# TVAAS

## Misconception: TVAAS cannot measure growth for groups of students who have missing data.

TVAAS can include students even if they have missing test data, and this is a critical advantage to a sophisticated value-added approach.

### TVAAS in Theory

Students with missing test scores are more likely to be low-achieving students, and it is important to include these students to avoid selection bias, which could provide misleading growth estimates to systems and schools that serve low-achieving or highly mobile populations of students. While more simplistic value-added or growth estimates might require that students have the same set of predictors or that students have all required predictors, this often has the result of excluding certain kind of students, and this would disproportionately affect educators serving those types of students.

TVAAS does not require that students have the same set of predictors or all required predictors, and this approach includes more students in the growth measures. When estimating students' entering achievement, the modeling considers the quantity and quality of information available to each student, as well as student mobility among schools from year to year.

To accomplish this without imputing student test scores, TVAAS uses a sophisticated modeling approach that provides more reliable estimates of growth.||

As a simple example, consider the following scenario. Ten students are given a test in two different years. The goal is to measure academic growth (gain) from one year to the next. The right side of the figure below shows the same students, some of whom now have missing scores. Two simple approaches when data are missing are to calculate the mean of the differences, or to calculate the differences of the means. When there are no missing data, these two simple methods provide the same answer (5.8 in the left side of the figure). However, when there are missing data, each method provides a different result (9.6 vs. 4.0 in the right side of the figure).

SCORES WITHOUT MISSING DATA AND SCORES WITH MISSING DATA

The problem of missing data is very common to student testing data and must be taken into consideration. As illustrated above, a more sophisticated model is needed to address this problem. The approach used by TVAAS estimates the means in each of these cells using relationships between students' test scores as if there were no missing test scores. In this way, the model provides more reliable and less biased growth measures without imputing any data. Furthermore, TVAAS uses much more student data to obtain these relationships in the growth estimates for systems and schools.

### TVAAS in Practice

For assessments analyzed with the gain model, all students are included, regardless of their testing histories, their number of prior test scores, and which test scores they have. For assessments analyzed with the predictive model, all students are included so long as they have three prior test scores in any test, grade, and subject.

Because TVAAS reporting is available statewide in Tennessee, students and their test histories can be tracked as they move within the state.

Furthermore, it is important from a philosophical perspective that as many students as possible be included in the system and school growth measures so that highly-mobile student populations receive the same level of attention as non-mobile ones.