STA 108 Course Project: Project STAR
February 5th 2020
Overview
This document contains instructions on the course project STA 108 in Winter 2020. This document is made with R markdown. The rmd file to generate this document is available on the course website.
Background
In this project, we study the dataset from a very influential randomized experient. Tennesses Student/Teacher Achievement Ratio study (Project STAR) was conducted in the late 1980s to evaluate the effect of class size on test scores. This dataset has been used as a classic examples in many textbooks and research papers. You are encouraged to read more about the experiment design and how others analyze this dataset. This document only provides a brief explanation of the dataset that suffices for this course project.
The study randomly assigned students to small classes, regular classes, and regular classes with a teacher’s aide. In order to randomize properly, schools were enrolled only if they had enough studybody to have at least one class of each type. Once the schools were enrolled, students were randomly assigned to the three types of classes, and one teacher was randomly assigned to one class.
The dataset contains scaled scores for math and reading from kindergarten to 3rd grade. We will only examine the math scores in 1st grade in this project.
Tasks
Any computational tasks should be completed using R.
1. Install the AER package and load the STAR dataset.
2. For each of the three class types, draw histgrams of gender, ethnicity, and birth (birth quarter) for participated students.
3. Write down a linear regression model to study the association between the class types and the scaled math scores in the 1st grade. You may want to include other covariates (predictors) of your choice. Explain your notation.
4. Fit the model in Task 3 and show your fits in the report with tables or plots.
5. Construct \(95\%\) confidence intervals for the coefficients of the class types.
6. Interpret the point estimates and the confidence intervals in a way that a non-statistician can understand.
7. Test the null hypothesis that there are no differences in math scaled scores across class types in the 1st grade. Justify your choice of test.
8. Explain your test result in a way that a non-statistician can understand.
9. Conduct model diagnostic and/or sensitivity analysis.