Table of Contents

Gain Model

Before analyzing the data, all students' scores are converted to normal curve equivalents, or NCEs. NCEs are similar to percentiles in that they represent where a score falls in a distribution. The NCEs for assessments analyzed with the gain model indicate where each score falls in the distribution of all students in the state in that grade and subject.

To generate NCEs for K-2 assessments, EVAAS uses both the book levels and performance levels. When these two items are combined for each student, a statewide distribution of students' performance can be created. Normal curve equivalents (NCEs) are then generated from this distribution. EVAAS measures growth in kindergarten through second grade using separate analytic pools for each SBE-approved assessment. In other words, there is not a statewide expectation of growth like there is in other tested subjects and grades. Instead, expected growth is based on the average growth observed by all districts administering a specific SBE-approved assessment. This is the most appropriate statistical approach given differences in the scales and test administration practices among the SBE-approved assessments.

This conversion to NCEs ensures that all assessment scores are on a common scale across years, grades, and subjects. This step is necessary to generate reliable measures of Growth. Converting to NCEs puts the scores on a common scale, but it does not affect how many districts, schools, or teachers fall into each Growth indicator range.

With that in mind, NCEs are easy to interpret. The center of the distribution, or state average, is 50. Values below 50 indicate that the students' average achievement level is below the state average. Likewise, values above 50 indicate that students' average achievement level is higher than the state average. NCEs can range below 0 and above 100 to preserve the equal-interval property of the distribution and to avoid truncating the test scale.

To estimate the average achievement of a group of students, EVAAS does not simply average the students' assessment scores in the selected subject and grade. Instead, it uses all scores across years and grades. For EOG reporting, the model includes available assessment scores from math and reading in grades 3 through 7. For K-2 reporting, the model includes MOY and EOY kindergarten scores, BOY and EOY first-grade scores, and BOY and EOY second-grade scores. Using this much data helps to minimize the impact of measurement error associated with any individual test score. It also allows all students to be included, even those with incomplete testing histories. The resulting estimates of each group's average achievement are more precise and reliable, and they better reflect the group of students served, despite missing test scores or high mobility.

Using this approach, EVAAS estimates the average entering achievement of a district's, school's, or teacher's students for each tested subject and grade. Then the students' average achievement in that subject at the end of the year is calculated. Finally, the two achievement estimates are compared to see if the group's average achievement increased, decreased, or remained about the same relative to the state distribution. When generating growth measures for teacherreports, students are weighted based on the proportion of instructional responsibility claimed during roster verification.

Expected Growth is simply the expectation that, regardless of their entering achievement level, students should make enough Growth during the school year to at least maintain that achievement level relative to their peers in the same grade and subject. This is a reasonable and attainable expectation of Growth. For example, if a high-achieving group of students starts the year at the 70th NCE and ends the year at the 70th NCE, then they met the standard, because they maintained their achievement level. Likewise, a low-achieving group of students that started the year at the 30th NCE and ended the year at the 30th NCE also met the standard. In both examples, the Value-Added report would display a growth measure of 0.0.

Remember, the growth measures are reported in state NCEs. Positive values suggest an increase in the group's average achievement relative to their peers in the state, while negative values suggest a decrease in the group's achievement. However, because the growth measures are estimates, consider their associated standard errors as you interpret the values.