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Table of Contents Statistical Tests Hypotheses Types of Errors | |
See also: hypothesis testing, power of a test |
In general, there are two different types of error that can occur when making a decision: the first kind ("type 1 errors") are those errors which occur when we reject the null hypothesis although the null hypothesis is true. The second kind ("type 2 errors") of errors arise when we accept the null hypothesis although the alternative hypothesis is true.
You formulate your hypotheses:
H_{0}: | iron concentration is less or equal to the specified limit |
H_{1}: | concencration is higher the limit |
Due to the uncertainties involved in the process of determining the iron content, there is a risk that your decision is wrong. When you decide to buy a particular batch of the ore, and it turns out that the specifications are not met, you have made a type I error (i.e. rejecting H_{0} when it is true). There is also the possibility that we accept H_{0}, although it is in fact wrong: we don't buy although the specification is met. That is called type 2 error.
Since our decision can be false or true, and the null hypothesis can also be false or true, there are four possible outcomes of a test. The probabilities for a type 1 error and type 2 error are usually denoted by a and b, respectively.
In the case given above a type II error does not harm us, except one of the rejected bidders offers a much lower price. But we are concerned about making a type I error, it would mean we would buy the ore without getting the required content of iron. A more elaborate description about type I and type II errors can be found in the following interacte example:
NOTES
Last Update: 2006-Jän-17