline
growth norms.
• Mean/Median SGPs can deviate from 50.
• Baseline SGPs can be calculated correcting for measurement error (SIMEX &
ranked SIMEX measurement error correction).
• Baseline SGPs can be calculated using previous “super-cohorts” of students.
Utah Growth Model Discussion (5/19/25) 11
Baseline Referenced SGPs: Benefits
• Not a “zero sum game”. All students can demonstrate high
growth.
• Allows for the detection of learning/growth acceleration
and deceleration.
• Allows for the calculation of SGPs using preliminary data
(don’t have to wait for entire cohort of data to be available).
• Unlike cohort-referenced SGPs, growth targets are NOT
updated as new growth norms become available because
growth norms remain fixed across years.
Utah Growth Model Discussion (5/19/25) 12
Baseline Referenced SGPs: Requirements & Detriments
• The use of baseline growth norms (to calculate baseline
referenced SGPs) requires scale equivalence across years.
• Scale drift will impact baseline SGP results.
• As such, baseline SGPs can be a valuable asset in
identifying scale drift (if growth acceleration is too good
to be true, it probably is.)
• Depending upon how far the state goes in communicating
details of the methodology, can be more complicated to
explain than cohort referenced SGPs.
Utah Growth Model Discussion (5/19/25) 13
Use Cases for Student Growth
Percentiles
We can keep or delete
slides 12-19
Utah Growth Model Discussion (5/19/25) 14
Actual and Potential Uses of SGPs in Utah
1. Accountability: SGPs are the foundation of the “other
academic indicator” and the “equity” indicator.
2. Monitoring: SGPs have been useful in understanding COVID
impacts and rates of recovery. They can also be used to
monitor local educational programs.
3. Evaluation: SGPs (or other student growth measures) can
support more defensible causal conclusions than changes in
proficiency when evaluating programs, curriculum, or
strategies.
4. Warning: Low SGPs are a red flag warning for students,
especially for low-achieving students.
Utah Growth Model Discussion (5/19/25) 15
How Do SGPs Work in Accountability?
• There are several ways that SGPs and AGPs can be used in
accountability.
• Utah has used both AGPs (SGTs) and SGPs in accountability for
many years.
• In April 2022, the U.S. Department of Education approved
Utah’s 2022 addendum, which proposed indexing points for
growth based on SGP only, as shown on the following slide.
Utah Growth Model Discussion (5/19/25) 16
Student Growth Points in Utah
Observed Student Met AGP
Student SGP
The total number of points across all students is divided by the number of tests. This
proportion is then multiplied by the total possible points for each subject area (for
growth) to arrive at the growth points for each school.
This represents about 1/3 of the total accountability weight for 3-8 schools.
Utah Growth Model Discussion (5/19/25) 17
Monitoring
• SGPs have been used for helping USBE
understand the impact and recovery from
the COVID pandemic interruptions.
• The following slide reports the baseline
SPGs to document the academic recovery
as of 2023.
Utah Growth Model Discussion (5/19/25) 18
2023 SGP Results
• Mean/Median/Count for baseline referenced SGPs in ELA and
mathematics are as follows:
ELA Mathematics
Grade
Utah Growth Model Discussion (5/19/25) 19
What We’re Learning From Growth Results
Rates of learning, on average, are slightly exceeding or at pre-
pandemic rates of growth. The SYSTEM has recovered, and then
some.
Student attainment, on average, is still lagging because rates of
learning have not accelerated enough to catch students up. In
other words, students have not fully “recovered,” but their levels
are, in most grades, close to pre-pandemic levels.
Utah Growth Model Discussion (5/19/25) 20
Growth as an Evaluation Metric
• Using student longitudinal growth measures in evaluation
studies avoids several of these pitfalls.
• Students serve as their own “control group.” If the growth
trajectories change noticeably, we can posit that the program
or policy had an effect.
• We recently evaluated a state’s accountability system. One of
the key questions was whether being identified for CSI had an
effect on the school’s outcomes.
▪ Aggregate measures of student growth are an important outcome
and leading indicator.
▪ In other words, increases in proficiency should follow increases in
growth.
Utah Growth Model Discussion (5/19/25) 21
Trade-offs
Utah Growth Model Discussion (5/19/25) 22
Advantages of Cohort- and Baseline-Referenced SGPS
Cohort-Referenced Baseline-Referenced
• Relatively straightforward to • Able to observe all students/
calculate, with a long history schools improve (or decline)
of doing so. • Helps to monitor trends in
performance over time at the
• Scale agnostic--can state, district, and school levels
transition across • Useful for monitoring potential
assessments and scale-drift scale drift and the quality of
• Accuracy improves equating for the tests
considerably with multiple
prior scores
Utah Growth Model Discussion (5/19/25) 23
Challenges with Cohort- and Baseline-Referenced SGPS
Cohort-Referenced Baseline-Referenced
• Essentially a zero-sum game • The inferences could change
each year, in that the depending on what years we
select as the baseline
average is always 50
• If the scale or the test
• As easy as we thought it undergoes substantial changes,
would be to understand, a new baseline will need to be
people still struggle to computed, and this could take
understand and act on the several years
results • May be harder to explain than
cohort-referenced SGPs
Utah Growth Model Discussion (5/19/25) 24
Revisiting the UAAD Claims and Responses
• Immediate Results:
▪ The baseline results can be produced faster than the cohort-
referenced SGPS, especially with preliminary data.
• Stable and Consistent Comparison:
▪ Yes, as long as the test scale remains stable, baseline-referenced
SGPs are useful for monitoring trends
• Enhanced Utility for Planning:
▪ This assumption is based on the immediate delivery of results.
The enhanced utility is still an open question.
Utah Growth Model Discussion (5/19/25) 25
Additional Considerations
• RISE is a vertically scaled test, so if the goal is to be able to
evaluate progress over time, schools and districts can track
their average gain scores
Utah Growth Model Discussion (5/19/25) 26
About this copy
Understanding and Using Student Growth Percentiles — Utah Technical Advisory Committee, May 15, 2025.
This is an image-based copy of the original Keynote slides; builds and animations are flattened.