Analyzing test scores (generalized linear mixed models)
The district school board wants to know if an experimental teaching method is effective at improving math scores. They select at random schools within the district, then some classrooms within each school. The classrooms are randomly assigned to the experimental or control group, and the classroom teachers are asked to use the new or standard method to teach mathematics in the coming school year. All students within the classrooms are tested at the beginning and end of the school year. The data have a hierarchical 3-level structure: school – class – student with 23 schools, 97 classes and 2209 students.
This information is collected in test_scores.sav . See the topic Sample Files for more information. Students from the same classroom should be correlated since they are taught by the same teacher, and classrooms within the same school may also be correlated, so we can include random effects at school and class levels to account for different sources of variability.
The target, Yijk, is the test score after a teaching method is applied for a year at school i, class j and student k. The possible predictors come from different levels.
| Level | Predictor | Values |
|---|---|---|
| School | School setting (school_setting) | 1 = Urban 2 = Suburban 3 = Rural |
| School | School type (school_type) | 1 = Public 2 = Non-public |
| Classroom | Teaching method (teaching_method) | 0 = Standard 1 = Experimental |
| Classroom | Number of students in the classroom (n_student) | Integer |
| Student | Gender (gender) | 0 = Male 1 = Female |
| Student | Reduced/Free lunch (lunch) | 1 = Qualifies 2 = Does not qualify |
| Student | Pre-test score (pretest) | 0-100 |
These predictors can be denoted by xijk for school i, class j and student k.