Clustering Based Small Area Estimation : an Application to Meap Data

Abstract

Abtsrcat The Michigan Educational Assessment Program, known as MEAP, conducted by the state department of education, is a standardized test. The test is taken by all public school students in Michigan and the results are being used for comparing schools and school districts. Because of widely varying school districts in size, the direct use of average score could be misleading. The direct averages for small school districts are, in particular, quite unstable. This requires “smoothing” the data before they can be used. There are several smoothing procedures available in statistical literature that “borrow strength” from other areas. We choose to apply small area estimation technique to analyze 4-th grade average math score available in MEAP. The standard small area estimation methods shrunk the direct averages towards overall statewide average but it can suffer from over-shrinkage problem. To resolve over-shrinkage, a clustering based small area estimation technique has been applied to the data. This allows borrowing strength both locally and globally. In terms of mean squared error and coefficient of variation, the resultant estimates are more stable and hence are more reliable to use.