The most important questions in life usually cannot be answered with absolute ce

Question

The most important questions in life usually cannot be answered with absolute certainty. Many important questions are answered by giving an estimate and a measure of confidence in the estimate. However, sometimes important questions must be answered in a more straightforward manner by a simple yes or no. Hypothesis testing is the statistical process of answering questions with a straightforward yes or no and providing an estimate of the risk in accepting the answer.

Review and discuss type I and type II errors associated with hypothesis testing. We indicated this week that selecting a level of significance which leads to an increase in Type I errors means a decrease in Type II errors...and vice versa.

Discuss which type of errors concern you more: Type I or Type II. Might there be situations in which it might be better to minimize Type II errors at the expense of having more Type I errors?

Explanation / Answer

Based on the common situations, generally statisticians prefer to minimized the type-I error,considering it to be more serious. Basically, type-I error means reject the null hypotheses when it is true. This might cause some serious problems. Like in legal matter someone is accused of a theft, say. If in a verdict he/she is proven guilty, but in reality the person did not commit theft, then it bear great consequences on the efficiency of the judicial system, and the convict suffers the most. Thus type-I error seems to be more serious. This is in genral true for most of the scenarios. The null hypothesis maintains a non prefertial attitude towards the problem in hand. Incorrectly rejecting it, results in accepting significantly high amount of preference/bias/difference , which lead us to erroneous conclusions.

However, there are scenarios where type-II errors are more serious. Medical scenarios are prominent example. If a patient is going through a terminal disease say cancer of aids. If the diagnosis commits a type-I error,this means the patient is diagnosed with the disease falsely,but due to suspicion more diagnosis will be made and ultimately it will be detected that there is no disease. But a type-II error will be more serious as it will assure both the patient and doctors that that there is no disease when there actually is. As a result the patient will go untreated costing his/her life. Clearly here minimizing type-II will be better

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