section_path: Methods/Inferential statistics/Terminology and theory of inferential statistics/Null hypothesis and alternative hypothesis
section_name: Null hypothesis and alternative hypothesis
paragraph_text: Null hypothesis and alternative hypothesis
  
  Interpretation of statistical information can often involve the development of a null hypothesis which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.
  
  The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H, asserts that the defendant is innocent, whereas the alternative hypothesis, H, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H (status quo) stands in opposition to H and is maintained unless H is supported by evidence "beyond a reasonable doubt". However, "failure to reject H " in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily accept H but fails to reject H. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test, which tests for type II errors.
  
  What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis.