The data sgp package allows users to work with growth percentiles calculated for individual students in ELA and math. This package includes lower level functions (studentGrowthPercentiles and studentGrowthProjections) as well as higher level wrapper functions. In general, the lower level functions require the use of WIDE formatted data while the higher level wrapper functions operate with LONG formatted data. If you intend to run operational analyses with data sgp on an ongoing basis, we recommend working with the longer formatted data as it offers numerous data preparation and storage advantages over WIDE formatted data.
It is a common assumption in the educational literature that the relationship between true student SGPs and observed student covariates is due primarily to unobserved student-level factors that may proxy for different aspects of student progress. If this is the case, then conditioning on additional prior achievement attributes that may reduce the correlation between true SGPs and other student-level characteristics would improve the accuracy of SGP estimation.
To explore this possibility, we modeled a simple situation: conditional mean estimates of the true student math SGP, e4,2,i, were estimated by assuming that the current and prior test scores for each student are from two different testing windows. The resulting error curves shown in Figure 1(a) show the expected RMSE for various estimates of e4,2,i, conditioned on different amounts of data.
Clearly, the error for conditioning on one set of prior scores is significantly less than for conditioning on both sets of prior scores. However, it is important to note that the error for conditioning on one set of prior results is not zero and should be accounted for in any analysis of student growth.
The spread in the 0.10 and 0.90 quantiles is slightly greater than in the mean, but much smaller than the spread between school-level means when comparing 2013 to 2014 4th grade math growth. It is also less than the spread between mean and medians when comparing the same groups of schools in both years. The lower variance in the SGP means than in the school-level mean and medians is an indication that mean SGPs are a more stable measure of student progress than medians.
The next article will explore further approaches for reducing the impact of variation in other student-level attributes on estimated student growth. In particular, we will consider the effects of combining multiple assessments to form an aggregated measure, as well as the potential benefits of using more than two assessments in the prior year to calculate a current SGP. We will also explore the effect of varying the reliability of prior assessment data on the estimates of student growth. The implications of these analyses for the underlying models that power the DESE SGP calculations will be discussed.