Predictive Model
i-Ready and Smarter Balanced
Assessments
Dr. Razak Garoui, Executive Director,
Assessment, Research, and Accountability
September 10, 2015
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SLIDE 2
THE BIG PICTURE
Purpose of the regression study
• We thought it would be useful to predict how our students would perform
on the spring Smarter Balanced Assessments, based on their i-Ready scores
for the winter, or second window of i-Ready.
• Using a regression analysis, we can predict an average value for Smarter
Balanced (Y), for given values of i-Ready scores (X).
• We compute the linear relationship between X and Y, shown on a scatter
graph, as the regression line.
• The strength of the relationship between X and Y is called the Pearson
correlation coefficient, or r.
– A high degree of correlation will be greater than 0.50 or less than -.50.
Correlations above .70 in magnitude are considered to be very strong.
• We did this for each grade, 3 – 6, in both reading/ELA and math
– Examples of scatter graphs for grade 3 and grade 7 are on the next
slides.
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SLIDE 3
The data showed a strong, positive relationship between i-Ready and Smarter Balanced.
At all grade levels 3 – 6, correlations were generally in the range of 0.80 to .90.
Regression of Grade 3 i-Ready Winter Scale Score
and Grade 3 ELA Scale Score
3000
2900
2800
2700
SBA ELA
2600
2500
2400
2300
y = 1670.1 + 1.4524x
R = 0.8446
2200
2100
2000
200
250
300
350
400
450
500
550
600
650
700
750
800
i-Ready Reading
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SLIDE 4
Regression of Grade 7 i-Ready Math Winter Scale Score
and Grade 7 SBA Math Scale Score
3000
2900
2800
2700
SBA Math
2600
2500
2400
y =1273.3 + 2.543x
R = 0.8668
2300
2200
2100
2000
200
250
300
350
400
450
500
550
600
650
700
i-Ready Math
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SLIDE 5
We worked with the data in a number of ways, which included:
•
.
Graphs displaying the relationship
of i-Ready and SBA by grade level,
for Reading/ELA and Math, (examples shown on previous slides),
• Cross tabulation to display the relationship between i-Ready proficiency
levels and SBA achievement levels,
•
An Excel template that allows you to input a score for i-Ready and
instantly get a prediction of SBA score by grade level and subject.
•
A lookup or crosswalk table with i-Ready scores and corresponding
scores predicted for Smarter Balanced
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Cross Tabulation: The cells with yellow highlights display the number and
percentages of students who achieve the same levels on both assessments. For
example, 89.3% of students scoring well below standard on the Grade 3 i-Ready in
window 2 also scored well below standard on the Grade 3 Smarter Balanced ELA
summative assessment.
Grade 3 SBA ELA
1 Well
Below
Grade 3 iReady
Reading W2
1 Well
Below
2 Below
Level
3 On Level
4 Above
Level
Total
Grade 3 iReady
Reading W2
4
Advanced
Total
326
36
2
1
365
174
160
57
4
395
45
218
412
447
1122
0
0
1
69
70
545
414
472
521
1952
1 Well
Below
1 Well
Below
2 Below
Level
3 On Level
4 Above
Level
Total
3
Proficient
2 Below
SLIDE 6
Grade 3 SBA ELA
3
2 Below
Proficient
4
Advanced
89.3%
9.9%
.5%
.3%
44.1%
40.5%
14.4%
1.0%
4.0%
19.4%
36.7%
39.8%
1.4%
98.6%
24.2%
26.7%
27.9%
21.2%
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SLIDE 7
Cross Tabulation (Continued) Over 90% of students not meeting grade level
standard on the Grade 3 i-Ready in window 2 also did not meet standard on the
Grade 3 Smarter Balanced ELA.
Almost 80% of students meeting standard on the Grade 3 i-Ready, window 2, also
met standard on the Grade 3 SBA ELA. Results were similar for the other grade
levels, and indicate that i-Ready would be useful in predicting SBA scores.
Grade 3 SBA ELA
No
No
Yes
91.6%
8.4%
22.1%
77.9%
49.1%
50.9%
Grade 3 i-Ready
Reading W2
Yes
Total
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SLIDE 8
Regression Analysis Method
Students needed to have both i-Ready Winter scores and
Smarter Balanced scores to be included in the study.
For this time around, we focused on grades 3 through 6.
Grade
3
4
5
6
7
8
11
Math
Sample Size
1,951
1,859
2,013
1,908
1,542
1,522
8
Reading
Sample Size
1,927
1,841
2,001
1,918
1,524
1,462
44
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SLIDE 9
Regression Analysis Results
Math
𝛽0 a
Grade
Reading
𝛽1 b
𝛽0 a
𝛽1 b
3
1,433
2.27
1,670
1.45
4
1,497
2.11
1,644
1.52
5
1,435
2.23
1,714
1.39
6
1,264
2.58
1,729
1.39
7
1,273
2.54
1,702
1.42
8
1,176
2.72
1,691
1.45
All coefficients are significant at the p<0.01 level
Grade 3 Example
𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑆𝐵𝐴 𝑆𝑐𝑜𝑟𝑒 = 𝑦𝑆𝐵𝐴𝑖 = 𝛽0 + ( 𝛽1 × 𝑥𝑖𝑅𝑒𝑎𝑑𝑦 )
𝑖
𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑆𝐵𝐴 𝑆𝑐𝑜𝑟𝑒 = 2,455 = 1,433 + (2.27 × 450 )
SUCCESSFULLY PREPARING ALL STUDENTS FOR THEIR FUTURES
12033 SE 256TH STREET, KENT, WA 98030 | WWW.KENT.K12.WA.US
SLIDE 10
Template: In Excel, Enter Grade, Subject and i-Ready score to
get Predicted SBA score. Examples shown below:
Grade
Subject
i-Ready (Winter) Scale Score
Predicted SBA Scale Score
SBA Predicted Performance Level
3
ELA
435
2302
Level 1
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SLIDE 11
Correlation Table
Example for Grade 3 i-Ready, all 3 windows and SBA ELA
Grade 3 i-Ready Reading and Smarter Balanced ELA Correlations
i-Ready
Reading W1
i-Ready Reading W1
i-Ready
Reading W2
.881**
i-Ready
Reading W3
.860**
SBA ELA Score
.833**
0.000
0.000
0.000
2058
1959
1934
1933
Pearson Correlation
.881**
1
.893**
.846**
Sig. (2-tailed)
0.000
0.000
0.000
N
1959
2026
1963
1952
Pearson Correlation
.860**
.893**
1
.846**
Sig. (2-tailed)
0.000
0.000
N
1934
1963
2038
1993
Pearson Correlation
.833**
.846**
.846**
1
Sig. (2-tailed)
0.000
0.000
0.000
N
1933
1952
1993
Pearson Correlation
1
Sig. (2-tailed)
N
i-Ready Reading W2
i-Ready Reading W3
SBA ELA Score
0.000
2026
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Crosswalk –
Example for Grade 3 Math and Reading
Part of Level 1 scores
SLIDE 12
i-Ready Scale Score and Predicted SBA Scale Score Crosswalk
Grade
3
4
5
6
Math
a
1,433
1,497
1,435
1,264
b
2.27
2.11
2.23
2.58
Reading
a
1670
1644
1714
1729
Grade
3
4
5
6
b
1.45
1.52
1.39
1.39
The regression equation is written as Y = a + bX
GRADE 3 Math
i-Ready
Scale Score
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
Predicted
SBA Scale
Score
2189
2191
2193
2196
2198
2200
2203
2205
2207
2209
2212
2214
2216
2218
2221
2223
GRADE 3 Reading
Predicted
SBA Level
i-Ready
Scale Score
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
Predicted
SBA Scale
Score
2114
2115
2117
2118
2120
2121
2122
2124
2125
2127
2128
2130
2131
2133
2134
2135
Predicted
SBA Level
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
L1
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12033 SE 256TH STREET, KENT, WA 98030 | WWW.KENT.K12.WA.US