My goal is to see if one student group has a disproportionate number of discipline incidents relative to the another group/s, to what degree, and with what margin of error. I will be speaking mostly in lay terms, and my intended audience is a lay audience.
I am going to simplify the problem as such: I have two groups (not samples, complete populations) of students, M and F, for a given school.
There are 500 M students and 200 F students.
Of the M students, there are 100 with >= 1 discipline incident. Of the F students, there are 20 with >= 1 discipline incident.
So: 500/700 (~71.4%) of students are M students and 200/700 (~28.6%) of students are M students
And: 100/120 (83.333%) of total students having >=1 incident are M students, while 20/120 (16.666%) of total students having >=1 incident are F students
Are the following calculations then valid?
Ratio of M students with >=1 incident per 100 students = 83.333% / 71.4% * 100 = ~117
Ratio of F students with >=1 incident per 100 students = 16.666% / 28.6% * 100 = ~58
If this is valid, with what margin of error, given the total students in each group and the number of students with incidents in each group, can I say that this accurately represents the proportionality of incidents between these groups?