These questions can be understood by examining the similarity of the American justice system to hypothesis testing in statistics and the two types of errors it can produce.(This discussion assumes that Others are similar in nature such as the British system which inspired the American system) True, the trial process does not use numerical values while hypothesis testing in statistics does, but It only takes one good piece of evidence to send a hypothesis down in flames but an endless amount to prove it correct. If the null hypothesis is rejected for a batch of product, it cannot be sold to the customer. http://u2commerce.com/type-1/type-1-and-type-2-error-statistics-examples.html
Needless to say, the American justice system puts a lot of emphasis on avoiding type I errors. In a sense, a type I error in a trial is twice as bad as a type II error. In statistical hypothesis testing used for quality control in manufacturing, the type II error is considered worse than a type I. Justice System - Trial Defendant Innocent Defendant Guilty Reject Presumption of Innocence (Guilty Verdict) Type I Error Correct Fail to Reject Presumption of Innocence (Not Guilty Verdict) Correct Type II http://www.investopedia.com/terms/t/type-ii-error.asp
Both statistical analysis and the justice system operate on samples of data or in other words partial information because, let's face it, getting the whole truth and nothing but the truth Amazing Applications of Probability and Statistics by Tom Rogers, Twitter Link Local hex time: Local standard time: Type I and Type However in both cases there are standards for how the data must be collected and for what is admissible. Civilians call it a travesty.
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. The null hypothesis has to be rejected beyond a reasonable doubt. Statisticians have given this error the highly imaginative name, type II error. Type 1 Error Psychology If the null is rejected then logically the alternative hypothesis is accepted.
Americans find type II errors disturbing but not as horrifying as type I errors. Probability Of Type 1 Error In both the judicial system and statistics the null hypothesis indicates that the suspect or treatment didn't do anything. This can result in losing the customer and tarnishing the company's reputation. http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/hypothesis-tests/basics/type-i-and-type-ii-error/ 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.
As mentioned earlier, the data is usually in numerical form for statistical analysis while it may be in a wide diversity of forms--eye-witness, fiber analysis, fingerprints, DNA analysis, etc.--for the justice Type 1 Error Calculator Obviously the police don't think the arrested person is innocent or they wouldn't arrest him. Type I errors: Unfortunately, neither the legal system or statistical testing are perfect. Also please note that the American justice system is used for convenience.
In statistics the standard is the maximum acceptable probability that the effect is due to random variability in the data rather than the potential cause being investigated. http://www.investopedia.com/terms/t/type-ii-error.asp Type II errors: Sometimes, guilty people are set free. Type 2 Error Example A data sample - This is the information evaluated in order to reach a conclusion. Probability Of Type 2 Error This standard is often set at 5% which is called the alpha level.
For example "not white" is the logical opposite of white. news Here the null hypothesis indicates that the product satisfies the customer's specifications. A type I error means that not only has an innocent person been sent to jail but the truly guilty person has gone free. Rejecting a good batch by mistake--a type I error--is a very expensive error but not as expensive as failing to reject a bad batch of product--a type II error--and shipping it Type 3 Error
In the justice system, failure to reject the presumption of innocence gives the defendant a not guilty verdict. Statisticians, being highly imaginative, call this a type I error. It does not mean the person really is innocent. http://u2commerce.com/type-1/type-1and-type-2-error-in-statistics.html In the justice system the standard is "a reasonable doubt".
It would take an endless amount of evidence to actually prove the null hypothesis of innocence. Types Of Errors In Accounting This means only that the standard for rejectinginnocence was not met. In other words, nothing out of the ordinary happened The null is the logical opposite of the alternative.
The null hypothesis - In the criminal justice system this is the presumption of innocence. This emphasis on avoiding type I errors, however, is not true in all cases where statistical hypothesis testing is done. If a jury rejects the presumption of innocence, the defendant is pronounced guilty. Types Of Errors In Measurement A jury sometimes makes an error and an innocent person goes to jail.
Colors such as red, blue and green as well as black all qualify as "not white".