Conditional standard errors of measurement, confidence interval, and reliability for individual level student growth percentiles

The importance of measuring and monitoring educational achievement longitudinally has led to a proliferation of growth models. The Student Growth Percentile (SGP) is one score metric which helps to make inferences about current relative student status given prior test scores. The major purpose of this study was to provide two Conditional Standard Errors of Measurement (CSEM) estimation approaches for individual-level SGPs with theoretical justifications and empirical elaborations of them. Estimation approaches were developed under two commonly used paradigms: Classical Test Theory (CTT) and Item Response Theory (IRT). Within each paradigm, measurement error was conceptualized as variability of individual-level test scores across hypothetical repeated measurement using parallel test forms. Under the CTT paradigm, the measurement errors were assumed to be distributed as a binomial model. Under the IRT paradigm, they were assumed to be distributed as a compound binomial model. In addition to CSEMs, the purpose of this study was to develop procedures for constructing individual-level SGP confidence intervals and for estimating reliability. The proposed methods were demonstrated using data for a large-scale assessment of mathematics achievement from Grades 3 to 4. For example, pertinent tables and graphs including outcome statistics showed that the mean and median values of CSEMs for individual SGPs were sizable, the length of tests influenced actual values of CSEM for SGP, but there were small differences in CSEM values between the two types of conversion relationships. The CSEM values on the SGP scale by each academic peer group were distributed in an arch shape. Also, compared to the SGP reliabilities under CTT, those under IRT had similar reliability coefficients in the three tests. The results of these demonstrations were used to evaluate measurement errors in the context of practical and policy implications of SGP use. In final chapter, the practical use of SGPs and important considerations regarding measurement issues are provided. Further research related to SGPs using different subjects or grade levels, or simulation studies on the effective of the developed methodologies are also discussed.