Errors In Hypothesis Tests

A hypothesis test generally begins by assuming that the null hypothesis is true.

If, in reality, such a null hypothesis is true, rejecting it may lead to an incorrect and misleading conclusion.

This mistake of rejecting the true null hypothesis is known as the Type-I error.

On the other hand, when the null hypothesis is false, but the test result indicates failure of its rejection, the decision again remains erroneous.

This mistake of failing to reject the false null hypothesis is known as the Type-II error.

A test result that indicates rejecting the null hypothesis when it is actually false, or failing to reject it when it is actually true, leads to a correct decision.

The acceptable probability value of Type-I error is the significance level ɑ, which is commonly 0.05 or 0.01.

The probability of Type-II error is denoted by β. It is calculated from the pre-determined probability of rejecting a false null hypothesis, commonly known as the power of the hypothesis test.