You may have heard of a recent study claiming that eating a low fat diet does nothing to prevent heart disease and cancer.
Well, that's not exactly what the study claimed. The researchers said that the effects on cancer and heart disease of eating a low fat diet are not statistically significant.
The media tends to interpret the phrase "statistically insignificant" as meaning non-existent, but that's wrong. The low fat diet study claimed that women that eat a certain low percentage of fat develop breast cancer nearly 10% less often than women who eat more fat. The study's authors called this result statistically insignificant because it didn't meet their statistical standards. However, this doesn't mean that eating a low fat diet does nothing to prevent disease. All the results mean is that the benefits of eating less fat weren't demonstrated beyond a reasonable doubt.
In other words, failing to prove something true doesn't mean that it's necessarily false.
Look at it this way. If it holds in the entire population that 10% of women on a low fat diet decrease their chances of getting breast cancer, that means something. It means that nearly one million women might avoid cancer.