Context and data
I am studying suicides among the military. I created a table that aggregates certain metrics (number of holidays, number of hours worked, etc...) for each officer, for each month preceding the suicide (up to 6 months). If the officer didn't commit suicide, I use the date of the suicide that took place in his company, so I can compare similar period of items. For companies that didn't suffer any suicide, I use an arbitrary reference date : July 1st 2018.
I created columns that contains the average of each numerical feature for the given period, both in the company where suicides took place, and both in the general population. That way I can detect cases where an officer worked a lot of hours while his colleagues were doing way less, or officers that were doing extra hours in a company where everyone was very busy, and the atmosphere may have been tensed.
So the question is , what test is more insightful for the task at hand :
a t-test to compare, for example, the average sick leaves amount of two independent populations : those who committed suicides, and those who didn't. The test could be on the average 6 months before the event, or 6 different test for each period.
a paired t-test on the population who committed suicide, where I would compare the difference between average sick leaves the month during the event, and 6 months before.
At the end of day, my objective is double :
- Identify risk factors for suicides
- Flag officers at greater risk of suicides.
My idea was to use t-test to detect which feature are significantly different from average population, and paired t-test to detect when the drift start to occur. Or put an other way, when could we be able to fire alarms.
Note : I think it doesn't matter for t-test but my 2 populations have big size difference. One is around 90 000 and the other around 100.
Because the population is very imbalanced, I am thinking I could obtain the same information as t-test by using the SMOTE algorithm to boost my minority class and then use a random-forest to study feature importance.
Am I making any sense ?