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.
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.
Probably not high school statistics accessible but Bayesian statistics and Gaussian noise and GR isn't.