Abstract:

In a variety of research areas data with natural hierarchies are frequently encountered. In these kinds of data, while observations of a group show similarity with each other it is independent from the observations of other groups. The similarity of observations of the same group results with the violation of the independence of the observations. This problem can be solved with the use of multi-level models. In this work, we apply the multilevel analysis approach to the data including the 2010-year SBS (Placement Test) achievement scores of the students at 20 elementary schools which were randomly selected in the Centrum of Van Province and the aim is to investigate the important factors on the achievement scores. The random intercept and random slope model was determined as the model which best explains the change in exam scores. The MCMC, which has the smallest deviation among the estimation methods, was preferred, as compared to IGLS and RIGLS methods. The results revealed that there is a significant difference in the student achievement scores across schools.

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