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.
> have been producing layperson-accessible science summaries for years/decades that address these and other questions.
Citation please. Every layperson accessible summary has said "we use advanced statistics and machine learning" and I haven't found a simple high school statistics accessible explanation yet. Unlike say the higgs boson, I think for this experiment a simple statistical treatment is not an unreasonable request.
Please show me and correct me. I would love to be able to believe we have detected gravitational waves.