# Statistical significance test for student performance variation among classes

I'm trying to find out if differences in the variation of student performance among different class sections (i.e., students enroll in the same class but have different sections) are statistically significant.

I got the values by grouping each student into their class section, then calculating the standard deviation for each of those sections. Now that I have a list of standard deviations for each sections (around 900) what test should I use to see if the difference among them are statistically significant?

Clarification: I use the term class and section in the context of education. Each student can only be enrolled in one section of the class (e.g., Math 101 section 01).

• Your previous question, Paul, and the way you phrase this one, make me wonder what you might mean by "class." Does it refer to a class taken at school, or is it perhaps a classification into which you have placed the student based on a previous analysis of their performance? Or maybe something else? – whuber Dec 4 '14 at 15:40
• @whuber I meant class taken in school. I couldn't think of a better term to use to make it less confusing – Paul Dec 4 '14 at 15:42
• Do you have the original data (for each student) or only the class standard deviations? Do you also have class means? Could you show us a plot, or share (a link to) the data? – kjetil b halvorsen Mar 8 at 7:13
• @kjetilbhalvorsen yes i have the original data and can also compute means from there. – Paul Mar 8 at 20:09
• This could still need some clarification. You have original data: Can the same student participate in multiple classes? Please clarify editing the Q. If same student in multiple classes, a mixed model, that is, if you want to compare means. Else clarify! – kjetil b halvorsen Mar 22 at 15:25

## 1 Answer

ANOVA (ANalysis Of VAriance) seems where to start. But with around 900 sections of a class (have I understood that right?) there must be some more structure to the problem, like the teacher (or TA) in more than one section. If so maybe random effects for instructor ... maybe there are other covariables?

I would also complement that with visualization, and check homoskedasticity.