Question

3.1

Probabilities are a “likelihood” that something is going to happen. It is not a certainty. How does this type of statistic help us when conducting research in criminal justice? How does it hurt the process? Find an example online to back your response.

Answer 1

Null Hypothesis	Type I Error / False Positive	Type II Error / False Negative
Person is not guilty of the crime	Person is judged as guilty when the person actually did notcommit the crime (convicting an innocent person)	Person is judged not guilty when they actually did commit the crime (letting a guilty person go free)
Cost Assessment	Social costs of sending an innocent person to prison and denying them their personal freedoms (which in our society, is considered an almost unbearable cost)	Risks of letting a guilty criminal roam the streets and committing future crimes

1. 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.
2. The null hypothesis - In the criminal justice system this is the presumption of innocence. In both the judicial system and statistics the null hypothesis indicates that the suspect or treatment didn't do anything. The null is the logical opposite of the the alternative. For example "not white" is the logical opposite of white. Colors such as red, blue and green as well as black all qualify as "not white".
3. A standard of judgment - In the justice system and statistics there is no possibility of absolute proof and so a standard has to be set for rejecting the null hypothesis. In the justice system the standard is "a reasonable doubt". The null hypothesis has to be rejected beyond a reasonable doubt. In statistics the standard is the maximum acceptable probability that the effect is due to random variability in the data rather than the cause being investigated. This standard is often set at 5% which is called the alpha level.

It only takes one good piece of evidence to send a hypothesis down in flames but an endless amount to prove it. 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. It's much easier to do. If a jury rejects the presumption of innocence, the defendant is pronounced guilty.

Unfortunately, neither the legal system or statistical testing are perfect. A jury sometimes makes an error and an innocent person goes to jail. Statisticians, being highly imaginative, call this a type I error. Civilians call it a travesty.

In the justice system, failure to reject the presumption of innocence gives the defendant a not guilty verdict. This means only that the standard for rejecting innocence was not met. It does not mean the person really is innocent. It would take an endless amount of evidence to actually prove the null hypothesis of innocence.

Sometimes, guilty people are set free. Statisticians have given this error the highly imaginative name, type II error.

Americans find type II errors disturbing but not as horrifying as type I errors. A type I error means that not only has an innocent person been sent to jail but the truly guilty person has also gone free. In a sense, a type I error is twice as bad as a type II error. Needless to say, the American justice system puts a lot of emphasis on avoiding type I errors. This emphasis on avoiding type I errors, however, is not true in all cases where hypothesis testing is done.