Type 2 errors
There is the possibility of a type of error, known as a type 2 error. Such possibilities have a probability of occurrence. They arise when it is reasonable to expect a difference and you find that the sampling has resulted in no difference being found.
Think about a drug trial, and in this instance think about the possibility that people taking the new drug will each react differently to the drug. Not everybody will respond in exactly the same way to the drug. Some will show a big improvement and for some it will be very minor, if any, improvement. So there is a probability that the trial group is unrepresentative if the sample that forms this group includes folk who do not respond to the new drug. In the end, the type 2 error means we find no difference when one should be found.
The probability of such an event can be determined. Researchers usually set the probability in this case at 0.2. That is, a one in five chance of a type 2 error.