Because hypothesis tests are heavily dependent on the samples used as "evidence," it is definitely possible, in the case of a bad sample, to make an error in the conclusion of a test.
When a hypothesis is tested, there are four possible outcomes:
A Type II error is only an error in the sense that an opportunity to reject the null hypothesis correctly was lost. It is not an error in the sense that an incorrect conclusion was drawn, since no conclusion is drawn when the null hypothesis is not rejected. It has nothing to do with α, other than the fact that it moves in the opposite direction from α (that is, the bigger the one, the smaller the other).
A Type I error, on the other hand, is an error in every sense of the word. A conclusion is drawn that the null hypothesis is false when, in fact, it is true. Therefore, Type I errors are generally considered more serious than Type II errors. The probability of a Type I error (α) is called the significance level; it is set by the experimenter. For example, a 5% level of significance means that there is a 5% probability of rejecting the null hypothesis when it is true.
There is a tradeoff between Type I and Type II errors. The more an experimenter protects him or herself against Type I errors by choosing a low level, the greater the chance of a Type II error. Requiring very strong evidence to reject the null hypothesis makes it very unlikely that a true null hypothesis will be rejected. However, it increases the chance that a false null hypothesis will not be rejected, thus lowering its power. The Type I error rate is almost always set at 0.05 or at 0.01, the latter being more conservative (since it requires stronger evidence to reject the null hypothesis at the 0.01 level then at the 0.05 level).
To reduce the probabilities of both types of errors simultaneously, the sample size n must be increased.
| laurenduvall: Type 1 is to reject a 1- true null|
Type 2 is to accept a ii- false null
| Sumit14: Type 1 error - Reject H0 when it was actually TRUE|
Type 2 error - DO NOT Reject H0 when it was actually FALSE
Correct Results -
Reject H0 when it was actually FALSE
DO NOT Reject H0 when it was actually TRUE
|hiyujie: I think the type 2 error is more serious. For example, the prosecutor accuses a person committing a crime when he doesn't. If the court fails to reject the decision made by the prosecutor, and that person goes to jail for 20 years. That's more serious result compared with declaring that person innocent when he is actually not.|
|JHangLi: When you fail to reject, it is not exactly the same as accepting. You just forgone an opportunity to reject a false null like the text says. But if you reject a null that is true, it is a more serious error.|