Data Visualization and Student Growth Percentiles
Damian W. Betebenner
National Center for the Improvement of Educational Assessment
Dover, NH
2013 NEERO Annual Conference, Portsmouth, New Hampshire
April 17th, 2013
Damian W. Betebenner Data Visualization and SGPs
From a Paucity to a Plethora of Data
The Economist: The Data Deluge
Historical records of student achievement
Historical records of student demographics, teachers, schools,
educational programs, . . .
Stakeholder interest in an examination of this longitudinal data
Interest in examining student achievement over time (student
growth) derives from data availability.
Damian W. Betebenner Data Visualization and SGPs
Describing Student Growth
Measuring student growth, even with a vertical scale, is not a simple
task.
Some believe a vertical scale simplifies the task of measuring
student growth.
Even with an interval (or ratio) scale, growth is not easy to interpret.
Consider, for example, height.
A child might grow 4 inches between ages 3 and 4.
4 inches is a well understood quantity.
The 4 inch increase becomes really meaningful only when understood
alongside the growth of other 3 to 4 year olds.
Student growth percentiles were developed to provide a normative
context for describing student growth.
Damian W. Betebenner Data Visualization and SGPs
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Student Growth Percentiles
Should we be surprised with a child’s current achievement given their prior
achievement?
Given a student’s prior scale scores and the associated conditional
density, their current scale score corresponds to a percentile of that
conditional distribution.
This percentile is the student’s growth percentile.
Growth percentiles are closely related to estimating the probability of
observing a student’s current achievement taking account of their
past achievement:
Pr(Current Achievement |Past Achievement ).
As such, growth percentiles describe the rarity of a student’s current
achievement conditional upon their prior achievement.
Damian W. Betebenner Data Visualization and SGPs
Student Growth Percentiles
Should we be surprised with a child’s current achievement given their
prior achievement?
Student growth percentiles answer this question.
Consider a low achieving student with 50th percentile growth and a
high achieving student with 50th percentile growth.
The low achieving student grew at a rate exceeding 50 percent of
similar students.
The high achieving student grew at a rate exceeding just 50 percent of
similar students.
The low achiever’s growth is probabilistically as rare as the high
achiever’s.
Equally rare does not mean equally good.
Judgments about the adequacy of student growth require external
criteria.
Damian W. Betebenner Data Visualization and SGPs
Model for Student Growth Percentiles
Student growth percentiles are calculated using quantile regression
with B-spline smoothing, a generalized additive model.
Quantile regression is used to model the complete distribution of the
response variable (current achievement)
B-spline smoothing is uses to accommodate non-linearity and
heteroscedasticity of the data.
The model/method is descriptive and all about data fit—it’s a data
mining procedure.
The model quantifies distance = rate · time probabilistically.
Damian W. Betebenner Data Visualization and SGPs
Model for Student Growth Percentiles
Conditional Decile Regression Curves Conditional Decile Regression Lines
2006−07 Math: Grade 5 versus 6 2006−07 Math: Grade 5 versus 6
1000 Unsatisfactory Partially Prof. 1000 Unsatisfactory Partially Prof.
Proficient Proficient
Partially Prof. Proficient Advanced Partially Prof. Proficient Advanced
Grade 6 Scale Score Grade 6 Scale Score
Grade 5 Scale Score Grade 5 Scale Score
Damian W. Betebenner Data Visualization and SGPs
Software for Student Growth Percentiles
Student Growth Percentiles and Percentile Growth Trajectories are
calculated using the open source R Software Environment [?] and
the open source SGP package [?]
The SGP package is hosted on GitHub and multiple state analysis
sites are present there. See https://github.com/SchoolView.
In working with state departments of education, the goal is to build
state capacity so states can perform and validate their own analyses
using software available and easily used by the state.
Arizona, Colorado, Georgia, Massachusetts, Idaho, Indiana,
Wisconsin are four states (that I know of) who have state staff
capable of generating the student growth percentiles together with
aggregations that follow from their calculation.
State ownership/oversight of the SGP calculations has been a big
plus in terms of buy-in from the state, enhancing their ability to
explain and work with local stakeholders.
Damian W. Betebenner Data Visualization and SGPs
About this copy
Data Visualization and Student Growth Percentiles — Northeastern Educational Research Organization, April 17, 2013.
This is an image-based copy of the original beamer slides; builds and animations are flattened.