Alpha

Alpha is chosen and represents the level of error the researcher can tolerate. Alpha is the probability of rejecting a correct null hypotheses. It is also referred to as the rejection region.

Alpha corresponds with a critical value. It is graphically defined as a 'tail' region - that is, the diminishing area under a bell-shaped curve, that extends either left of a negative critical value, or right of a positive critical value. See an image at: rejection region.

Assuming that a hypothesis is true, then sample measurements are not expected to fall in this tail region, since it is a small area. When such a sample measurement occurs, it is unlikely, and, therefore, indicates that the hypothesis could be wrong. Researchers will reject an hypothesis if it falls into this alpha region.

However, these unlikely values do occur, even if they are less likely. When the hypothesis is rejected due to an unlikely sample measurement, when, in fact, the hypothesis is true, this is called "Type I error."

Popular alpha values are .01, .05, and .10.

If an alpha value of .10 is used, then type I error is 10% likely to occur.

The terms type I error and alpha are sometimes used synonymously, depending on context.

Critical Value

A critical value (C.V.) is a number that is used to make estimates and test hypotheses. Critical values always correspond to a probability.

This number represents the distance from itself to the center of a bell-shaped graph, either the z or t distribution. The area in this section represents the probability of the C.V.

For example, using the z distribution, the number 1.96 is 47.5% likely. When you also include -1.96, then the likelihood is doubled.

Alpha and Confidence Level are probabilities that correspond to critical values.