Technical Notes
Standard Conventions used in the 200607 ABCs Analyses
95R – Percent tested below 95% for the 200607 ABCs, a percentage of students tested was computed by combining information from EOG reading, EOG mathematics, EOC and alternate assessments across all grades in a school. The percentage must be greater than or equal to 95, when rounded to the nearest whole number. (To determine the 95% participation rate for meeting Adequate Yearly Progress (AYP) per the No Child Left Behind legislation, the cohort of 10^{th} grade students on the first day of spring testing for the school were analyzed to determine the number of students who had taken the required tests.) Schools identified as having fallen below the 95% threshold for the ABCs were asked to justify their rate. Their explanations were reviewed at DPI and if rejected, the school was assigned a 95R status. This assigned status means that the school was in violation of the rule and ineligible to receive incentive awards or recognition (other than low performing). A school in violation for two consecutive years may be identified as lowperforming by the State Board of Education.
Full Academic Year
Students must have been in membership in a school for at least 140 days as of the first day of spring testing in order for their test scores to be included in the growth calculations or AYP. By contrast for ABCs in block scheduled high schools, the student must be in membership 70 days in the semester the course is taught.
Medical Exclusions
In compliance with NCLB and in light of the full availability of alternate assessments, only exclusions for serious medical emergencies and/or conditions were allowed in 200506. Examples included students who were (1) in the final stages of terminal or degenerative illnesses, (2) comatose, or (3) receiving extensive shortterm medical treatment due to a medical emergency. In response to a request from the student’s LEA the Director of Accountability Services provides a written statement of the decision to the LEA; any exception granted is limited to the testing period for the specific test(s) for which it was requested and does not carry forward to future test administrations, unless noted in the decision. In the rare case that a student was still administered an assessment, the score from the assessment was used.
Algebra I Scores in the Performance Composite
Algebra I scores for current ninth graders who took Algebra I prior to grade 9 were included in the performance composite for the high school where they were currently enrolled. Algebra I scores of students in grades 6, 7, or 8 during the current school year were included in the K8 performance composite of the middle school where they were currently enrolled. Algebra I scores of students currently enrolled in grade 10 in a senior high school (Grades 1012) who took Algebra I while in earlier grades were included in the performance composite of the senior high school.
Confidence Interval Applied to the Performance Composite to Identify LowPerforming Schools
The performance composite is the percent of students’ scores at or above grade level (i.e., in Achievement Levels III or IV) on endofgrade (and Computer Skills in grade 8 where applicable) and/or endofcourse tests. The performance composite is computed by adding all scores at or above Achievement Level III on each of the tests, and then dividing the sum by the total number of valid scores on the tests. If a school did not make expected growth and its performance composite was significantly less than 50, the school is given the status of lowperforming.
The confidence interval is a way of taking into account the precision of the performance composite. By applying the confidence interval, the likelihood of incorrectly assigning a lowperforming status to a school that does not deserve it is decreased while the likelihood of correctly assigning a status to schools is not hindered. The confidence interval itself will be narrow or wide depending on the size of the school and the variation of the student scores in the school. In general, the confidence interval is narrower when the number of students is larger, or the scores are more homogeneous; the confidence interval is wider when the number of students is smaller, or the scores are less homogeneous.
This means that a potentially lowperforming school may have a performance composite that is considerably below 50% but when the confidence interval is applied (correcting for the precision of the performance composite), the school is not considered lowperforming (because the confidence interval for that school is wide i.e., there is less confidence in the value of the performance composite). This situation would likely be true for a school that has few students or has wide variation in test scores. It is also possible for a school to have a performance composite that is fairly close to 50% and is considered lowperforming because the confidence interval for that school is very narrow (i.e., there is high confidence in the performance composite). This situation would likely be true for a school that has a large number of students or students all have about the same test score.
As long as the value, 50, lies within or on the upper boundary of the confidence interval for an observed performance composite, then the performance composite is not significantly less than 50 and hence the school is not classified as lowperforming.
Preliminary
Analyses of the ABCs Model for 200506
The technical notes present preliminary analyses of the proposed ABCs model for 200506 using the cscale. Eighteen tables are included and many compare findings from the proposed model and the original ABCs model. Please note that academic change is calculated using either 0.9 or 0.8 in all table unless otherwise noted.
Table 1. Standard Setting Years, Means and Standard Deviations for EndofGrade (EOG) CScale Computation
EOG 
Standard Setting Year 
Mean 
Standard Deviation 
Reading (1st Edition) 



Grade 3 Pretest 
1997 
137.7 
8.57 
Grade 3 
1997 
146.9 
9.29 
Grade 4 
1997 
150.3 
9.34 
Grade 5 
1997 
160.0 
9.62 
Grade 6 
1997 
156.7 
9.61 
Grade 7 
1997 
159.9 
8.50 
Grade 8 
1997 
163.1 
8.04 
Reading (2nd Edition) 



Grade 3 Pretest 
2003 
238.7 
9.94 
Grade 3 
2003 
247.9 
9.06 
Grade 4 
2003 
252.3 
8.68 
Grade 5 
2003 
256.9 
8.03 
Grade 6 
2003 
258.7 
8.55 
Grade 7 
2003 
261.1 
9.06 
Grade 8 
2003 
263.9 
9.05 
Mathematics (1st Edition) 



Grade 3 Pretest 
1997 
130.9 
7.96 
Grade 3 
1997 
142.9 
11.09 
Grade 4 
1997 
152.3 
10.28 
Grade 5 
1997 
159.3 
9.99 
Grade 6 
1997 
164.8 
10.84 
Grade 7 
1997 
170.8 
10.58 
Grade 8 
1997 
174.2 
11.96 
Mathematics (2nd Edition) 



Grade 3 Pretest 
2001 
236.1 
8.10 
Grade 3 
2001 
250.6 
7.75 
Grade 4 
2001 
255.8 
8.32 
Grade 5 
2001 
260.0 
9.62 
Grade 6 
2001 
263.2 
9.91 
Grade 7 
2001 
267.1 
10.63 
Grade 8 
2001 
270.0 
10.95 
2^{nd} Edition Math 2005 Special Transition Conversion Used when Comparing with 3^{rd} Edition 



Grade 3 Pretest 
2005 
237.9 
7.7 
Grade 3 
2005 
253.1 
7.0 
Grade 4 
2005 
258.6 
8.0 
Grade 5 
2005 
262.0 
9.6 
Grade 6 
2005 
266.1 
9.6 
Grade 7 
2005 
268.8 
11.0 
Grade 8 
2005 
272.1 
10.9 
3^{rd} Edition Math 2006 



Grade 3 Pretest 
2006 
329.7 
11.35 
Grade 3 
2006 
343.20 
9.70 
Grade 4 
2006 
348.90 
9.46 
Grade 5 
2006 
353.74 
9.25 
Grade 6 
2006 
354.91 
9.70 
Grade 7 
2006 
357.76 
9.65 
Grade 8 
2006 
359.15 
9.21 
All values are rounded. Full precision was used for actual calculations.
Table 2. Standard Setting Years, Means and Standard Deviations for EndofCourse (EOC) CScale Computation
EOC 
Standard Setting Year 
Mean 
Standard Deviation 
Algebra I 
1994 
55.1 
9.12 

2001 
61.1 
9.31 

2006 
63.3 
10.1 

2007 
150.3 
8.9 
Algebra II 
1997 
58.5 
10.26 

2001 
63.8 
9.90 

2007 
150.2 
9.3 
Biology 
1995 
55.5 
8.67 

2002 
57.9 
7.61 

2007 
57.3 
7.47 
Chemistry 
1997 
56.8 
8.53 

2002 
60.0 
8.16 
Civics and Economics 
2006 
150.2 
9.19 

2007 
150.5 
9.04 
English I 
2003 
57.7 
7.63 

2007 
150.36 
8.93 
Geometry 
2001 
59.8 
8.85 

2007 
150.2 
9.27 
Physics 
1997 
56.5 
8.65 

2002 
60.7 
9.24 
Physical Science 
1997 
54.0 
9.41 

2002 
55.8 
7.90 
U.S. History 
2006 
150.0 
9.14 
Table 3. N Counts for EOG Proposed Formulas

Reading 
Mathematics 
Grade 3 
545,120 
545,862 
Grade 4 
534,515 
536,147 
Grade 5 
587,547 
589,558 
Grade 6 
525,760 
453,806 
Grade 7 
450,087 
450,838 
Grade 8 
397,382 
397,852 
• The N counts for grades 38 for Reading and Mathematics correspond to the EOG correlations for the proposed formulas in Tables 4 and 5.
Table 4. EOG Correlations Between Predicted Values and Actual Performance
Proposed Formulas 

Original Formulas 


Reading 
Mathematics 


Reading 
Mathematics 
Grade 3 
0.71 
0.75 

Grade 3 
0.76 
0.79 
Grade 4 
0.81 
0.82 

Grade 4 
0.80 
0.82 
Grade 5 
0.84 
0.86 

Grade 5 
0.81 
0.84 
Grade 6 
0.85 
0.86 

Grade 6 
0.82 
0.85 
Grade 7 
0.85 
0.87 

Grade 7 
0.83 
0.87 
Grade 8 
0.85 
0.88 

Grade 8 
0.83 
0.87 
All proposed formulas’ correlations, except grade 3, are at least as high as those from the current method of calculation. This suggests comparable prediction accuracy.
Table 5. EOG Correlations Between Predicted Values and Residuals*
Proposed Formulas 


Reading 
Mathematics 
Grade 3 
0.13 
0.13 
Grade 4 
0.04 
0.02 
Grade 5 
0.19 
0.003 
Grade 6 
0.01 
0.04 
Grade 7 
0.04 
0.06 
Grade 8 
0.05 
0.02 
Original Formulas 


Reading 
Mathematics 
Grade 3 
0.15 
0.30 
Grade 4 
0.03 
0.25 
Grade 5 
0.30 
0.14 
Grade 6 
0.07 
0.35 
Grade 7 
0.15 
0.06 
Grade 8 
0.15 
0.19 
All numbers are Pearson’s r.
* A residual is the difference between the predicted value and the actual value.
Table 6. N Counts and Equations for Proposed EOC Formulas
Algebra I 
109,585 
Grade 8 Mathematics EOG*0.8 
Algebra II 
265,165 
Algebra I EOC*0.8 
Biologya 
197,455 
Grade 8 Reading EOG*0.8 
Biologyb 
193,548 
The average of English I EOC and grade 8 Reading EOG*0.9 
Chemistry 
84,620 
Biology EOC*0.8 
English I 
280,400 
Grade 8 Reading EOG*0.8 
Geometrya 
172,713 
Algebra I EOC*0.8 
Geometryb 
149,943 
The average of Algebra I EOC and grade 8 Mathematics EOG*0.9 
Physical Science 
110,722 
Grade 8 Mathematics EOG*0.8 
Physics 
12,084 
The average of Chemistry and Geometry EOCs*0.9 
US History ^{b} 
74,235 
The average of English I and Biology EOC *0.92 
US History ^{a} 
75,174 
Biology EOC * 0.82 
Civics and Economics ^{b} 
49,494 
The average of English I and Biology EOC *0.92 
Civics and Economics ^{a} 
90,197 
English I EOC * 0.82 
^{a} denotes only one predictor used.^{ b}denotes two predictors used.
The N counts correspond to the EOC correlations for the proposed formulas in Tables 7 and 8.
The predicted values for Algebra I and Physical Science are computed by multiplying the grade 8 Mathematics cscale score by 0.8.
The predicted value for Algebra II is computed by multiplying the Algebra I cscale score by 0.8.
The predicted value for Biology^{a} is computed by multiplying the grade 8 Reading cscale score by 0.8, whereas the predicted value for Biology^{b} is computed by multiplying the average of the English cscale score and the grade 8 Reading cscale score by 0.9.
The predicted value for Chemistry is computed by multiplying the Biology cscale score by 0.8.
The predicted value for English I is computed by multiplying the grade 8 Reading cscale score by 0.8.
The predicted value for Geometry^{a} is computed by multiplying the Algebra I cscale score by 0.8, whereas the predicted value for Geometry^{b} is computed by multiplying the average of the Algebra I cscale score and the grade 8 Mathematics cscale score by 0.9.
The predicted value for Physics is computed by multiplying the average of the Chemistry cscale score and the Geometry cscale score by 0.9.
Table 7. EOC Correlations Between Predicted Values and Actual Performance
Proposed Formulas
Algebra I 
0.78 
Algebra II 
0.73 
Biologya 
0.73 
Biologyb 
0.78 
Chemistry 
0.71 
English I 
0.79 
Geometrya 
0.77 
Geometryb 
0.83 
Physical Science 
0.73 
Physics 
0.77 
US History^{b} 
0.77 
Civics^{b} and Ecnomics^{b} 
0.83

Original Formulas
Algebra I 
0.75 
Algebra II 
0.76 
Biology 
0.03 
Chemistry 
0.76 
English I 
0.80 
Geometry 
0.82 
Physical Science 
0.72 
Physics 
0.72 
US History ^{a} 
0.75 
Civics^{a} and Economics^{a} 
0.74 
All numbers are Pearson’s r.
^{a}denotes only one predictor used.
^{b} denotes two predictors used.
Table 8. EOC Correlations Between Predicted Values and Residuals Proposed Formulas
Original Formulas
Algebra I 
0.06 
Algebra II 
0.009 
Biologya 
0.01 
Biologyb 
0.04 
Chemistry 
0.06 
English I 
0.006 
Geometrya 
0.02 
Geometryb 
0.09 
Physical Science 
0.11 
Physics 
0.02 
New Formulas
Algebra I 
0.18 
Algebra II 
0.28 
Biology 
0.63 
Chemistry 
0.08 
English I 
0.20 
Geometry 
0.30 
Physical Science 
0.40 
Physics 
0.11 
All numbers are Pearson’s r.
^{a} denotes only one predictor used.
^{b} denotes two predictors used.
All correlations between predicted values and residuals are lower using the proposed formulas than the original formulas. A lower correlation of residuals suggests a weaker relationship between the predicted score and the amount of error in the prediction. This implies less systematic bias in predicting student performance.
Table 9. Standard Error of Estimation (SEE) for EOG and EOC Predictions EOG EOC
Reading 
Proposed Formulas 
Original Formulas 
Grade 3 
0.663 
0.635 
Grade 4 
0.571 
0.579 
Grade 5 
0.530 
0.505 
Grade 6 
0.513 
0.569 
Grade 7 
0.503 
0.438 
Grade 8 
0.489 
0.439 



Mathematics 
Proposed Formulas 
Original Formulas 
Grade 3 
0.565 
0.564 
Grade 4 
0.530 
0.640 
Grade 5 
0.444 
0.432 
Grade 6 
0.489 
0.604 
Grade 7 
0.469 
0.467 
Grade 8 
0.446 
0.506 

Proposed Formulas 
Original Formulas 
Algebra I 
0.620 
0.774 
Algebra II 
0.699 
0.704 
Biologya 
0.685 
1.370 
Biologyb 
0.629 

Chemistry 
0.734 
0.681 
English I 
0.586 
0.657 
Geometrya 
0.659 

Geometryb 
0.596 
0.630 
Physical Science 
0.634 
1.083 
Physics 
0.922 
1.284 
^{a} denotes only one predictor used. denotes two predictors used.
^{b} denotes only one predictor used. denotes two predictors used.
Table 10. Percent of Students Meeting Expectations in the Lower 10% and 50% and Upper 50% and 10% Using the Proposed Formulas Compared to the Original Formulas
Reading


Proposed Formulas 




Overall 
Lower 10% 
Lower 50% 
Upper 50% 
Upper 10% 
Grade 3 
46.6 
53.1 
51.8 
41.7 
30.4 
Grade 4 
47.5 
45.5 
50.4 
44.7 
39.7 
Grade 5 
49.9 
64.3 
56.6 
43.4 
35.1 
Grade 6 
60.4 
60.1 
58.4 
62.4 
59.6 
Grade 7 
58.6 
55.4 
56.5 
60.8 
57.7 
Grade 8 
52.8 
58.5 
54.5 
51.1 
48.6 


Original Formulas 




Overall 
Lower 10% 
Lower 50% 
Upper 50% 
Upper 10% 
Grade 3 
55.7 
53.3 
59.6 
51.8 
35.0 
Grade 4 
45.4 
50.5 
46.1 
44.8 
38.6 
Grade 5 
54.0 
73.9 
64.2 
44.9 
33.1 
Grade 6 
26.0 
31.7 
27.8 
24.5 
19.5 
Grade 7 
54.1 
62.5 
58.4 
50.7 
37.5 
Grade 8 
39.6 
55.3 
46.6 
33.3 
28.8 
Mathematics


Proposed Formulas 




Overall 
Lower 10% 
Lower 50% 
Upper 50% 
Upper 10% 
Grade 3 
56.4 
65.4 
59.6 
53.5 
44.8 
Grade 4 
57.1 
59.3 
57.0 
57.2 
56.6 
Grade 5 
54.3 
59.7 
53.5 
55.1 
58.7 
Grade 6 
65.2 
70.4 
64.5 
66.0 
64.2 
Grade 7 
57.2 
63.9 
54.9 
59.8 
68.4 
Grade 8 
60.6 
64.7 
60.0 
61.3 
60.0 


Original Formulas 




Overall 
Lower 10% 
Lower 50% 
Upper 50% 
Upper 10% 
Grade 3 
66.7 
78.2 
75.0 
59.1 
44.4 
Grade 4 
73.9 
77.7 
75.3 
72.6 
69.5 
Grade 5 
47.6 
62.8 
51.5 
44.3 
54.6 
Grade 6 
65.8 
47.5 
48.7 
78.6 
94.2 
Grade 7 
54.1 
54.7 
51.7 
56.3 
69.9 
Grade 8 
52.2 
48.6 
41.5 
62.1 
77.3 






· Using the proposed formulas, academic change is calculated by subtracting the predicted values from the posttests. The predicted values for grade 3 Reading and Mathematics are computed by multiplying 0.8 by the grade 3 pretest. The computation for grades 48 Reading and Mathematics is the product of 0.9 and the average of the two previous assessments (ATPA). This table shows the percent of students meeting expectations, where academic change is greater or equal to zero, at the lower 10%, lower 50%, upper 50% and upper 10% percentile of predicted values.
Table 11. Percent of Students Meeting Expectations by Quartiles Using the Proposed Formulas Compared to the Original Formulas
Reading

Proposed Formulas 



1st Quartile 
2nd Quartile 
3rd Quartile 
4th Quartile 
Grade 3 
52.2 
51.6 
46.2 
36.3 
Grade 4 
49.6 
51.3 
46.4 
43.1 
Grade 5 
61.4 
51.4 
46.7 
40.4 
Grade 6 
58.8 
57.9 
62.0 
62.7 
Grade 7 
56.0 
57.0 
61.2 
60.2 
Grade 8 
56.9 
52.0 
51.9 
50.4 
Original Formulas 


1st Quartile 
2nd Quartile 
3rd Quartile 
4th Quartile 
Grade 3 
56.2 
63.0 
59.0 
41.1 
Grade 4 
47.8 
44.7 
46.5 
41.8 
Grade 5 
67.6 
57.1 
49.3 
39.0 
Grade 6 
28.5 
26.5 
25.4 
21.7 
Grade 7 
59.3 
55.0 
57.5 
42.1 
Grade 8 
33.2 
41.2 
34.0 
30.4 
Mathematics

Proposed Formulas 



1st Quartile 
2nd Quartile 
3rd Quartile 
4th Quartile 
Grade 3 
60.8 
58.2 
55.1 
51.0 
Grade 4 
57.5 
56.4 
56.8 
57.7 
Grade 5 
55.7 
51.1 
52.6 
57.8 
Grade 6 
66.1 
62.6 
65.7 
66.5 
Grade 7 
57.9 
51.7 
54.8 
65.0 
Grade 8 
61.3 
58.7 
60.6 
61.9 
Table 12. Correlations Between Growth Composite Scores and Selected School Characteristics
at the School Level (Grades 38), 200304
Proposed Formulas

Total Number of Students 
Percent of Minority Students 
Academic Change 
0.005 
0.32 
Original Formulas

Total Number of Students 
Percent of Minority Students 
Expected Growth 
0.26 
0.19 
Correlation analyses for the proposed formulas were performed using the academic change composite for Reading and Mathematics for grades 38.
Correlation analyses for the original formulas were performed using the expected standardized growth composite for Reading and Mathematics for grades 38.
Table 13. Correlations Between Growth Composite Scores and Percent of Minority Students by
School Size (Grades 38), 200304
Proposed Formulas

Percent of Minority Students 

Small Schools1 
Medium Schools2 
Large Schools3 

Academic Change 
0.25 
0.37 
0.47 
Original Formulas

Percent of Minority Students 

Small Schools1 
Medium Schools2 
Large Schools3 

Expected Growth 
0.16 
0.21 
0.34 
School size range: 16 to 1,706
^{1 }Less than 200 students: 28.8%
^{2 }Between 200 and 400 students: 42.4%
^{3 }More than 400 students: 28.8%
Correlation analyses for the proposed formulas were performed using the academic change composite for Reading and Mathematics for grades 38.
Correlation analyses for the original formulas were
performed using the expected
standardized growth composite for Reading and Mathematics for grades 38.
Table 14. Percent of Schools (Grades 38) Meeting or Exceeding Growth Expectations by Quartiles of Percent Minority, 20032004


Proposed Formulas 



1st Quartile 
2nd Quartile 
3rd Quartile 
4th Quartile 
Met Academic Change 
89.6 
82.6 
63.2 
41.3 
Original Formulas 


1st Quartile 
2nd Quartile 
3rd Quartile 
4th Quartile 
Met Expected Growth 
76.9 
71.0 
57.7 
55.8 
The results using the proposed formulas show less equity across the range of percent minority students compared to the original formulas. 9 The percent of schools meeting expected growth declines over the quartiles as the percent of minority students in the school increases. 9 For both formulas, the expectation is neutral toward demographic factors because the formulas use only student’s past achievement to predict future achievement.
Note: When viewing the results of analyses correlating demographic factors and school growth, as one demographic factor decreases in importance, others appear to increase in importance.
Table 15. Percent of Schools (Grades 38) Meeting or Exceeding Expectations by Quartiles of Number of Students, 20032004


Proposed Formulas 



1st Quartile 
2^{nd} Quartile 
3rd Quartile 
4th Quartile 
Met Academic Change 
64.9 
75.2 
79.4 
72.3 
Original Formulas 


1st Quartile 
2^{nd} Quartile 
3rd Quartile 
4th Quartile 
Met Expected Growth 
72.0 
83.9 
77.8 
34.9 
In the proposed formulas, the percent of schools meeting academic change remains stable over the quartiles as the number of students in the school increases. A majority of schools are meeting academic change across all school sizes.
In the original formulas, the percent of schools meeting expected growth declines after the second quartile as the number of students in the school increases.
Note: When viewing the results of analyses correlating demographic factors and school growth, as one demographic factor decreases in importance, others appear to increase in importance.
Table 16. Percent of Schools (Grades 38) Meeting or Exceeding Expectations by Average Pretest Score Quartiles
Reading


Proposed Formulas 


Year 
1st Quartile 

2nd Quartile 
3rd Quartile 
4th Quartile 
1999 
27.6 

44.9 
52.3 
62.5 
2000 
14.1 

35.7 
47.0 
62.7 
2001 
15.7 

38.8 
53.1 
73.3 
2002 
30.0 

51.9 
61.8 
73.7 
2003 
17.5 

36.0 
47.5 
72.3 
2004 
25.3 

47.4 
63.4 
81.0 

Original Formulas 

Year 
1st Quartile 

2nd Quartile 
3rd Quartile 
4th Quartile 
2002 
29.8 

44.1 
55.1 
68.4 
2004 
30.5 

40.5 
39.9 
45.0 
Mathematics


Proposed Formulas 


Year 
1st Quartile 

2nd Quartile 
3rd Quartile 
4th Quartile 
1999 
41.6 

64.0 
72.6 
86.0 
2000 
32.3 

53.7 
73.5 
85.7 
2001 
19.0 

25.3 
38.9 
68.2 
2002 
33.5 

59.3 
72.7 
88.0 
2003 
82.5 

96.9 
98.7 
98.9 
2004 
58.3 

82.2 
92.2 
98.0 

Original Formulas 

Year 
1st Quartile 

2nd Quartile 
3rd Quartile 
4th Quartile 
2004 
68.8 

83.4 
94.3 
98.5 
Table 17. Trend in Percent of Schools with a CRatio of 1.5 or Greater by Reading Quartiles, Using the Proposed Formulas
Year 
1st Quartile 
2nd Quartile 
3rd Quartile 
4th Quartile 
1999 
11.8 
15.8 
20.7 
19.9 
2000 
2.3 
7.9 
10.0 
18.4 
2001 
2.5 
6.9 
11.7 
22.0 
2002 
8.1 
6.2 
12.0 
18.9 
2003 
4.6 
3.5 
4.8 
16.7 
2004 
6.6 
6.1 
10.7 
18.6 
The cratio is computed by dividing the number of students who met their expectation for academic change (“0” or greater) by the number of students who did not meet their expectation.
The schools are classified in quartiles based on the average previous year’s Reading average cscale score.
A cratio is an indicator of school performance. Fundamentally, cratios greater than 1.5 mean that schools are helping a vast majority of their students meet individual growth standards.
In most years, schools in the lowest quartile have a lower ratio of students meeting the growth standard than the upper quartiles.
Schools that have a lower ratio of students who are meeting the growth standard should also be less likely to meet the growth standard. This is reflected in Tables 15 and 16.
Table 18. Trend in Percent of Schools Meeting or Exceeding Expectations by EOGs
Reading


Proposed Formulas 



Grade 
199899 
199900 
200001 
200102 
200203 
200304 
3 
29.3 
22.8 
29.1 
38.2 
50.1 
51.2 
4 
51.1 
33.8 
38.8 
43.3 
22.0 
49.4 
5 
19.2 
55.0 
59.1 
56.8 
46.5 
45.0 
6 
90.5 
76.8 
72.1 
75.8 
63.9 
68.4 
7 
71.7 
58.4 
71.8 
65.6 
57.3 
66.0 
8 
39.1 
36.0 
44.9 
64.7 
58.4 
52.1 


Original Formulas 



Grade 
199899 
199900 
200001 
200102 
200203 
200304 
3 
85.8 
76.2 
51.1 
54.6 
70.0 
68.1 
4 
22.4 
17.9 
26.4 
29.2 
61.5 
28.3 
5 
58.0 
80.2 
85.4 
87.0 
97.3 
73.0 
6 
44.0 
19.7 
18.1 
24.9 
15.3 
2.2 
7 
72.9 
33.2 
44.9 
29.7 
76.4 
70.4 
8 
55.2 
31.4 
51.9 
56.2 
57.8 
10.9 
Mathematics


Proposed Formulas 



Grade 
199899 
199900 
200001 
200102 
200203 
200304 
3 
51.1 
50.0 
49.3 
49.0 
91.2 
86.5 
4 
54.0 
59.1 
31.4 
62.4 
94.6 
82.2 
5 
61.5 
55.8 
36.8 
56.6 
90.5 
62.5 
6 
79.0 
60.0 
49.3 
75.9 
90.9 
78.5 
7 
68.3 
60.8 
40.5 
62.2 
67.5 
47.0 
8 
71.9 
74.8 
40.4 
65.3 
78.0 
73.6 


Original Formulas 



Grade 
199899 
199900 
200001 
200102 
200203 
200304 
3 
39.9 
38.1 
51.9 
54.9 
93.9 
91.2 
4 
85.9 
86.3 
83.2 
93.1 
99.8 
95.8 
5 
74.3 
66.0 
56.0 
72.2 
92.0 
46.4 
6 
71.4 
55.5 
66.2 
81.3 
94.4 
83.8 
7 
82.6 
61.0 
80.2 
86.6 
81.1 
57.4 
8 
66.8 
64.6 
32.1 
49.1 
58.9 
48.8 
The percent of schools making growth at any grade level in any year is expected to be different using the proposed formulas compared to the original formulas since the proposed formulas use a different standard of growth.
Some of the notable differences are at the years when the posttest is the second edition and the pretest is the first edition. A fundamental strength of the proposed formulas is the ability to more accurately predict growth across test editions.
Using the original formulas, the percent of schools meeting growth in grade 6 Reading is low across all years. Using the proposed formulas, the results show a higher percentage. This is a function of using a different method of setting the growth standards and more closely reflects the implementation of curriculum.
Table 19. Trend in Percent of Schools Meeting or Exceeding Expectations by EOCs
Proposed Formulas

200102 

200203 
200304 
Algebra I 
59.4 

56.3 
52.7 
Algebra II 
24.6 

26.8 
15.4 
Biology 
52.1 

18.2 
12.8 
Chemistry 
14.4 

18.9 
24.2 
English I 
92.8 

39.3 
42.0 
Geometry 
20.3 

16.3 
13.1 
Physical Sciences 
50.2 

52.6 
62.3 
Physics 
1.3 

1.6 
0.7 
Original Formulas

200102 

200203 
200304 
Algebra I 
91.8 

89.0 
89.1 
Algebra II 
71.4 

63.6 
56.0 
Biology 
61.4 

26.1 
26.3 
Chemistry 
70.0 

77.3 
72.9 
ELPS 
44.5 

39.6 

English I 
61.3 

97.9 
98.7 
Geometry 
34.0 

30.1 
26.8 
Physical Sciences 
58.4 

61.8 
67.6 
Physics 
76.2 

69.4 
70.2 
US History 
20.4 

28.5 

The percent of schools making growth across EOCs in any year is expected to be different using the proposed formulas compared to the original formulas since the proposed formulas use a different standard of growth.
Table 20. Percent of Schools Meeting Expected Growth and High Growth
Proposed Formulas

200102 
200203 
200304 


N 
Percent 
N 
Percent 
N 
Percent 
Met At Least Expected Academic Change 
1,424 
65.4 
1,839 
85.0 
1,582 
72.1 
Met High Academic Change 
395 
18.1 
751 
34.6 
536 
24.4 
Original Formulas

200102 
200203 
200304 


N 
Percent 
N 
Percent 
N 
Percent 

Met At Least Expected Growth 
1,642 
74.8 
2,092 
94.3 
1,676 
75.1 

Met High Growth 
779 
35.5 
1,617 
72.9 
785 
35.2 

• In the proposed formulas, high growth is met when Academic Change is greater or equal to “0” and the cratio is greater than 1.5.
Using the proposed formulas, the percent of schools meeting both the expected and high growth expectations in these three years is similar except for results for the high growth standard in 200203.
The percent of schools meeting these standards is different between the two sets of formulas.
Table 21. Percent of Schools Meeting Expected Growth and High Growth by Grade Span*
Proposed Formulas

Grade Span 
200102 
200203 
200304 

Met At Least Expected Academic Change 
K5 
577 
52.8% 
964 
86.4% 
842 
75.0% 
68 
299 
78.9% 
327 
85.8% 
279 
71.9% 

912 
319 
96.4% 
319 
98.1% 
246 
73.6% 

Met 
K5 
125 
11.4% 
472 
42.3% 
359 
32.0% 
High Academic 
68 
139 
36.7% 
162 
42.5% 
104 
26.8% 
Change 
912 
70 
21.1% 
12 
3.7% 
8 
2.4% 
Original Formulas

Grade Span 
200102 
200203 
200304 

Met At Least 
K5 
904 
79.6% 
1151 
98.9% 
988 
85.1% 
Expected Growth 
68 
222 
59.4% 
320 
84.0% 
124 
32.0% 

912 
264 
81.7% 
277 
85.7% 
310 
96.9% 

K5 
486 
42.8% 
1095 
94.1% 
504 
43.3% 
Met High Growth 
68 
126 
33.7% 
214 
56.2% 
46 
11.9% 
912 
63 
19.5% 
96 
29.7% 
139 
43.4% 
* Elementary (K5) schools include schools with students no lower than kindergarten and no higher than grade 5.
Middle (68) schools are schools with students no lower than grade 6 and no higher than grade 8.
High schools (912) consist of schools with students no lower than grade 9.
The percent of schools making growth among the three grade spans in any year is expected to be different using the proposed formulas compared to the original formulas since the proposed formulas use a different standard of growth.
Using the original formulas, the percent of middle (68) schools meeting growth is low in 200102 and 200304. Using the proposed formulas, the results show a higher percentage.
Table.22 Correlations between Residuals and the Average of the Two Previous Assessment Scores (ATPA)

Reading 
Mathematics 
Grade 3* 
0.39 
0.41 
Grade 4 
0.20 
0.18 
Grade 5 
0.36 
0.19 
Grade 6 
0.16 
0.23 
Grade 7 
0.13 
0.13 
Grade 8 
0.23 
0.23 
*The grade 3 pretest cscale score is used since two previous assessment scores are not available.
√ In the original proposal, a factor of 0.1 was used to help offset the correlation between residuals and predicted values. See Table 24 below for the results of this adjustment (including the adjustment for PA). Since in Table 24 all correlations to residuals decreased to the hundredths place of the decimal, the decision was made to leave the factor at 0.1 since is reduced (along with the 0.2) a vast majority of the systematic error except for grade 5 reading. Additionally, the grade 3 systematic error was deemed inherent in the pretest post test system and other factors due to the age of the students involved.
Table.23 Correlations between Residuals and the Assessment Scores (PA)

Reading 
Mathematics 
Grade 3* 
0.39 
0.41 
Grade 4 
0.17 
0.14 
Grade 5 
0.32 
0.19 
Grade 6 
0.05 
0.19 
Grade 7 
0.20 
0.10 
Grade 8 
0.20 
0.22 
*The grade 3 pretest cscale score is used since two previous assessment scores are not available.
√ In the original proposal, a factor of 0.2 was used when only a single predictor was used (due to the similarity between those correlations and 0.2). The results of incorporating the 0.1 factor are shown below.
Table 24. EOG Correlations Between Predicted Values and Residuals using 0.1 and 0.2 for Regression Coefficients*
Proposed Formulas 


Reading 
Mathematics 
Grade 3 
0.13 
0.13 
Grade 4 
0.04 
0.02 
Grade 5 
0.19 
0.003 
Grade 6 
0.01 
0.04 
Grade 7 
0.04 
0.06 
Grade 8 
0.05 
0.02 
*After careful consideration of the effects on traditionally high achieving students, the regression factor was adjusted to 0.08 for two previous assessments and 0.18 for a single previous assessment.
Table 25. Correlations Between Predicted Values and Residuals using 0.08 and 0.18 for Regression Coefficients*

Reading 
Mathematics 
Grade 3 
0.16 
0.16 
Grade 4 
0.08 
0.05 
Grade 5 
0.23 
0.04 
Grade 6 
0.02 
0.07 
Grade 7 
0.01 
0.02 
Grade 8 
0.09 
0.06 
*After careful consideration of the effects on traditionally high achieving students, the regression factor was adjusted to 0.08 for two previous assessments and 0.18 for a single previous assessment.
Scale Score Ranges
Subject/Grade 
Level I 
Level II 
Level III 
Level IV 
Reading PT3 3 4 5 6 7 8

213223 216229 223235 228238 228241 228242 231243

224232 230239 236243 239246 242251 243251 244253

233244 240249 244254 247258 252263 252263 254265

245264 250272 255275 259277 264283 264287 266290

Achievement Level Descriptions:
Level I: Students performing at this level do not have sufficient mastery of knowledge and skills in this subject area to be successful at the next grade level.
Level II: Students performing at this level demonstrate inconsistent mastery of knowledge and skills in this subject are and are minimally prepared to be successful at the next grade level.
Level III: Students performing at this level consistently demonstrate mastery of grade level subject matter and skills and are well prepared for the next grade level.
Level IV: Students performing at this level consistently perform in a superior manner clearly beyond that required to be proficient at grade level work.
EndOfCourse (EOC) Achievement Levels (July 2004)
Description 
Level I 
Level II 
Level III 
Level IV 
Algebra I 
3144 
4554 
5565 
6696 
Algebra II 
3345 
4657 
5868 
69102 
Biology 
2846 
4754 
5564 
6585 
Chemistry 
3147 
4855 
5664 
6590 
Civics and Economics 
>139139 
140149 
150159 
160<160 
English I 
2842 
4351 
5260 
6182 
Geometry 
3245 
4656 
5766 
6793 
Physics 
2342 
4351 
5262 
6391 
Physical Science 
3043 
4453 
5463 
6486 
US History 
>139  139 
140149 
150159 
160 <160 
200506 and 200607
Achievement Level Ranges for North Carolina
EndofCourse Tests
Test 
Level I 
Level II 
Level III 
Level IV 
Algebra I 
Less than or equal to 44 
4554 
5565 
Greater than or equal to 66 
Algebra I (Interim for 200607) 
Less than or equal to 139 
140147 
148157 
Greater than or equal to 158 
English I 
Less than or equal to 42 
4351 
5260 
Greater than or equal to 61 
English I (Interim for 200607) 
Less than or equal to 137 
138145 
146156 
Greater than or equal to 157 
Biology 
Less than or equal to 46 
4754 
5564 
Greater than or equal to 65 
U.S. History (Interim for 200506) 
Less than or equal to 139 
140149 
150159 
Greater than or equal to 160 
U.S. History (for 200607 and beyond) 
Less than or equal to 139 
140148 
149159 
Greater than or equal to 160 
Civics and Economics (Interim for 200506) 
Less than or equal to 139 
140148 
149158 
Greater than or equal to 159 
Civics and Economics (for 200607 and beyond) 
Less than or equal to 140 
141147 
148159 
Greater than or equal to 160 
Algebra II 
Less than or equal to 45 
4657 
5868 
Greater than or equal to 69 
Algebra II (Interim for 200607) 
Less than or equal to 138 
139146 
147157 
Greater than or equal to 158 
Chemistry 
Less than or equal to 47 
4855 
5664 
Greater than or equal to 65 
Geometry 
Less than or equal to 45 
4656 
5766 
Greater than or equal to 67 
Geometry (Interim for 200607) 
Less than or equal 138 
139147 
148157 
Greater than or equal to 158 
Physics 
Less than or equal to 42 
4351 
5262 
Greater than or equal to 63 
Physical Science 
Less than or equal to 43 
4453 
5463 
Greater than or equal to 64 