Data SGP and Distributional Properties of Latent Achievement Attributes

The goal of data sgp is to provide a fair assessment of student progress by ranking students against others with similar prior achievement. In theory, comparing students in this way removes bias caused by unadjusted test scores that may overstate student ability or understate teacher effectiveness. Moreover, since SGPs rank students against students with similar background characteristics, they are viewed as more relevant to student achievement than non-adjusted measures of student performance such as average test scores. Despite these purported benefits, recent research has shown that SGPs estimated from standardized test scores are often biased due to the finite number of items on each test. The error-prone nature of these SGPs, along with their natural correlations with student background characteristics, make them unreliable measures of true student progress.

Hence, a fair SGP measure should have distributional properties that are independent of student background characteristics. In this article, we define a model for latent achievement attributes and propose a method for estimating unbiased SGPs from standardized tests. We then use this new estimate of a student’s true SGP to assess the distributional properties of that attribute. We show that the true SGP for a student can be represented by its percentile rank in a sample of students with the same prior SGP and that, for this student, it follows a normal distribution. We also show that the relationship between the true SGP and the student’s background variables is dependent on how those variables are measured.

We conclude that for most analyses that use SGPs, the WIDE data format is preferable to the LONG format. The lower level SGP functions studentGrowthPercentiles and studentGrowthProjections work with WIDE data, while the higher level wrapper functions (such as the sgp_regress function) work with LONG data. If you plan on running these analyses operationally year after year, we recommend using LONG data for ease of preparation and storage.

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