How to Organize Student Growth Plots Using the Data SGP Package

The data sgp package offers an efficient means of organizing longitudinal (time dependent) student assessment data into statistical growth plots for each individual student. The data sgp package supports two common formats, WIDE and LONG. The lower level functions that do the actual calculations require WIDE formatted data whereas the higher level wrappers, such as studentGrowthPercentiles and studentGrowthProjections, use LONG data formats.

The most common way to organize data for SGP analyses is by using the sgpData table provided with the data sgp package. Each row of sgpData provides information for one individual student over time, with each column representing an assessment taken by the student in that year. For example, in the table below, the first row contains a student identifier, the second row shows the MCAS assessment given by that student in 2013, the third row displays the MCAS assessment given by that student in 2014, the fourth row lists the MCAS assessments given by that student in 2015, and the fifth row lists the MCAS assessments given by that students in 2016.

These assessment records are used to generate SGPs for each individual student. SGPs measure the amount of growth a student has demonstrated on an assessed topic compared to other students with similar prior performance. For example, a student with a SGP of 75 would have a better MCAS score than 75% of the other students who performed similarly on their previous assessments.

SGPs based on student test scores are widely used in educational policy in the United States to evaluate educator effectiveness and student achievement. They are also seen as a more meaningful measure of student performance than unadjusted measures such as percentile rank because they consider both the student’s current ability and the level of effort with which they have worked to attain that ability (Betebenner, 2009).

Unfortunately, despite their popularity, SGP estimates based on student standardized test scores suffer from substantial estimation errors, particularly for prior achievement. These errors make estimates of SGPs noisy measures of student learning.

Fortunately, researchers have developed methods to correct these estimation errors to produce more accurate SGP estimates for individual students. This process is called latent trait modeling, and the results are shown in the graph below. The graph shows the reliability – or error – of conditional mean estimators of a student’s true SGP based on their prior and current assessments, as well as the variance in these estimated SGPs that can be explained by differences in the covariates measured in the model. The graph demonstrates that latent trait models, when implemented properly, have the potential to provide more reliable and useful SGP estimates than those obtained using conventional standardized tests. The graph also reveals that the relationships between covariates and SGPs can be quite complicated. In fact, the RMSE for the SGP estimates in the graph can vary by as much as a factor of 10. For example, students who are absent from school frequently tend to have poorer SGPs for math than those who attend regularly.