Purpose
Alpha risk (a) is the probability of rejecting the null hypothesis Ho when it is actually true. It is the risk of saying there is a difference in the sample characteristic of interest (e.g. the mean) when in reality such a difference does not exist.
It is also known as the Significance Level or the risk of making a Type 1 Error.
Anatomy
Probability of rejecting the null hypothesis Ho when it is actually true.
Reference:Juran' Quality Control Handbook
Terminology
A - The null hypothesis will either be true or false for the population under investigation. Alpha risk is probability of making the wrong decision when the null hypothesis is in fact true.
B - If the null hypothesis Ho is true, then accepting H0 will be the correct decision. If the null hypothesis Ho is true, then rejecting H0 will be the wrong decision, and in this case a type 1 error will be committed.
C - The risk of committing a type 1 error, i.e. the probability of rejecting H0 when it is really true, can be set in advance. If the consequences of a Type 1 error are very serious, then the probability of such an error should be kept low.
D - Common levels of Type 1 risk, include 10, 5 and 1 percent, with a 1 percent risk being selected over a 10 per cent risk, if the consequences of a type 1 error are extremely serious. Minimizing this risk, will make it more difficult to accept the alternative hypothesis Ha.
Purpose
Beta Risk (b) is the probability of accepting the null hypothesis H0 when it is actually false. It is the risk of not discovering a difference in the sample characteristic of interest (e.g. the mean), when in reality such a difference does exist. It is also known as the risk of making a Type 2 Error.
Anatomy
Probability of accepting the null hypothesis H0 when it is actually false.
Reference: Juran’s Quality Control Handbook
Terminology
A - The null hypothesis will either be true or false for the population under investigation. Beta risk is the probability of making a wrong decision when the null hypothesis is in fact false.
B - If the null hypothesis Ho is false, then accepting H0 will be the wrong decision and a type 2 error is made. The risk of committing a type 2 error is known as the beta risk b, which is important because it is an insurance against saying there is no difference when in actual fact there is.
C - If the null hypothesis Ho is false, then rejecting H0 will be the correct decision.
Note: A type 1 and type 2 error cannot be committed simultaneously, since the null hypothesis cannot be true and false at the same time.
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