# Regression to analyze differences between and within groups over time?

My data are 500 children learning a skill. About half of the children are male, and about half are female. These children are in one of 20 classrooms, each classroom has a different teacher. 12 of these 20 classrooms are at a private, the other 8 at a public institution. About half of these classrooms are for children who are 3 years old, the other half for children who are 5. The time spent on learning this skill varies by classroom and semester. E.g. Classroom1 spent a total of 100 hours on this in the first semester and 80 in the second semester, Classroom2 50 in the first and second semester.

The knowledge of the skill was evaluated at three times, at the beginning of the course (test0), after one semester (test1), and after another semester (test2), using the same test on which the students can get 0-300 points. Histograms of each of the three tests show that the scores do not follow a normal distribution. From 150 participants, I only have data from test0, not from test1 and test2. Should I still include them in the study?

For some children, I only have data from the first test.

I am interested in the following questions:

Are there differences between the 20 classrooms’ knowledge of the skill at test0? Are there differences between the 20 classrooms’ knowledge of the skill at test1? Are there differences between the 20 classrooms’ knowledge of the skill at test2? Are there differences between how much the 20 classrooms’ have improved the skill in the first semester (test1-test0)? Are there differences between how much the 20 classrooms’ have improved the skill in the second semester (test2-test1)? Are there differences between how much the 20 classrooms’ have improved the skill over the course of a year (test2-test0)?

7.-30. - replace classroom with: private vs. public institution gender hours spent on instruction age

Would a multiple regression be the best way to go, as I can add all of my independent variables at the same time?

I can only get this far: lm(Skill_test0 ~ ClassroomName + PublicPrivate + Gender + Age, data=mydata) lm(Skill_test1 ~ ClassroomName + PublicPrivate + Gender + Hours_1sem + Age, data=mydata) lm(Skill_test2 ~ ClassroomName + PublicPrivate + Gender + Hours_1sem-2sem + Age, data=mydata) lm(Skill_test1_test0 ~ ClassroomName + PublicPrivate + Gender + Hours_1sem + Age, data=mydata) lm(Skill_test2_test1 ~ ClassroomName + PublicPrivate + Gender + Hours_1sem-2sem + Age, data=mydata) lm(Skill_test2_test0 ~ ClassroomName + PublicPrivate + Gender + Hours_1sem-2sem + Age, data=mydata)

Will this allow me to answer what the effects of classroom, school type, age, and hours are on learning this skill over the course of two semesters?

I already know that there is a highly significant difference between 3- and 5-year-olds in all three tests, so I don’t think it makes sense to compare classrooms across different age groups with each other, so I’m looking for a solution that accounts for this.

Any help is much appreciated.