I once organized a workshop on reasoning about uncertainty and in it a woman attended who was in charge of cycling safety for a large government organization of some EU country. She confirmed that, statistically speaking, cycling without a helmet is safer than with but mentioned this as a good example of likely confounding factors and a case where you cannot take the statistics itself for policy making.
But besides that, even if the average nation-wide number of accidents can be taken as a basis for nation-wide policy making because confounders can be ignored (a huge assumption), you can still not use this data reliably for individual decision making or policy making for smaller groups without further analysis. You need to account the variance, where the confounders occur, and what these confounding factors are. For example, regarding individual decision making, it could be the case that certain people who cycle with helmets on the average cycle more recklessly, but you cycle even more carefully with a helmet and are better protected. If so, you cannot take the average to inform your cycling. The same holds for other groups, such as professional cyclists for a company like in this article.
To give another example, consider accident statistics of self-driving cars versus human drivers nationwide. The human driver statistics include each and every reckless and drunk driver in the country, including many people with whom you'd never share a car ride. At the same time, you might have been driving accident-free for more than 40 years. For you personally, or a specific group you belong to, self-driving cars could thus be way more dangerous than driving yourself.
But besides that, even if the average nation-wide number of accidents can be taken as a basis for nation-wide policy making because confounders can be ignored (a huge assumption), you can still not use this data reliably for individual decision making or policy making for smaller groups without further analysis. You need to account the variance, where the confounders occur, and what these confounding factors are. For example, regarding individual decision making, it could be the case that certain people who cycle with helmets on the average cycle more recklessly, but you cycle even more carefully with a helmet and are better protected. If so, you cannot take the average to inform your cycling. The same holds for other groups, such as professional cyclists for a company like in this article.
To give another example, consider accident statistics of self-driving cars versus human drivers nationwide. The human driver statistics include each and every reckless and drunk driver in the country, including many people with whom you'd never share a car ride. At the same time, you might have been driving accident-free for more than 40 years. For you personally, or a specific group you belong to, self-driving cars could thus be way more dangerous than driving yourself.