Calculating Student Growth Percentiles: Method and Software

Computation of Student Growth Percentiles (SGP) has been thoroughly described by Betebenner (2011). SGP is based on conditional density estimates associated with a student’s score at time t using the student’s prior scores at times 1, 2, …, t-1 as the conditional variables. For example, Grade 4 students’ SGP may be computed using Grade 3 prior achievement, Grade 5 using both Grade 3 and Grades 3 and 4 prior achievements, and Grade 6 using Grade 5, and Grades 4 and 5, Grades 3, 4, and 5 prior achievements. Thus, the percentile result reflects the likelihood of such an outcome given the student’s prior scores. Qualifying SGP as “low,” “typical,” or “high” growth is a standard setting procedure requiring external criteria (e.g., growth related to a state’s performance standards) combined with stakeholders’ input. Estimation of the conditional density is completed using quantile regression (Koenker, 2005). While linear regression models estimate the conditional mean of a response variable Y, quantile regression is more general and estimates a family of conditional quantiles of Y. Major advantages of using the quantile regression for estimation of SGP is robustness to outliers and equivariance to monotone transformation of scale, where SGP results do not change due to alterations in scale. Additionally, SGP is uncorrelated with prior achievement. The computation of SGP may be completed using R (R Development Core Team, 2010), a free language and environment for statistical computing using the SGP package (Betebenner & Iwarrden, 2011). Other possible software includes SAS and Stata.