I am doing a project on effect of alcohol ban on women and children. My objectives are effect on violence,income etc.. I have collected the data like domestic violence before and after ban, income before and after ban etc... . How can I compare these before and after data statistically?
The best way to estimate causal impact is to conduct a controlled experiment before the intervention (the alcohol ban in your case) and perform some statistical test (such as t test) on it.
But you want to estimate the causal impact of a intervention that is already happened, standard controlled experiments no longer work. You need to apply some counter factual analysis techniques to deal with such a situation.
The idea of counter factual analysis is using statistical models to "mimic" the behavior of the control group as if the intervention didn't happen. There are two models most popular in this field. You can pick one based on your own situation:
- Model1: Difference-in-difference(DID). It's a simple yet effective model; you can find its descriptions everywhere.
- Model2: Structural time series. It's more flexible than DID. Here's a paper describing how to use Bayesian structural time series for causal impact analysis: Brodersen, Kay H., et al. "Inferring causal impact using Bayesian structural time-series models." The Annals of Applied Statistics 9.1 (2015): 247-274 They even have a R package for it.