Statistics cannot prove causation. It can sometimes conclude an association. We depend in many ways on statistics and probability to "show us the way" to the truth. The beauty of statistics is the availability of several models or approaches to study a phenomena. It is not a source of weakness.
Here, we show gographical aras with elevated cancer risks after having removed the effects of different gender and age distributiobs across Florida. The associated probability of having reached this conclusion erroneously is provided. It helps with using common sense planning that is based on statistical evidence.
In Florida (a lawyer obce told me), if a law case is based solely on data, then the probability of an erroneous conclusion may not exceed 1/1000 (ot 1/10,000?) for the case to be
admissible.
The safety of medical drugs is based on clinical trials (statistics). The FDA makes sures that the appropriate statistical mrthods were used.