Question

The notion of Type I and Type II Errors is very important in hypothesis testing. The Ho/Ha should be set up such that a Type I Error is more serious than a Type II Error. A common example used to discuss Type I and Type II errors is the example of a trial in the US. Under US law, a defendant is considered "innocent until proven guilty." You could set up this hypothesis test as follows:

                                          Ho: defendent is innocent

                                          Ha: defendent is guilty

If there is enough "evidence" the jury will reject the Ho. Note that here, using the "stickler" language a defendant is never "proven innocent" in a trial but only failed to be found "guilty." The errors then are defined:

                            Type I: (Reject Ho|Ho is true) or in this example, find an innocent person to be guilty.

                            Type II: (Fail to reject Ho|Ha is true) or in this example, fail to find a guilty person guilty.

Note that the set-up "innocent until proven guilty" creates a null/alternative for which a Type I Error is considered more serious than a Type II error. In our system, sending an innocent person to jail is considered worse than letting a guilty person go free. Note that this embodies assumptions about what is more serious. I have heard (but not rigorously researched) that in the Chinese and Russian justice systems a defendant is assumed guilty and must prove his/her innocence. That would mean the Ho/Ha would be reversed from what we have in the US and also means that, if true, those countries view it to be a more serious error to let a guilty person go free than an innocent person go to jail.

In your response to this post, please think of an example of a hypothesis test, set up the Ho/Ha and discuss why your set-up demonstrates that a Type I Error is more serious. (In most cases you should be able to use your example from the Discussion Board for Unit #1).   

Answer 1

Let us consider a case of credit card fraud, where a company wants to determine if the potential customer for the credit is a fraud or not based on there previous records of credit and demographics.

On similar lines to the given example:

Ho: person is fraud

Ha: person is not fraud

Type I: (Reject Ho|Ho is true) or in this example, find an fraud person to be not fraud.

Type II: (Fail to reject Ho|Ha is true) or in this example, fail to find a non fraud person as not fraud.

Type I Error is considered more serious than a Type II error. Here, giving loan an fraud person is considered worse than not giving loan to a non fraud person. Since, giving loan to a fraud will result in loss the whole loan amount, where as not giving loan to non fraud will only result in loss of potential interest earned in monetary terms.