Statistics Tip: Alpha and p are Cumulative Probabilities; z and z-critical are point values.

Alpha, p, Critical Value, and Test Statistic are 4 concepts which work together in many statistical tests. In this tip, we'll touch on part of the story. The pictures below show two graphs which are close-ups of the right tail of a Normal Distribution. The graphs show the result of calculations in 2 different tests.

The horizontal axis shows values of the Test Statistic, z. So, z is a point value on this horizontal z-axis. z = 0 is to the left of these close-ups of the right tail. The value of z is calculated from the Sample data. 

• Note that the calculated z defines the boundary of a hatched area. The  hatched areas under the curve represent the value of the Cumulative Probability, p.
• And z-critical (the Critical Value of z) defines the boundary of the shaded area representing α.

 
For more on how these four concepts work together, there is an article in the book, "Alpha, p, Critical Value and Test Statistic -- How They Work Together". I think this is the best article in the book. You can also see that article's content on my YouTube video. There are also individual articles and videos on each of the 4 concepts. My YouTube Channel is "Statistics from A to Z -- Confusing Concepts Clarified".