Presentation on Type I and Type II Errors How can someone be arrested if they really are presumed innocent? Why do some individuals who really are guilty go free? The answer to these questions can be understood in the context of hypothesis testing, which shares four common elements with the justice system.

First Commonality: the Alternative Hypothesis The alternative hypothesis - This is the reason a criminal is arrested. Obviously the police don't think the arrested person is innocent or they wouldn't arrest him. In statistics the alternative hypothesis is the hypothesis the researchers wish to evaluate.

Second Commonality: the Null Hypothesis The null hypothesis - In the criminal justice system a person is presumed innocent. In both the judicial system and statistics the null hypothesis states that the suspect or treatment didn't do anything, i.e., nothing out of the ordinary happened. The null is the logical opposite of the alternative hypothesis.

Third Commonality A standard of judgment - In the justice system and in statistics there are no absolute proofs. A standard has to be set for rejecting the null hypothesis. – In the justice system the standard is "reasonable doubt". Reject the null hypothesis when there is reasonable doubt. – In statistics the standard is the probability that the effect is due to random. This standard is often set at 5% which is called the alpha level.

Fourth Commonality: Sample Data This is the information evaluated in order to reach a conclusion. In a statistical analysis the data are usually numerical. In the justice system, the data can occur in a wide diversity of forms – eye-witness, fiber analysis, fingerprints, DNA analysis, etc. Both statistical analysis and the justice system operate partial information (i.e., the samples of data) – Getting the whole truth and nothing but the truth is not possible in the real world.

Criteria for Rejecting Null It only takes one good piece of evidence to reject a null, but an endless amount to prove it correct. If the null is rejected then logically the alternative hypothesis is accepted. – This is why both the justice system and statistics concentrate on disproving or rejecting the null hypothesis rather than proving the alternative.

Type I and Type II Errors Type I errors: Neither the legal system or statistical testing are perfect. A jury sometimes makes an error and an innocent person goes to jail. Statisticians sometimes reject the null hypothesis when it is actually TRUE. Type II errors: Sometimes, guilty people are set free. Statisticians sometimes fail to reject a null hypothesis when it really is false.

Type I and Type II Error Truth Table Null hypothesis (H 0 ) is true Null hypothesis (H 0 ) is false Reject null hypothesis Type I error False positive Correct outcome True positive Fail to reject null hypothesis Correct outcome True negative Type II error False negative