Statistical tests are educated guesses. Based on incomplete data - that is, data from only a subset of the population - they seek to make conclusions. The incompleteness of the data guarantees that statistical tests will sometimes lead to the wrong conclusion, particularly in situations where there is little data or the differences being examined are small (i.e., to use the jargon, the tests are particularly inaccurate when power is low). Nevertheless, statistical tests are in widespread use because when they are conducted correctly they are the most educated form of guessing that is possible.
All statistical tests make a large number of assumptions. When these assumptions are not satisfied the consequence is that the conclusions from statistical testing become less reliable. The more egregious the violation of the assumptions, the less accurate the conclusions.
Click here to see the most common technical assumptions.