ERB Growth Model Development
Analyses and Results
Damian Betebenner — Center for Assessment
January 9th, 2023
Data preparation
• Current data being utilized for growth model proof of concept
includes both CTP and Milestones:
Reading Comprehension CTP Fall 49,549 73,204 0
Reading Comprehension CTP Spring 0 118,075 145,927
Reading Comprehension MS Fall 11,380 17,902 0
Reading Comprehension MS Winter 12,786 20,914 0
Reading Comprehension MS Spring 0 6,523 12,371
Data preparation
• LONG formatted data was produced as the first step in SGP
analyses.
• LEVEL was used as the indicator of GRADE
• The R script utilized or data preparation is available here:
SGP Analyses
• With data prepared, the next step is to run SGP analyses using
this data.
• Three sets of analyses were conducted based upon discussions of
student test taking:
• CTP to CTP: Fall to Fall and Spring to Spring
• MS to MS: Fall to Winter, Fall to Spring, Winter to Spring
• MS to CTP: Fall to Spring
• Specifying these analyses is done through configurations available
here.
SGP Analyses
• As a first step we calculate SGPs for students based upon the
configurations specified.
• The SGP model utilized for ERB Reading Comprehension data takes
account of:
• The student’s prior score
• The date in which the student took their test in the current window
• The time span between when they took their current test and
when they took their prior test
• The R script utilized to run the SGP analyses is available here.
SGP Analyses
• Analyses ran with no errors and SGPs were produced for all
cohorts.
• Once LEVEL was used instead of GRADE, everything lined up and
worked
• A selection of Goodness of fit results are presented on the
following slides
• Based upon cutscores provided by Adrienne, I updated the ERB
meta-data in the SGP package. Those outscores and other meta-
data can be found here.
SGP Results
• Analyses ran with no errors and SGPs were produced for all
cohorts.
• Goodness of fit would benefit from larger sample sizes
• Goodness of fit plots indicates some minor issues with ceilings
on the exam (a few students repeatedly scoring perfectly on the
exam).
• Growth and achievement plots suggest an “unevenness” of the
achievement level outscores
ERB: 2022 Reading (Spring) ERB: 2022 Reading (Spring)
Norm & Criterion Referenced Growth & Achievement Norm & Criterion Referenced Growth & Achievement
Percentile Growth Trajectory Percentile Growth Trajectory
Scale Score Scale Score
2022 Achievement Percentile 2022 Achievement Percentile
200 SGP trajectories
SGP trajectories for
for aa 1st
1st grade
grade student
student starting
starting from
from the
the Level
Level 1/Level
1/Level 22 cut.
cut. 200 SGP trajectories
SGP for aa 1st
trajectories for 1st grade
grade student
student starting
starting from
from the
the Level
Level 2/Level
2/Level 33 cut.
cut.
Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10
Jonah Mitchell Sample School
How to interpret this student
growth & achievement report Reading
Scale Score
Exceeds Expectations
(Spring)
Achievement
Achievement Reading
Levels (Spring)
Scale Score
Above Year's Growth
Student Growth
Growth
Percentile Year's Growth Level Percentiles
Meets Expectations
Suggested Uses Below Year's Growth
> Year's Growth 77th − 99th
Review past growth to assess A Year's Growth 23rd − 76th
student academic progress toward
achievement goals.
Develop remediation or enrich−
ment plans based on rate of < Year's Growth 1st − 22nd
growth needed to reach higher Does Not Meet
achievement levels.
Identify the rate of progress
needed in order to reach or
−− Grade 2 Grade 3 Grade 4
maintain proficient status
on the next year. 2020 2021 2022 2023
Scale Score −− 312 400
Achievement Level −− Does Not Meet Does Not Meet
Achievement
Growth Percentile −− 39
Growth Level −− At or Near Year's Growth
Growth
For more information please visit the () at or contact
Cooperatively developed by & the Center for Assessment, Inc. Distributed by .
Fall 2020 CTP to Fall 2021 CTP
Student Growth Percentile Goodness−of−Fit Descriptives Student Growth Percentile Goodness−of−Fit Descriptives
2021 Reading Comprehension Ctp Fall SGP, Grade 2 (N = 1,804) 2021 Reading Comprehension Ctp Fall SGP, Grade 3 (N = 4,105)
SGP Deciles by Prior Achievement Level (Reading Comprehension Ctp Fall) SGP Deciles by Prior Achievement Level (Reading Comprehension Ctp Fall)
Exceeds Expectations (3.6%)
Prior Achievement Level Prior Achievement Level
Exceeds Expectations (39.2%)
Meets Expectations (76.2%)
Meets Expectations (44.3%)
Does Not Meet (20.2%) Does Not Meet (16.5%)
Median Student Growth Percentile Median Student Growth Percentile
Ceiling / Floor Effects Test Ceiling / Floor Effects Test
Student Growth Percentile Range Student Growth Percentile Range
Current Observed Score Current Observed Score
5 9 to to to to to to to to to to
to to 19 29 39 49 59 69 79 89 94 99
1 5 10 20 30 40 50 60 70 80 90 95 5 9 to to to to to to to to to to
to to 10 20 30 40 50 60 70 80 90 95
Lowest OSS: [260,314) 52.0 20.0 28.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 25
Lowest OSS: [310,354) 81.8 13.6 4.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 22
Extremes (Range) Extremes (Range)
Highest OSS: [ 701 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 28.6 22.9 48.6 N = 35
(701,710] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 15.6 84.4 N = 32 Highest OSS: [ 750 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.8 40.4 23.8 29.1 N = 265
Student Growth Percentile Range QQ−Plot: Student Growth Percentiles Student Growth Percentile Range QQ−Plot: Student Growth Percentiles
19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution 19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution
9 to to to to to to to to to 9 to to to to to to to to to
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 1
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100
1st/[126,287) 9.71 9.14 10.86 8.00 12.00 11.43 9.71 11.43 8.57 9.14 (9.7%) 100 1st/[260,406) 9.83 10.32 9.58 10.81 9.58 10.07 9.34 9.58 10.57 10.32 (9.9%) 100
2nd/[287,333) 7.33 12.00 11.33 10.67 7.33 6.00 10.67 11.33 10.00 13.33 (8.3%) 2nd/[406,437) 8.21 9.68 9.97 12.90 12.32 8.21 10.85 9.38 9.97 8.50 (8.3%)
Prior Scale Score Decile/Range * Prior Scale Score Decile/Range *
3rd/[333,367) 11.24 11.24 9.55 10.67 12.36 11.80 8.99 9.55 9.55 5.06 (9.9%) 3rd/[437,461) 12.66 9.50 9.76 10.29 6.07 8.97 6.86 11.61 11.08 13.19 (9.2%)
Empirical SGP Distribution Empirical SGP Distribution
4th/[367,385) 10.24 7.83 12.65 10.24 11.45 5.42 10.84 7.83 10.24 13.25 (9.2%) 4th/[461,489) 8.45 12.26 8.72 9.54 10.35 12.81 11.44 8.45 8.72 9.26 (8.9%)
5th/[385,419) 10.75 9.68 6.99 9.14 6.45 15.05 8.06 13.44 9.14 11.29 (10.3%) 5th/[489,512) 9.09 8.91 10.95 10.58 10.95 7.98 11.87 12.99 8.91 7.79 (13.1%)
6th/[419,445) 8.76 13.36 12.90 9.68 11.98 13.36 4.61 6.91 11.52 6.91 (12%) 6th/[512,525) 7.69 10.41 15.84 11.31 8.14 9.95 10.86 0.45 14.48 10.86 (5.4%)
7th/[445,477) 11.63 9.88 10.47 13.95 4.65 9.88 12.21 6.40 8.72 12.21 (9.5%) 7th/[525,550) 10.91 11.31 10.51 3.03 16.16 6.26 10.30 13.13 7.07 11.31 (12.1%)
8th/[477,519) 11.31 11.31 7.14 10.71 4.76 13.10 4.17 19.64 5.36 12.50 (9.3%) 8th/[550,586) 10.18 8.55 10.39 13.03 6.11 11.20 9.98 11.81 8.55 10.18 (12%)
9th/[519,589) 7.91 8.47 10.17 12.99 17.51 3.39 18.64 0.00 12.99 7.91 (9.8%) 9th/[586,632) 9.35 9.83 12.23 6.47 16.07 9.59 6.24 8.63 14.15 7.43 (10.2%)
10th/[589,650] 11.16 9.77 12.09 9.77 10.70 7.91 11.16 9.77 11.63 6.05 (11.9%) 10th/[632,710] 10.27 13.62 6.47 12.05 8.04 12.95 8.26 11.83 16.52 0.00 (10.9%)
*Prior score deciles can be uneven depending upon the prior score distribution *Prior score deciles can be uneven depending upon the prior score distribution
Student Growth Percentile Goodness−of−Fit Descriptives Student Growth Percentile Goodness−of−Fit Descriptives
2021 Reading Comprehension Ctp Fall SGP, Grade 4 (N = 5,152) 2021 Reading Comprehension Ctp Fall SGP, Grade 5 (N = 4,859)
SGP Deciles by Prior Achievement Level (Reading Comprehension Ctp Fall) SGP Deciles by Prior Achievement Level (Reading Comprehension Ctp Fall)
Prior Achievement Level Prior Achievement Level
Exceeds Expectations (50.4%)
Exceeds Expectations (57%)
Meets Expectations (36.4%)
Meets Expectations (36.6%)
Does Not Meet (13.3%)
Does Not Meet (6.3%)
Median Student Growth Percentile Median Student Growth Percentile
Ceiling / Floor Effects Test Ceiling / Floor Effects Test
Student Growth Percentile Range Student Growth Percentile Range
Current Observed Score Current Observed Score
5 9 to to to to to to to to to to 5 9 to to to to to to to to to to
to to 10 20 30 40 50 60 70 80 90 95 to to 10 20 30 40 50 60 70 80 90 95
Lowest OSS: [350,397) 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 20 Lowest OSS: [380,455) 94.3 5.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 35
Extremes (Range) Extremes (Range)
Highest OSS: [ 790 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 37.2 0.0 26.1 36.7 N = 226 Highest OSS: [ 860 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 30.8 9.9 59.3 N = 91
Student Growth Percentile Range QQ−Plot: Student Growth Percentiles Student Growth Percentile Range QQ−Plot: Student Growth Percentiles
19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution 19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution
9 to to to to to to to to to 9 to to to to to to to to to
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 1
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100
1st/[310,445) 10.56 9.76 9.76 9.56 9.96 9.36 10.36 9.36 11.16 10.16 (9.7%) 100 1st/[350,497) 9.47 9.47 9.67 9.67 11.11 9.47 11.52 9.47 9.26 10.91 (10%) 100
2nd/[445,484) 9.18 10.35 10.16 11.33 8.20 9.96 11.91 9.18 9.96 9.77 (9.9%) 2nd/[497,521) 8.40 11.70 10.43 10.43 6.36 11.45 9.92 10.43 11.20 9.67 (8.1%)
Prior Scale Score Decile/Range * Prior Scale Score Decile/Range *
3rd/[484,513) 8.28 11.19 11.86 9.40 13.20 9.17 7.16 12.30 7.83 9.62 (8.7%) 3rd/[521,541) 10.86 8.77 14.61 7.31 11.69 10.44 7.10 9.81 9.81 9.60 (9.9%)
Empirical SGP Distribution Empirical SGP Distribution
4th/[513,543) 10.79 9.35 7.01 7.55 11.51 10.61 11.87 8.09 10.79 12.41 (10.8%) 4th/[541,564) 10.47 10.08 6.98 12.02 8.53 11.82 10.47 8.14 10.08 11.43 (10.6%)
5th/[543,567) 7.96 11.30 11.48 12.41 8.15 9.81 7.96 10.56 12.41 7.96 (10.5%) 5th/[564,577) 9.01 9.63 13.98 9.63 6.83 9.32 9.32 15.22 8.70 8.39 (6.6%)
6th/[567,594) 11.72 11.13 9.77 12.11 10.35 10.16 10.16 8.40 6.84 9.38 (9.9%) 6th/[577,606) 10.92 10.19 7.86 12.08 12.66 9.02 8.59 7.57 9.46 11.64 (14.1%)
7th/[594,622) 6.80 9.48 9.48 7.22 9.69 9.07 11.55 12.37 12.78 11.55 (9.4%) 7th/[606,623) 9.01 7.51 13.81 8.71 9.31 9.31 11.41 14.11 7.81 9.01 (6.9%)
8th/[622,663) 13.36 10.12 10.93 8.50 11.54 11.54 8.70 10.32 6.28 8.70 (9.6%) 8th/[623,667) 9.23 10.74 10.59 8.02 13.01 8.77 9.83 11.65 8.62 9.53 (13.6%)
9th/[663,731) 7.35 9.28 13.54 10.44 8.51 7.16 16.83 9.67 6.96 10.25 (10%) 9th/[667,720) 10.09 9.87 7.17 14.80 7.62 11.43 10.99 7.85 10.54 9.64 (9.2%)
10th/[731,750] 10.56 11.24 8.52 11.07 9.03 14.65 9.20 18.91 1.87 4.94 (11.4%) 10th/[720,790] 11.38 11.57 9.51 10.63 9.14 7.84 10.45 10.82 12.13 6.53 (11%)
*Prior score deciles can be uneven depending upon the prior score distribution *Prior score deciles can be uneven depending upon the prior score distribution
Student Growth Percentile Goodness−of−Fit Descriptives Student Growth Percentile Goodness−of−Fit Descriptives
2021 Reading Comprehension Ctp Fall SGP, Grade 6 (N = 5,404) 2021 Reading Comprehension Ctp Fall SGP, Grade 7 (N = 4,536)
SGP Deciles by Prior Achievement Level (Reading Comprehension Ctp Fall) SGP Deciles by Prior Achievement Level (Reading Comprehension Ctp Fall)
Exceeds Expectations (14.7%) Exceeds Expectations (16.6%)
Prior Achievement Level Prior Achievement Level
Meets Expectations (34.2%) Meets Expectations (34.6%)
Does Not Meet (51.1%) Does Not Meet (48.8%)
Median Student Growth Percentile Median Student Growth Percentile
Ceiling / Floor Effects Test Ceiling / Floor Effects Test
Student Growth Percentile Range Student Growth Percentile Range
Current Observed Score Current Observed Score
5 9 to to to to to to to to to to 5 9 to to to to to to to to to to
to to 10 20 30 40 50 60 70 80 90 95 to to 10 20 30 40 50 60 70 80 90 95
Lowest OSS: [407,462) 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 24 Lowest OSS: [400,505) 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 23
Extremes (Range) Extremes (Range)
Highest OSS: [ 900 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 16.8 9.8 26.0 47.4 N = 173 Highest OSS: [ 950 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 29.9 32.2 0.0 37.9 N = 87
Student Growth Percentile Range QQ−Plot: Student Growth Percentiles Student Growth Percentile Range QQ−Plot: Student Growth Percentiles
19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution 19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution
9 to to to to to to to to to 9 to to to to to to to to to
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 1
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100
1st/[380,514) 10.47 9.53 10.47 9.53 10.65 9.91 9.91 9.91 8.79 10.84 (9.9%) 100 1st/[400,552) 8.55 10.39 9.24 10.39 9.93 9.93 11.09 10.85 9.70 9.93 (9.5%) 100
2nd/[514,549) 8.01 12.12 8.01 12.34 11.69 9.09 8.87 9.74 11.90 8.23 (8.5%) 2nd/[552,584) 12.62 8.81 11.43 9.05 9.05 11.19 7.38 11.43 8.33 10.71 (9.3%)
Prior Scale Score Decile/Range * Prior Scale Score Decile/Range *
3rd/[549,574) 10.37 8.44 12.13 7.56 9.14 11.95 10.90 8.44 9.31 11.78 (10.5%) 3rd/[584,607) 8.41 11.36 8.41 11.59 10.68 9.55 13.41 6.59 9.55 10.45 (9.7%)
Empirical SGP Distribution Empirical SGP Distribution
4th/[574,601) 10.25 11.15 10.43 10.79 8.45 7.73 9.17 13.85 7.73 10.43 (10.3%) 4th/[607,631) 8.81 7.99 12.50 9.63 9.02 9.22 10.86 11.07 9.63 11.27 (10.8%)
5th/[601,623) 9.04 9.58 6.87 9.40 15.73 8.68 8.86 7.96 15.19 8.68 (10.2%) 5th/[631,651) 10.39 11.32 8.31 13.63 7.85 9.24 7.62 11.09 10.85 9.70 (9.5%)
6th/[623,646) 10.07 11.27 11.03 10.07 7.43 11.99 13.91 7.91 6.00 10.31 (7.7%) 6th/[651,672) 11.23 9.36 10.43 7.75 16.31 9.89 9.09 8.56 8.82 8.56 (8.2%)
7th/[646,681) 10.82 10.36 9.12 10.66 10.05 8.04 9.74 11.59 9.74 9.89 (12%) 7th/[672,705) 9.60 12.28 6.53 10.75 9.02 11.90 9.40 11.90 7.49 11.13 (11.5%)
8th/[681,722) 7.60 11.23 10.19 9.15 9.50 11.23 10.02 8.46 12.44 10.19 (10.7%) 8th/[705,746) 8.98 9.18 14.45 9.57 8.79 7.03 10.74 7.03 13.87 10.35 (11.3%)
9th/[722,773) 13.10 7.38 12.36 10.15 12.55 9.41 10.15 9.41 4.80 10.70 (10%) 9th/[746,806) 11.26 10.14 9.01 10.36 9.46 11.26 9.68 10.36 8.11 10.36 (9.8%)
10th/[773,860] 8.27 10.66 8.27 9.56 13.05 11.03 8.09 14.34 8.46 8.27 (10.1%) 10th/[806,900] 9.77 10.83 10.40 11.04 11.68 8.07 9.98 14.23 10.83 3.18 (10.4%)
*Prior score deciles can be uneven depending upon the prior score distribution *Prior score deciles can be uneven depending upon the prior score distribution
Student Growth Percentile Goodness−of−Fit Descriptives
2021 Reading Comprehension Ctp Fall SGP, Grade 7 (N = 4,536)
SGP Deciles by Prior Achievement Level (Reading Comprehension Ctp Fall)
Exceeds Expectations (16.6%)
Prior Achievement Level
Meets Expectations (34.6%)
Does Not Meet (48.8%)
Median Student Growth Percentile
Ceiling / Floor Effects Test
Student Growth Percentile Range
Current Observed Score
5 9 to to to to to to to to to to
to to 10 20 30 40 50 60 70 80 90 95
Lowest OSS: [400,505) 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 23
Extremes (Range)
Highest OSS: [ 950 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 29.9 32.2 0.0 37.9 N = 87
Student Growth Percentile Range QQ−Plot: Student Growth Percentiles
19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution
9 to to to to to to to to to
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100
1st/[400,552) 8.55 10.39 9.24 10.39 9.93 9.93 11.09 10.85 9.70 9.93 (9.5%) 100
2nd/[552,584) 12.62 8.81 11.43 9.05 9.05 11.19 7.38 11.43 8.33 10.71 (9.3%)
Prior Scale Score Decile/Range *
3rd/[584,607) 8.41 11.36 8.41 11.59 10.68 9.55 13.41 6.59 9.55 10.45 (9.7%)
Empirical SGP Distribution
4th/[607,631) 8.81 7.99 12.50 9.63 9.02 9.22 10.86 11.07 9.63 11.27 (10.8%)
5th/[631,651) 10.39 11.32 8.31 13.63 7.85 9.24 7.62 11.09 10.85 9.70 (9.5%)
6th/[651,672) 11.23 9.36 10.43 7.75 16.31 9.89 9.09 8.56 8.82 8.56 (8.2%)
7th/[672,705) 9.60 12.28 6.53 10.75 9.02 11.90 9.40 11.90 7.49 11.13 (11.5%)
8th/[705,746) 8.98 9.18 14.45 9.57 8.79 7.03 10.74 7.03 13.87 10.35 (11.3%)
9th/[746,806) 11.26 10.14 9.01 10.36 9.46 11.26 9.68 10.36 8.11 10.36 (9.8%)
10th/[806,900] 9.77 10.83 10.40 11.04 11.68 8.07 9.98 14.23 10.83 3.18 (10.4%)
*Prior score deciles can be uneven depending upon the prior score distribution
Fall Milestones to Spring Milestones
Student Growth Percentile Goodness−of−Fit Descriptives Student Growth Percentile Goodness−of−Fit Descriptives
2022 Reading Comprehension MS Spring SGP, Grade 4 (N = 578) 2022 Reading Comprehension MS Spring SGP, Grade 5 (N = 746)
Ceiling / Floor Effects Test Ceiling / Floor Effects Test
Student Growth Percentile Range Student Growth Percentile Range
Current Observed Score Current Observed Score
5 9 to to to to to to to to to to 5 9 to to to to to to to to to to
to to 10 20 30 40 50 60 70 80 90 95 to to 10 20 30 40 50 60 70 80 90 95
Lowest OSS: [405,476) 70.0 10.0 10.0 10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 20 Lowest OSS: [450,494) 66.7 16.7 16.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 24
Extremes (Range) Extremes (Range)
Highest OSS: [697,733) 0.0 0.0 0.0 13.3 0.0 6.7 23.3 0.0 16.7 16.7 6.7 16.7 N = 30 Highest OSS: [ 790 ] 0.0 0.0 0.0 0.0 0.0 0.0 23.1 7.7 20.5 10.3 17.9 20.5 N = 39
Student Growth Percentile Range QQ−Plot: Student Growth Percentiles Student Growth Percentile Range QQ−Plot: Student Growth Percentiles
19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution 19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution
9 to to to to to to to to to 9 to to to to to to to to to
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 1
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100
1st/[343,463) 13.95 9.30 6.98 11.63 6.98 13.95 4.65 13.95 6.98 11.63 (7.4%) 100 1st/[368,513) 13.04 7.25 13.04 10.14 10.14 8.70 13.04 7.25 10.14 7.25 (9.2%) 100
2nd/[463,507) 8.96 10.45 17.91 5.97 7.46 10.45 16.42 8.96 7.46 5.97 (11.6%) 2nd/[513,539) 10.17 8.47 11.86 5.08 11.86 10.17 11.86 8.47 11.86 10.17 (7.9%)
Prior Scale Score Decile/Range Prior Scale Score Decile/Range
3rd/[507,521) 8.00 4.00 24.00 8.00 16.00 4.00 0.00 4.00 16.00 16.00 (4.3%) 3rd/[539,568) 10.26 12.82 6.41 10.26 11.54 7.69 11.54 14.10 5.13 10.26 (10.5%)
Empirical SGP Distribution Empirical SGP Distribution
4th/[521,550) 12.16 10.81 4.05 13.51 12.16 12.16 4.05 10.81 12.16 8.11 (12.8%) 4th/[568,585) 9.80 5.88 11.76 17.65 9.80 0.00 13.73 3.92 19.61 7.84 (6.8%)
5th/[550,565) 4.76 9.52 11.90 14.29 7.14 23.81 0.00 16.67 4.76 7.14 (7.3%) 5th/[585,623) 12.61 10.81 9.01 7.21 9.91 16.22 4.50 9.01 11.71 9.01 (14.9%)
6th/[565,596) 12.79 8.14 11.63 9.30 11.63 4.65 11.63 11.63 6.98 11.63 (14.9%) 6th/[623,646) 4.62 13.85 10.77 7.69 10.77 13.85 13.85 6.15 7.69 10.77 (8.7%)
7th/[596,613) 15.79 7.89 10.53 5.26 21.05 15.79 0.00 7.89 5.26 10.53 (6.6%) 7th/[646,672) 15.38 9.23 3.08 18.46 7.69 10.77 6.15 6.15 16.92 6.15 (8.7%)
8th/[613,651) 12.99 9.09 7.79 10.39 11.69 11.69 11.69 2.60 15.58 6.49 (13.3%) 8th/[672,702) 12.50 6.25 20.31 4.69 10.94 6.25 10.94 10.94 6.25 10.94 (8.6%)
9th/[651,699) 1.61 9.68 17.74 8.06 9.68 1.61 16.13 17.74 4.84 12.90 (10.7%) 9th/[702,758) 8.26 12.84 5.50 11.93 12.84 15.60 0.00 17.43 9.17 6.42 (14.6%)
10th/[699,750] 20.31 3.12 15.62 6.25 14.06 10.94 4.69 12.50 7.81 4.69 (11.1%) 10th/[758,790] 12.00 12.00 10.67 13.33 8.00 12.00 4.00 10.67 17.33 0.00 (10.1%)
*Prior score deciles can be uneven depending upon the prior score distribution *Prior score deciles can be uneven depending upon the prior score distribution
Student Growth Percentile Goodness−of−Fit Descriptives Student Growth Percentile Goodness−of−Fit Descriptives
2022 Reading Comprehension MS Spring SGP, Grade 6 (N = 1,004) 2022 Reading Comprehension MS Spring SGP, Grade 7 (N = 856)
Ceiling / Floor Effects Test Ceiling / Floor Effects Test
Student Growth Percentile Range Student Growth Percentile Range
Current Observed Score Current Observed Score
5 9 to to to to to to to to to to 5 9 to to to to to to to to to to
to to 10 20 30 40 50 60 70 80 90 95 to to 10 20 30 40 50 60 70 80 90 95
Lowest OSS: [413,516) 71.0 16.1 9.7 3.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 31 Lowest OSS: [472,553) 50.0 14.3 21.4 7.1 3.6 0.0 0.0 0.0 3.6 0.0 0.0 0.0 N = 28
Extremes (Range) Extremes (Range)
Highest OSS: [ 824 ] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 17.1 0.0 54.3 8.6 20.0 N = 35 Highest OSS: [ 844 ] 0.0 0.0 0.0 0.0 0.0 18.6 0.0 16.3 7.0 39.5 9.3 9.3 N = 43
Student Growth Percentile Range QQ−Plot: Student Growth Percentiles Student Growth Percentile Range QQ−Plot: Student Growth Percentiles
19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution 19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution
9 to to to to to to to to to 9 to to to to to to to to to
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 1
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100
1st/[423,536) 11.11 13.89 9.72 9.72 8.33 9.72 9.72 8.33 9.72 9.72 (7.2%) 100 1st/[433,568) 10.67 8.00 12.00 8.00 12.00 12.00 9.33 10.67 6.67 10.67 (8.8%) 100
2nd/[536,578) 11.21 7.48 6.54 13.08 14.95 10.28 8.41 12.15 7.48 8.41 (10.7%) 2nd/[568,605) 14.13 10.87 10.87 7.61 8.70 7.61 11.96 6.52 13.04 8.70 (10.7%)
Prior Scale Score Decile/Range Prior Scale Score Decile/Range
3rd/[578,608) 9.00 15.00 13.00 5.00 10.00 6.00 7.00 11.00 11.00 13.00 (10%) 3rd/[605,631) 7.69 8.97 6.41 11.54 8.97 16.67 14.10 7.69 8.97 8.97 (9.1%)
Empirical SGP Distribution Empirical SGP Distribution
4th/[608,627) 12.20 7.32 10.57 10.57 13.01 8.94 14.63 8.13 7.32 7.32 (12.3%) 4th/[631,659) 10.59 11.76 11.76 9.41 11.76 8.24 9.41 12.94 5.88 8.24 (9.9%)
5th/[627,658) 3.39 10.17 10.17 10.17 10.17 11.86 8.47 10.17 15.25 10.17 (5.9%) 5th/[659,674) 13.33 6.67 11.67 8.33 11.67 6.67 8.33 6.67 16.67 10.00 (7%)
6th/[658,698) 12.69 10.45 11.94 8.96 10.45 12.69 8.96 7.46 11.19 5.22 (13.3%) 6th/[674,707) 8.26 12.40 6.61 8.26 13.22 14.88 9.09 9.09 7.44 10.74 (14.1%)
7th/[698,721) 12.50 10.00 3.75 3.75 13.75 8.75 13.75 7.50 6.25 20.00 (8%) 7th/[707,726) 7.69 9.23 12.31 13.85 9.23 12.31 15.38 7.69 4.62 7.69 (7.6%)
8th/[721,747) 6.49 12.99 18.18 7.79 10.39 0.00 25.97 0.00 11.69 6.49 (7.7%) 8th/[726,771) 12.96 12.96 12.96 4.63 10.19 5.56 6.48 10.19 17.59 6.48 (12.6%)
9th/[747,817) 11.51 11.51 9.35 7.91 6.47 20.14 7.91 9.35 10.79 5.04 (13.8%) 9th/[771,800) 4.35 8.70 0.00 17.39 10.87 15.22 17.39 8.70 6.52 10.87 (5.4%)
10th/[817,860] 9.73 14.16 7.08 11.50 7.96 15.93 5.31 9.73 13.27 5.31 (11.3%) 10th/[800,900] 14.29 11.11 13.49 3.97 14.29 10.32 5.56 9.52 11.90 5.56 (14.7%)
*Prior score deciles can be uneven depending upon the prior score distribution *Prior score deciles can be uneven depending upon the prior score distribution
Student Growth Percentile Goodness−of−Fit Descriptives
2022 Reading Comprehension MS Spring SGP, Grade 8 (N = 1,049)
Ceiling / Floor Effects Test
Student Growth Percentile Range
Current Observed Score
5 9 to to to to to to to to to to
to to 10 20 30 40 50 60 70 80 90 95
Lowest OSS: [468,550) 63.6 13.6 13.6 9.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 N = 22
Extremes (Range)
Highest OSS: [954,1] 0.0 0.0 0.0 0.0 0.0 0.0 16.7 0.0 26.7 26.7 23.3 6.7 N = 30
Student Growth Percentile Range QQ−Plot: Student Growth Percentiles
19 29 39 49 59 69 79 89 99 Theoretical SGP Distribution
9 to to to to to to to to to
to 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100
1st/[430,605) 12.20 10.98 8.54 9.76 8.54 12.20 8.54 10.98 8.54 9.76 (7.8%) 100
2nd/[605,643) 8.79 10.99 10.99 13.19 9.89 7.69 9.89 10.99 8.79 8.79 (8.7%)
Prior Scale Score Decile/Range
3rd/[643,668) 11.24 8.99 5.62 16.85 11.24 13.48 4.49 7.87 10.11 10.11 (8.5%)
Empirical SGP Distribution
4th/[668,695) 13.57 3.57 17.14 0.00 9.29 10.71 14.29 10.71 12.86 7.86 (13.3%)
5th/[695,710) 10.23 13.64 6.82 4.55 22.73 4.55 18.18 5.68 0.00 13.64 (8.4%)
6th/[710,726) 12.79 15.12 5.81 18.60 0.00 16.28 0.00 8.14 13.95 9.30 (8.2%)
7th/[726,762) 6.62 7.28 16.56 11.92 5.30 9.27 11.26 11.26 11.26 9.27 (14.4%)
8th/[762,784) 11.63 8.14 5.81 5.81 24.42 6.98 13.95 5.81 15.12 2.33 (8.2%)
9th/[784,843) 14.17 11.67 8.33 12.50 5.00 9.17 7.50 13.33 8.33 10.00 (11.4%)
10th/[843,950] 12.07 11.21 6.90 14.66 10.34 12.93 3.45 15.52 6.03 6.90 (11.1%)
*Prior score deciles can be uneven depending upon the prior score distribution
About this copy
ERB Growth Model Development — ERB, January 9, 2023.
This is an image-based copy of the original Keynote slides; builds and animations are flattened.