They can't. You should know that.

It is precisely the MISuse of statistics that leads to so much misinformation and outright lies in too many research interpretations. Particularly guilty are commercial firms (expected) and governments (deplorable, even if expected). Statistics may provide some additional guidance or suggestions about whether one should risk very much on the validity of some data, but they never provide "proofs" of any certainties. The whole point of REAL Science is that we should always be questioning everything!

"Statistics" is simply how we interpret data results that we received. True there are people who falsify data, or more likely (a question I often received) "Can't you make that chart look any better" (my answer was no).

We can infer social and cultural results. A company I worked for used "Behavior Based Safety" to collect observations of conditions and people doing work to see what risks we had. I've run many employee surveys that gave the leadership team insight into culture. For example, we found the question "Senior management (above my manager) vists my workplace" with options of Strongly Agree, Agree, Neutral, Disagree, and Strongly Disagree to be a bell-weather question. If that question was trending to the negative, we knew to start asking questions. True, some Vice Presidents said "But I always visit the workplace" - but if the workers' perception was that they were no - then that was important.

There is an interesting book out there "How to measure anything".

As a counter, I often in class would ask - "I love my spouse more than you love your spouse / significant other - Now prove or disprove that with data". Of course that is a silly question - but does bring up a good discussion.

Because nothing is certain, nothing can tell you with certainty what will happen. Statistics can tell you what you can reliably expect to happen, and even give you an estimate of how likely it is to be wrong.

Statistics are used to make most of our everyday life work better and on the whole properly. Statistics are used to make sure the parts of your car fit together properly. They are used to design your phone so that it usually picks up a signal, and to make the battery last long enough, and to determine the bandwidth and signal strength you need for your home connection. They are used to get roughly the right amount of the right food in your supermarket. Statistics are used in the same way in scientific confirmation, and do a good job. Learn how to use them and understand them, and they are a powerful and reliable tool. They can give a wrong answer. If I throw a die 100 times and get 6 every time, statistics tells me the odds are about 6-100 that I have a fair die, so I almost certainly have a biased die. However, it is always possible I have a fair one, however I wouldn't want to risk much time or effort on anything that relied on it being fair. Scientific results are judged the same way.

Same as ever, by Morgan Housel (2023). I highly recommend this book, it explains the futility and fallacies of such attempts to predict likelihood. I listened to it on Audible.

Another great book for beginners is Fundamental Statistics for the Social and Behavioral Sciences by Howard T. Tokunaga.