There are a number of seesaws (aka "teetertotters" 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:
The seesaw 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? 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.
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I just uploaded a new video. It's on Covariance, and it is the first in a playlist on Regression.
Most users of statistics are familiar with the Ftest for Variances. But there is also a ChiSquare Test for the Variance. What's the difference? The Ftest compares the Variances from 2 different Populations or Processes. It basically divides one Variance by the other and uses the appropriate F Distribution to determine whether there is a Statistically Significant difference. If you're familiar with ttests, the Ftest is analogous to the 2Sample ttest. The Ftest is a Parametric test. It requires that the data from both the 2 Samples each be roughly Normal. The following compareandcontrast table may help clarify these concepts: ChiSquare (like z, t, and F) is a Test Statistic. That is, it has an associated family of Probability Distributions.
The ChiSquare Test for the Variance compares the Variance from a Single Population or Process to a Variance that we specify. That specified Variance could be a target value, a historical value, or anything else. Since there is only 1 Sample of data from the single Population or Process, the ChiSquare test is analogous to the 1Sample ttest. In contrast to the the Ftest, the ChiSquare test is Nonparametric. It has no restrictions on the data. Videos: I have published the following relevant videos on my YouTube channel, "Statistics from A to Z"

AuthorAndrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z  Confusing Concepts Clarified, published by Wiley. Archives
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