Statistics Tip of the Week: How the selection of a value for Alpha specifies the Critical Value

In Hypothesis Testing, before the data is collected, a value for Alpha, the Level of Significance,  is selected. The person performing the test selects the value. Most commonly, 5% is selected. 

Alpha is a Cumulative Probability -- the Probability of a range of values. It is shown as a shaded area under the curve of the Distribution of a Test Statistic, such as z.

If we have Distribution of a Test Statistic and a Cumulative Probability at one or both tails of the curve of the Distribution, software or tables will tell us the value of the Test Statistic which forms the boundary of the Cumulative Probability.

In this concept flow diagram, we show how selecting Alpha = 5% for a one-tailed (right tailed) test results in the Critical Value being 1.645.