Quant #15: Type I Error and Type II Error

The starting assumption in hypothesis testing is that there is no difference between groups or relationship among variables (null hypothesis).  The alternative hypothesis assumes the opposite: there is a difference between groups or a relationship among variables. Rejecting the null hypothesis confers credence to the alternative hypothesis, thus implying that there is indeed a difference or a relationship. Comparatively, failing to reject the null hypothesis lends support to the null hypothesis, thus suggesting that there is indeed no difference or relationship.

Since the decision to reject or fail to reject the null hypothesis involves a certain degree of uncertainty, it is not impossible for errors to arise; that is, it is possible to draw wrong conclusions. For example, a Type I error or a false positive arises when the null hypothesis is rejected when it should not have been rejected. This error happens when we detect a relationship that is not there. Correspondingly, we may fail to reject the null hypothesis while we should have rejected it. This error – called Type II error – indicates that we missed a relationship that, in reality, exists. Type II error is also known as a false negative.