Analyzing whether a relationship changes after an event

[besa2]

I apologize in advance if this is worded poorly.

Let's say I have a strong correlation between two variables like political interest and voting participation.

After an unexpected event (disaster), the observable participation rate skyrockets.

How can I analyze whether or not the event itself had an effect on voting participation (and/or political interest)?

Furthermore, how can I analyze whether this is a unique event or part of a cycle? All of the information I'm finding about time series analysis is for forecasting.

 

[hlsmith]

It will be hard to figure out unless the exposure is randomized. One thing you could do is find another population not exposed to show they did not have the same jump (interrupted time series with control group).

 

[besa2]

Regrettably according to the literature, it was such a major event it had repercussions both politically, but also for civil society. Because this affected the entire country to some degree, I don't think I can find any sampling data to use as a control.

What I was thinking of is doing a forecast using pre-event variables, for the post-event period. Then using those results to compare to the actual post-event data, but I don't know if that would be at all meaningful.

Ultimately what I want to look at is whether that relationship between my two variables changed significantly following the event.

 

[noetsi]

You can try something like interrupted time series with controls.

Find an area where the intervention did occur and one where it did not occur. Plot the correlation before and after the intervention where it did occur. Plot the correlation at the same time frame in the area where it did not occur. See how the correlation differs in both areas after the intervention. The change or lack of change in the intervention will clue you in to this.

Note this is not formal proof. It is not a statistical test per se. You are just using judgement.