Statistics Tip: the Alpha and Beta Error Seesaw

There are a number of see-saws (aka "teeter-totters" or "totterboards") like this in statistics. Here, we see that, as the Probability of an Alpha Error goes down, the Probability of a Beta Error goes up. Likewise, as the Probability of an Alpha Error goes up, the Probability of a Beta Error goes down.

​This being statistics, it would not be confusing enough if there were just one name for a concept.  So, you may know Alpha and Beta Errors by different names:

• Alpha Error: false positive, type I error, error of the first kind
• Beta Error: false negative, type II error, error of the second kind

The following compare-and-contrast table should help explain the difference:

The see-saw effect is important when we are selecting a value for Alpha (α) as part of a Hypothesis test. Most commonly, α = 0.05 is selected. This gives us a 1 – 0.05 = 0.95  (95%) Probability of avoiding an Alpha Error.

Since the person performing the test is the one who gets to select the value for Alpha, why don't we always select α = 0.000001 or something like that?
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The answer is, selecting a low value for Alpha comes at price. Reducing the risk of an Alpha Error increases the risk of a Beta Error, and vice versa.

There is an article in the book devoted to further comparing and contrasting these two types of errors. Some time in the future, I hope to get around to adding a video on the subject. (Currently working on a playlist of videos about Regression.) See the  videos page of this website for the latest status of videos completed and planned.