Statistics Tip of the Week: Beta is the Probability of a Beta Error, but Alpha is not the Probability of an Alpha Error

​One of the things which make statistics confusing is the confusing language. For example, there is the triple negative of "Fail to Reject the Null Hypothesis". Then there are several instances where a single concept has multiple names.  
 
And this Tip of the Week is about what one might call an "asymmetry" in names for statistical concepts.

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• Beta, β, is the Probability of a Beta ("False Negative") Error
• So, one would think that "Alpha", α, would be the Probability of an Alpha ("False Positive") Error. Right?
• Wrong! p, the p-value, is the Probability of an Alpha Error.

 
So, what is Alpha? First of all, the person performing the a statistical test  selects the value of Alpha. Alpha is (called the "Significance Level"). It is 1 minus the Confidence Level.

Alpha is the maximum value for p (the probability of an Alpha Error) which the tester is willing to tolerate and still call the test results "Statistically Significant". 
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For more on Alpha and p you can view 2 videos on my YouTube channel.

• Alpha, the Significance Level   
• p, p-value