The significance of two categorical variables on students' scores

Question

I am analysing a set of students' scores on a Maths test.

My data set includes 41 students. I have the students' marks on each question of the test. I have the gender of each student. I also have whether each student studies Physics or not.

The first five rows of my data set:

I am particularly interesting in students' performance on question number 9. The question carries a maximum of ten marks.

Boys earned on average 2 marks more than girls on this question. Students who study Physics earned on average 1.9 marks more than those who don't study Physics.

20 boys study Physics and 9 girls study Physics.

I want to know whether gender had a significant effect on students' scores on question 9, or whether the difference in boys' and girls' average scores is driven by the fact that more boys study Physics.

Is there a test that I can perform?

(My sample size may be too small at the moment, but more students will be sitting the test in future, so my data set will grow.)

Answer 1

This looks like a great scenario for an OLS regression model. The score on question 9 should be a response variable, with the student's genders as one dichotomous predictor and whether or not they study physics as the other.

By including both the 'gender' and the 'physics' predictors you can control for the possible effect of students studying physics on their question 9 score (the 'physics' predictor could be acting as a confounder, which you seem to have already recognized).

If you end up with an estimated effect for the 'gender' predictor that is non-zero, and it is paired with a p-value to your liking, then you've uncovered some evidence that gender does in fact affect the student's score on question 9.