Editing Statistical hypothesis test (section)

===Courtroom trial===
A statistical test procedure is comparable to a criminal [[trial (law)|trial]]; a defendant is considered not guilty as long as his or her guilt is not proven. The prosecutor tries to prove the guilt of the defendant. Only when there is enough evidence for the prosecution is the defendant convicted.

In the start of the procedure, there are two hypotheses <math>H_0</math>: "the defendant is not guilty", and <math>H_1</math>: "the defendant is guilty". The first one, <math>H_0</math>, is called the ''[[null hypothesis]]''. The second one, <math>H_1</math>, is called the ''alternative hypothesis''. It is the alternative hypothesis that one hopes to support.

The hypothesis of innocence is rejected only when an error is very unlikely, because one does not want to convict an innocent defendant. Such an error is called ''[[error of the first kind]]'' (i.e., the conviction of an innocent person), and the occurrence of this error is controlled to be rare. As a consequence of this asymmetric behaviour, an ''[[error of the second kind]]'' (acquitting a person who committed the crime), is more common.

{|class="wikitable"
|
! H<sub>0</sub> is true <br /> Truly not guilty
! H<sub>1</sub> is true <br /> Truly guilty
|- align="center"
! Do not reject the null hypothesis <br /> Acquittal
| {{success|Right decision}}
| {{failure|Wrong decision}} <br /> Type II Error
|- align="center"
! Reject null hypothesis <br /> Conviction
| {{failure|Wrong decision}} <br /> Type I Error
| {{success|Right decision}}
|}

A criminal trial can be regarded as either or both of two decision processes: guilty vs not guilty or evidence vs a threshold ("beyond a reasonable doubt"). In one view, the defendant is judged; in the other view the performance of the prosecution (which bears the burden of proof) is judged. A hypothesis test can be regarded as either a judgment of a hypothesis or as a judgment of evidence.