RHODE ISLAND GROWTH ANALYSES USING PSAT Damian W Betebenner National Center for the Improvement of Educational Assessment Providence, Rhode Island May 15th, 2018

BACKGROUND • Rhode Island’s switch from PARCC to RI-CAS/PSAT10/SAT leads to changes in the way that growth is calculated. • In general, SGPs are using a students’ current test scores combined with at least one prior test score subject to the condition that scores come from the same test taken at the same time. • That is, test transitions like those happening in Rhode Island do not prevent the calculation of growth. However, communicating how growth is calculated across a test transition can be more difficult. • This presentation provides an overview of due diligence analyses conducted for PARCC to PSAT10.

BACKGROUND • Despite the versatility of SGP analyses not requiring a common scale across years, problems can arise with analyses. • The most common problems are related to ceiling/floor issues on tests as well as too few score points on which to calculate the 99 conditional quantile curves. • All source code associated with these analyses (no data) can be found on the Center’s GitHub repository for Rhode Island analyses at: https:// github.com/CenterForAssessment/Rhode_Island

2016 ELA Growth Analyses PARCC G3 PARCC G4 PARCC G4 PARCC G5 PARCC G5 PARCC G6 Growth Calculations PARCC G6 PARCC G7 PARCC G7 PARCC G8 PARCC G8 PARCC G9 PARCC G9 PARCC G10

2016 Mathematics Growth Analyses PARCC G3 PARCC G4 PARCC G4 PARCC G5 PARCC G5 PARCC G6 Growth PARCC G6 PARCC G7 Calculations PARCC G7 PARCC G8 PARCC G7 PARCC ALGEBRA I PARCC G8 PARCC ALGEBRA I PARCC ALGEBRA I PARCC GEOMETRY

2017 ELA Growth Analyses PARCC G3 PARCC G4 PARCC G3 PARCC G4 PARCC G5 PARCC G4 PARCC G5 PARCC G6 Growth PARCC G5 PARCC G6 PARCC G7 Calculations PARCC G6 PARCC G7 PARCC G8 PARCC G7 PARCC G8 PARCC G9 PARCC G8 PARCC G9 PARCC G10 PARCC G9 PSAT10

2017 Mathematics Growth Analyses PARCC G3 PARCC G4 PARCC G3 PARCC G4 PARCC G5 PARCC G4 PARCC G5 PARCC G6 PARCC G5 PARCC G6 PARCC G7 2017 PARCC G6 PARCC G7 PARCC G8 Growth Calculations PARCC G6 PARCC G7 PARCC ALGEBRA I PARCC G7 PARCC G8 PARCC ALGEBRA I PARCC G7 PARCC ALGEBRA I PARCC GEOMETRY PARCC G8 PARCC ALGEBRA I PARCC GEOMETRY PARCC G8 PARCC ALGEBRA I PSAT 10 PARCC ALGEBRA I PARCC GEOMETRY PSAT 10 Note: Several analyses using PSAT 10 in 2018 were conducted including: PARCC ALGEBRA I 2015 to PSAT 10 2017 without the GEOMETRY in 2016

2018 ELA Growth Analyses (Proposed) PARCC G3 RICAS G4 PARCC G3 PARCC G4 RICAS G5 Growth PARCC G4 PARCC G5 RICAS G6 Calculations PARCC G5 PARCC G6 RICAS G7 PARCC G6 PARCC G7 RICAS G8 PARCC G9 PSAT10 Note: Several analyses using PSAT 10 in 2018 were conducted including: PARCC G8 (2016) to PSAT 10, PARCC G10 (2017) to PSAT 10

2018 Mathematics Growth Analyses (Proposed) PARCC G3 RICAS G4 PARCC G3 PARCC G4 RICAS G5 PARCC G4 PARCC G5 RICAS G6 Growth PARCC G5 PARCC G6 RICAS G7 Calculations PARCC G6 PARCC G7 RICAS G8 PARCC ALGEBRA I PSAT10 PARCC GEOMETRY PSAT 10 PARCC G8 PSAT 10

2019 ELA Growth Analyses (Proposed) RICAS G3 RICAS G4 PARCC G3 RICAS G4 RICAS G5 2019 PARCC G4 RICAS G5 RICAS G6 Growth Calculations PARCC G5 RICAS G6 RICAS G7 PARCC G6 RICAS G7 RICAS G8 PARCC G8 PSAT10 PSAT 10 SAT

2019 Mathematics Growth Analyses (Proposed) RICAS G3 RICAS G4 PARCC G3 RICAS G4 RICAS G5 2019 PARCC G4 RICAS G5 RICAS G6 Growth Calculations PARCC G5 RICAS G6 RICAS G7 PARCC G6 RICAS G7 RICAS G8 PARCC G8 PSAT10 PARCC ALGEBRA I PSAT10 PSAT 10 SAT

PRELIMINARY ANALYSES • All analyses using 2017 PSAT data ran without any analytic issues • No ceiling or floor effects were observed in any of the analyses. • No issues related to “granularity” of scale were observed. • Analyses that combined data for which there was a 1 year gap with data for which there was a 2 year gap indicated a large effect depending upon which group the student belonged. • Algebra I (2015) to PSAT10 Math (2017): Median 59 • Algebra I (2016) to PSAT 10 Math (2017): Median 42

2015 ELA Grade 8; 2017 PSAT 10 ELA Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Ebrw SGP, Grade EOCT (N = 6,840) SGP Deciles by Prior Achievement Level (ELA) Level 5 (6.7%) Prior Achievement Level Level 4 (32.6%) Level 3 (27.1%) Level 2 (19%) Level 1 (14.5%) 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: [160,250) 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 = 28 Extremes (Range) Highest OSS: [690,710) 0.0 0.0 0.0 4.5 0.0 0.0 4.5 4.5 4.5 13.6 9.1 59.1 N = 22 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/[−4.09,−1.41) 8.77 10.96 9.94 10.53 9.06 9.80 9.21 9.94 11.11 10.67 (10%) 100 2nd/[−1.41,−0.879) 10.40 9.08 10.25 8.49 12.01 10.83 10.10 9.66 9.08 10.10 (10%) Prior Scale Score Decile/Range * 3rd/[−0.879,−0.5253) 9.78 9.64 8.76 11.24 9.49 9.93 11.09 10.80 9.20 10.07 (10%) Empirical SGP Distribution 4th/[−0.5253,−0.2245) 8.48 9.80 10.96 9.06 8.63 9.36 10.38 9.21 11.11 13.01 (10%) 5th/[−0.2245,0.0388) 10.53 11.40 10.96 10.82 10.82 9.36 8.77 9.36 10.23 7.75 (10%) 6th/[0.0388,0.2991) 9.06 9.94 10.23 9.36 9.80 11.26 9.50 10.82 9.50 10.53 (10%) 7th/[0.2991,0.573) 9.50 10.09 8.48 10.53 10.09 9.94 11.40 9.65 10.09 10.23 (10%) 8th/[0.573,0.8929) 9.65 8.63 9.80 10.09 9.36 9.94 9.06 10.09 10.53 12.87 (10%) 9th/[0.8929,1.35) 10.23 10.67 10.82 9.50 10.96 9.50 10.96 10.67 8.33 8.33 (10%) 10th/[1.35,3.903] 9.06 9.94 9.94 10.23 9.65 10.38 9.36 9.65 10.82 10.96 (10%) *Prior score deciles can be uneven depending upon the prior score distribution

2015 ELA Grade 8; 2016 ELA Grade 9, 2017 PSAT 10 ELA Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Ebrw SGP, Grade EOCT (N = 6,624) SGP Deciles by Prior Achievement Level (ELA) Level 5 (7%) Prior Achievement Level Level 4 (30%) Level 3 (25.2%) Level 2 (20.8%) Level 1 (17%) 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: [170,250) 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 = 25 Extremes (Range) Highest OSS: [690,710) 0.0 0.0 0.0 0.0 0.0 5.0 0.0 10.0 15.0 10.0 20.0 40.0 N = 20 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/[−6.136,−1.415) 10.44 9.98 10.29 9.83 9.98 9.53 9.53 10.89 10.29 9.23 (10%) 100 2nd/[−1.415,−0.9472) 9.35 9.65 9.50 9.95 9.65 11.16 11.01 8.45 10.26 11.01 (10%) Prior Scale Score Decile/Range * 3rd/[−0.9472,−0.58) 8.44 10.62 10.00 10.00 10.47 8.75 10.78 10.16 9.53 11.25 (9.7%) Empirical SGP Distribution 4th/[−0.58,−0.2776) 11.23 8.98 10.03 10.78 9.43 11.08 8.68 10.33 9.73 9.73 (10.1%) 5th/[−0.2776,0.0063) 8.47 10.59 10.29 9.53 10.59 9.53 9.98 9.98 10.14 10.89 (10%) 6th/[0.0063,0.3021) 7.69 10.21 9.17 9.91 10.36 9.47 10.50 10.36 10.65 11.69 (10.2%) 7th/[0.3021,0.5653) 12.14 10.19 10.34 9.15 9.30 10.34 10.19 9.15 10.19 9.00 (10.1%) 8th/[0.5653,0.9058) 10.69 9.47 10.84 11.45 10.08 10.84 8.70 10.38 7.94 9.62 (9.9%) 9th/[0.9058,1.367) 7.51 10.51 8.71 10.06 9.91 9.46 11.86 9.31 10.81 11.86 (10.1%) 10th/[1.367,4.1] 10.34 9.75 10.94 9.30 10.19 9.90 8.85 10.64 10.49 9.60 (10.1%) *Prior score deciles can be uneven depending upon the prior score distribution

2016 ELA Grade 9; 2017 PSAT 10 ELA Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Ebrw SGP, Grade EOCT (N = 7,824) SGP Deciles by Prior Achievement Level (ELA) Level 5 (6.7%) Prior Achievement Level Level 4 (28.9%) Level 3 (24.9%) Level 2 (21.2%) Level 1 (18.3%) 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: [160,240) 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: [690,710) 0.0 0.0 0.0 0.0 0.0 0.0 4.3 13.0 13.0 4.3 17.4 47.8 N = 23 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/[−15,−1.495) 9.63 9.88 9.88 10.78 9.88 9.76 9.37 10.40 10.27 10.14 (10%) 100 2nd/[−1.495,−1.008) 9.73 10.76 10.24 8.45 10.76 10.50 11.27 9.35 9.22 9.73 (10%) Prior Scale Score Decile/Range * 3rd/[−1.008,−0.6279) 9.77 8.87 8.87 11.18 8.23 10.28 10.80 9.90 9.51 12.60 (9.9%) Empirical SGP Distribution 4th/[−0.6279,−0.332) 10.21 11.39 10.47 8.90 11.39 9.29 7.98 10.47 10.73 9.16 (9.8%) 5th/[−0.332,−0.0389) 8.78 8.65 10.56 11.58 10.43 10.56 9.67 9.67 9.80 10.31 (10%) 6th/[−0.0389,0.2342) 8.43 10.09 10.09 10.09 9.07 8.68 11.24 10.60 11.49 10.22 (10%) 7th/[0.2342,0.5284) 10.21 10.47 9.43 8.79 11.37 10.47 9.43 9.43 8.53 11.89 (9.9%) 8th/[0.5284,0.8676) 10.70 10.95 10.20 10.70 9.70 9.20 9.33 10.57 10.32 8.33 (10.3%) 9th/[0.8676,1.329) 8.59 7.95 9.72 10.23 9.47 11.74 10.86 9.47 10.61 11.36 (10.1%) 10th/[1.329,4.892] 9.83 10.98 10.47 9.20 9.96 9.32 9.96 10.09 9.32 10.86 (10%) *Prior score deciles can be uneven depending upon the prior score distribution

2015 ELA Grade 9; 2016 ELA Grade 10; 2017 PSAT 10 ELA Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Ebrw SGP, Grade EOCT (N = 4,136) SGP Deciles by Prior Achievement Level (ELA) Level 5 (10.8%) Prior Achievement Level Level 4 (27.3%) Level 3 (19.7%) Level 2 (16.8%) Level 1 (25.3%) 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: [170,280) 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 Extremes (Range) Highest OSS: [710,720) 0.0 0.0 0.0 0.0 0.0 6.2 6.2 9.4 12.5 9.4 18.8 37.5 N = 32 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/[−15,−1.514) 9.05 9.54 10.27 11.00 10.76 9.29 9.78 9.29 10.27 10.76 (9.9%) 100 2nd/[−1.514,−1.056) 11.06 11.06 8.89 7.93 9.38 10.82 10.34 10.58 9.38 10.58 (10.1%) Prior Scale Score Decile/Range * 3rd/[−1.056,−0.6395) 9.07 10.54 10.78 9.56 11.03 10.78 10.05 10.29 10.29 7.60 (9.9%) Empirical SGP Distribution 4th/[−0.6395,−0.3176) 8.61 9.09 10.29 12.44 9.57 9.09 9.57 9.33 9.81 12.20 (10.1%) 5th/[−0.3176,−0.0257) 12.17 8.52 9.73 7.06 11.19 9.25 9.73 9.73 10.95 11.68 (9.9%) 6th/[−0.0257,0.2876) 8.47 12.59 8.72 11.14 10.17 9.69 9.93 9.93 9.93 9.44 (10%) 7th/[0.2876,0.5992) 8.67 8.19 12.53 9.40 7.95 12.05 10.84 11.08 10.12 9.16 (10%) 8th/[0.5992,0.9513) 9.73 11.44 9.49 11.44 10.46 9.73 8.76 9.00 9.25 10.71 (9.9%) 9th/[0.9513,1.441) 10.48 9.52 7.62 10.24 11.19 9.05 10.71 10.95 9.05 11.19 (10.2%) 10th/[1.441,4.188] 9.88 9.88 10.84 9.64 8.92 9.88 10.84 9.16 11.08 9.88 (10%) *Prior score deciles can be uneven depending upon the prior score distribution

2016 ELA Grade 10; 2017 PSAT 10 Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Ebrw SGP, Grade EOCT (N = 4,867) SGP Deciles by Prior Achievement Level (ELA) Level 5 (10%) Prior Achievement Level Level 4 (26.2%) Level 3 (19.3%) Level 2 (16.9%) Level 1 (27.6%) 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: [170,280) 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 = 29 Extremes (Range) Highest OSS: [710,720) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.8 13.9 19.4 11.1 52.8 N = 36 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/[−15,−1.592) 8.71 9.54 10.17 11.20 10.58 9.54 10.58 9.34 9.96 10.37 (9.9%) 100 2nd/[−1.592,−1.133) 11.63 10.57 11.21 8.88 8.67 10.36 9.30 9.94 10.15 9.30 (9.7%) Prior Scale Score Decile/Range * 3rd/[−1.133,−0.7404) 7.97 9.56 8.76 10.96 8.76 9.96 11.16 11.55 10.56 10.76 (10.3%) Empirical SGP Distribution 4th/[−0.7404,−0.3969) 10.19 9.77 10.19 9.98 11.85 11.43 9.15 10.19 7.90 9.36 (9.9%) 5th/[−0.3969,−0.0801) 10.12 11.36 10.95 9.09 8.47 6.82 9.71 7.23 12.81 13.43 (9.9%) 6th/[−0.0801,0.2212) 10.04 9.64 8.84 10.84 11.04 11.65 8.43 12.05 7.83 9.64 (10.2%) 7th/[0.2212,0.5313) 8.62 9.03 11.29 10.06 9.03 10.06 11.70 10.06 9.86 10.27 (10%) 8th/[0.5313,0.8961) 9.38 10.00 8.54 9.17 11.04 11.46 10.21 8.54 11.46 10.21 (9.9%) 9th/[0.8961,1.372) 9.86 10.06 11.09 10.06 9.65 8.83 10.06 11.91 9.65 8.83 (10%) 10th/[1.372,4.188] 9.74 10.14 9.33 10.75 9.94 10.34 9.13 9.13 9.74 11.76 (10.1%) *Prior score deciles can be uneven depending upon the prior score distribution

2015 Math Grade 8; 2016 Algebra I, 2017 PSAT 10 Math Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Math SGP, Grade EOCT (N = 4,334) SGP Deciles by Prior Achievement Level (Algebra I) Level 5 (0.1%) Level 4 (14.3%) Prior Achievement Level Level 3 (29.3%) Level 2 (33.8%) Level 1 (22.5%) 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: [160,250) 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 = 25 Extremes (Range) Highest OSS: [ 560 ] 0.0 0.0 0.0 0.0 0.0 3.0 3.0 3.0 9.1 15.2 15.2 51.5 N = 33 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/[−15,−1.577) 10.29 9.56 9.56 9.80 11.03 9.80 10.29 9.31 9.80 10.54 (9.4%) 100 2nd/[−1.577,−1.182) 9.11 10.10 9.36 10.84 9.36 10.84 9.85 11.08 9.11 10.34 (9.4%) Prior Scale Score Decile/Range * 3rd/[−1.182,−0.8656) 10.41 10.85 11.06 8.89 9.54 10.41 9.11 9.76 10.41 9.54 (10.6%) Empirical SGP Distribution 4th/[−0.8656,−0.707) 9.93 10.40 10.40 10.87 9.22 8.75 9.93 9.22 10.40 10.87 (9.8%) 5th/[−0.707,−0.4556) 7.99 7.99 10.05 9.82 9.36 10.05 10.73 12.79 10.50 10.73 (10.1%) 6th/[−0.4556,−0.1869) 10.35 11.01 9.69 9.91 12.56 10.13 8.59 7.71 9.47 10.57 (10.5%) 7th/[−0.1869,0.0541) 9.61 8.92 8.92 11.21 9.15 11.21 11.44 9.15 9.61 10.76 (10.1%) 8th/[0.0541,0.3381) 9.88 11.29 9.88 8.71 8.94 9.18 8.94 12.24 10.59 10.35 (9.8%) 9th/[0.3381,0.7411) 10.14 7.88 10.59 9.91 11.49 9.68 10.81 9.23 10.36 9.91 (10.2%) 10th/[0.7411,3.079] 9.13 11.87 10.05 10.27 9.59 9.82 10.27 9.36 9.82 9.82 (10.1%) *Prior score deciles can be uneven depending upon the prior score distribution

2016 Algebra I, 2017 PSAT 10 Mathematics Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Math SGP, Grade EOCT (N = 5,643) SGP Deciles by Prior Achievement Level (Algebra I) Level 5 (0.2%) Level 4 (14.5%) Prior Achievement Level Level 3 (28.4%) Level 2 (33.3%) Level 1 (23.7%) 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: [160,230) 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 = 27 Extremes (Range) Highest OSS: [ 560 ] 0.0 0.0 0.0 0.0 0.0 2.1 6.4 0.0 0.0 21.3 21.3 48.9 N = 47 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/[−15,−1.585) 8.60 10.75 8.06 13.80 9.32 10.57 8.96 8.78 10.39 10.75 (9.9%) 100 2nd/[−1.585,−1.192) 10.07 10.25 9.36 8.83 11.66 7.95 11.13 11.66 9.01 10.07 (10%) Prior Scale Score Decile/Range * 3rd/[−1.192,−0.9506) 11.57 7.78 16.27 5.42 7.41 11.75 12.66 7.78 10.85 8.50 (9.8%) Empirical SGP Distribution 4th/[−0.9506,−0.708) 11.32 10.75 9.79 10.75 9.60 9.40 9.21 10.17 8.25 10.75 (9.2%) 5th/[−0.708,−0.47) 6.12 10.95 6.28 10.79 9.98 11.43 11.27 9.50 11.92 11.76 (11%) 6th/[−0.47,−0.1972) 10.71 9.11 12.32 12.68 10.89 6.96 4.46 13.04 8.93 10.89 (9.9%) 7th/[−0.1972,0.0541) 9.73 7.61 8.85 11.15 9.91 10.09 12.92 9.20 10.09 10.44 (10%) 8th/[0.0541,0.3381) 9.48 11.90 11.52 6.69 9.29 10.22 11.15 8.92 10.41 10.41 (9.5%) 9th/[0.3381,0.7411) 9.14 11.55 7.07 10.52 11.72 10.69 10.17 10.17 10.17 8.79 (10.3%) 10th/[0.7411,3.275] 10.33 8.95 11.70 10.15 9.12 9.81 9.29 9.81 9.47 11.36 (10.3%) *Prior score deciles can be uneven depending upon the prior score distribution

2015 Algebra I, 2016 Geometry, 2017 PSAT Mathematics Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Math SGP, Grade EOCT (N = 4,138) SGP Deciles by Prior Achievement Level (Geometry) Level 5 (1.3%) Level 4 (21.7%) Prior Achievement Level Level 3 (32.5%) Level 2 (32.1%) Level 1 (12.4%) 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: [160,270) 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 = 22 Extremes (Range) Highest OSS: [660,690) 0.0 0.0 0.0 0.0 0.0 0.0 3.8 15.4 7.7 23.1 15.4 34.6 N = 26 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/[−15,−1.294) 11.58 9.36 10.59 10.10 9.11 10.59 9.36 9.85 10.10 9.36 (9.8%) 100 2nd/[−1.294,−0.9311) 7.94 11.17 9.68 9.18 12.16 10.17 9.93 9.43 8.44 11.91 (9.7%) Prior Scale Score Decile/Range * 3rd/[−0.9311,−0.6366) 9.56 9.07 10.29 9.56 8.33 10.54 10.54 10.05 10.78 11.27 (9.9%) Empirical SGP Distribution 4th/[−0.6366,−0.3776) 10.31 10.55 9.83 11.03 9.83 10.07 10.07 10.55 9.11 8.63 (10.1%) 5th/[−0.3776,−0.087) 8.56 9.29 9.54 10.51 10.76 8.56 10.02 9.78 11.98 11.00 (9.9%) 6th/[−0.087,0.2218) 9.32 9.56 10.96 9.79 8.86 10.96 11.19 10.72 9.09 9.56 (10.4%) 7th/[0.2218,0.502) 11.49 11.25 8.56 9.29 11.25 10.76 7.58 9.54 9.29 11.00 (9.9%) 8th/[0.502,0.8384) 8.86 9.32 11.19 9.32 10.49 8.16 11.19 9.56 12.12 9.79 (10.4%) 9th/[0.8384,1.254) 10.29 9.07 10.05 11.27 7.60 10.54 10.78 11.03 8.58 10.78 (9.9%) 10th/[1.254,3.338] 9.52 10.71 9.52 9.76 11.43 10.00 9.29 9.76 9.52 10.48 (10.1%) *Prior score deciles can be uneven depending upon the prior score distribution

2016 Geometry, 2017 PSAT Mathematics Student Growth Percentile Goodness−of−Fit Descriptives 2016−2017 Psat Math SGP, Grade EOCT (N = 5,070) SGP Deciles by Prior Achievement Level (Geometry) Level 5 (1.3%) Level 4 (21.9%) Prior Achievement Level Level 3 (33.2%) Level 2 (31.6%) Level 1 (12.1%) 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: [160,250) 95.7 4.3 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: [680,710) 0.0 0.0 3.8 0.0 0.0 3.8 0.0 0.0 15.4 19.2 23.1 34.6 N = 26 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/[−15,−1.294) 11.50 9.65 11.70 8.21 9.45 9.24 12.11 9.24 10.06 8.83 (9.6%) 100 2nd/[−1.294,−0.9311) 8.92 11.41 7.88 13.28 9.34 11.83 5.60 9.75 9.54 12.45 (9.5%) Prior Scale Score Decile/Range * 3rd/[−0.9311,−0.6366) 8.04 9.48 10.10 6.80 17.11 4.74 10.52 11.13 10.72 11.34 (9.6%) Empirical SGP Distribution 4th/[−0.6366,−0.328) 10.41 8.99 12.35 10.23 4.94 13.76 12.52 9.35 8.82 8.64 (11.2%) 5th/[−0.328,−0.0701) 9.11 11.54 8.70 9.11 8.91 9.11 8.70 10.93 11.74 12.15 (9.7%) 6th/[−0.0701,0.2265) 8.97 9.94 8.58 11.31 11.89 10.72 11.50 8.77 9.36 8.97 (10.1%) 7th/[0.2265,0.5126) 10.38 8.27 13.85 9.23 11.35 8.46 8.27 10.58 8.27 11.35 (10.3%) 8th/[0.5126,0.8534) 9.65 11.81 9.06 10.04 9.25 8.46 10.24 9.45 12.99 9.06 (10%) 9th/[0.8534,1.259) 9.78 9.18 9.18 9.18 7.98 12.77 11.98 9.38 8.78 11.78 (9.9%) 10th/[1.259,3.338] 9.36 10.53 9.94 10.53 11.70 8.77 9.16 10.33 9.94 9.75 (10.1%) *Prior score deciles can be uneven depending upon the prior score distribution

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Rhode Island Growth Analyses Using PSAT — Rhode Island Department of Education, September 9, 2018.

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