I've recently conducted a survey of students in a class who had recently taken a difficult examination. Part of the output data is like so:
- x_Jan=Hours spent studying weekly in Jan [0 ... n hrs/wk]
- x_Feb=Hours spent studying weekly in Feb [0 ... n hrs/wk]
- (and so on to x_Dec)
- y=Exam score
How can I analyze this data to know what amount of time spent studying weekly per month is best correlated with examination outcomes? For the sake of simplicity, I think the question & answer can be simplified to a single month (x), and the solution to multiple months can be easily extrapolated.
On the surface, one might guess those who spend the most time studying perform the best, but, looking at the data qualitatively, it is evident that it isn't quite the case--for example, perhaps some students spend too much time studying too early, or too much time studying too late. I hope to use the data to help students prepare an effective study plan and schedule.
I considered doing linear regression comparing 0 hours to each of X hours vs test score, but sample size quickly becomes a limiting factor. I'd have to bin the data fairly wide to get any significance. (i.e. 0 to 20, 21 to 40, etc.).
Any suggestions? I appreciate your insight!