One technique that is straightforward to understand is that folks have done "time-slide" analyses for many years - i.e. offsetting one detector's data in time - to understand what the "baseline" rate of correlations is in data streams where there is no possible physical origin.

Naturally, much more statistical analysis has been done to ground the claims of "detection"; beyond detailed academic publications, LIGO and others have been producing layperson-accessible science summaries for years/decades that address these and other questions.