This is perhaps a basic question: I have high school drop out data over a number of years. There is a significant increase in the percentage of students that dropped out from 2015 to 2016. I want to be able to explain the increase: was it girls, was it boys, was it school A, school B, etc. I could calculate the percentage change for each variable, but is there some other way to analyze this?
It depends on the data you have available
If you have micro data, i.e. records of individuals, you might want to look into multiple logistic regression, i.e. modelling the probability of dropping out based on various explanatory variables, e.g. gender. It will also allow you to assess if the effect has changed over time.
If you have aggregated data, i.e. tabular data, you might want to look into chi-sqaure test, e.g. to see if there is any differences between drop outs based on gender.