Peter T. Saunders of the Mathematics Department of King's College, in London, published an article titled "Use and Abuse of the Precautionary Principle" that deals with a highly specific and unique problem when it comes to the use of statistical information. Many statistical abuses occur when conclusions not fully supported by statistics are asserted, or when differences that are not statistically significant are made to appear greater than they really are. According to Saunders, there are certain situations where it is actually good to use statistics in this way -- specifically, in cases where there is a potential for harm if a correlation exists. That is, things like cigarettes and possible carcinogens should be assumed to be unsafe as soon as any evidence suggests that they might be, unless there is a compelling reason that a potentially harmful substance should be used. Saunders advocates and over-reaction to statistical data in such cases as a means of offering the greatest protection. This is called the "precautionary principle," and it is common sense according to Saunders' explanation. In situations where the precautionary principle applies, any observed change on a population should be taken as a sign that the substance/action/etc. is correlated with that change until it can be positively demonstrated that this is not the case.

After explaining the precautionary principle in great deal and making the foundational logic and ethicality behind this principle quite clear, Saunders turns to how statistics can be abused when this principle is discarded. Despite some evidence that genetically modified crops might be harmful to people and the environment -- something Saunders thinks falls under the umbrella of the precautionary principle -- companies and some governments are claiming that they have "proven the crops are safe" when in fact all they have done is failed to prove that it is unsafe. A study that doesn't show a statistically significant correlation between genetically modified foods and specific harms to people/the environment is not proof the genetically modified foods are safe, that is, it simply doesn't show them to be unsafe. While failing to show a statistically significant correlation is sufficient grounds to assume there is no correlation in some statistical applications (assuming the study was carried out properly, of course), in cases where there is potential harm and the precautionary principle applies, the exact opposite should be the case -- the correlation should be assumed to exist until it can be positively shown not to. Saunders example of a coin is the simplest way to understand this: if you're worried that a coin might be biased towards heads and you flip it three times in a row and get a heads each time, you haven't proven that the coin is biased as the p-value is still 0.125, but you certainly haven't proven that the coin is unbiased just because the p-value is well within the realm of possibility.

Article: http://www.ratical.com/co-globalize/MaeWanHo/PrecautionP.html