Hypothesis Testing is useful tool to judge the true or false.
But there are two weakness, "type I error" and "type II error".
Edge area of distribution is the low probability area. Hypothesis Testing thinks if the data is in the area, the data might not be the sample of the distribuion.
Type I error is that we judge the data is not sample of the group evenif the data is a sample of the group.
For example, average of group 1 is 70 points. And group 2 is 80 points.
A - group 1 - 78 points
B - group 2 - 73 points
If judge rule is
"Less than 79 is group 1. More than 79 is group 2"
, judge for A is right. But judge for B is wrong. This is one of the type II error.
We need to check type II error when there are more than two groups.
In SPC for the factory, if judge range to pass the process is narrow, no-go products increase evenif it is not bad product. It is type I error.
But if the range is wide, bad products are passed the process. It is type II error.
Users need good products. But the maker do not want to throw away good products. So decision of size of the range is not easy. We need consider the balance of I and II.
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