Is there a fancy terminology/jargon for Not rejecting true null?

[kuromusha]

If we reject a false null, it is called “power of a test”.
if we do not reject a false null, it is called “type II error”
If we reject a true null, it is called “Type I error” or “level of significance” or “alpha”.
if we do not reject a true null, then is there a fancy terminology for this probability?

 

[tickersu]

kuromusha wrote:
If we reject a false null, it is called “power of a test”.

The power of a test is the probability that you reject a false null. Rejecting a false null in itself is a correct decision and is not referred to as the power of a test.

kuromusha wrote:if we do not reject a false null, it is called “type II error”

Yup– this occurs with probability beta. This probability is (1-power).

kuromusha wrote:If we reject a true null, it is called “Type I error” or “level of significance” or “alpha”.

It’s called a Type I error, and it occurs with probability alpha (which is your chosen significance level– not to be confused with the observed significance level).

kuromusha wrote:if we do not reject a true null, then is there a fancy terminology for this probability?

This is another correct decision. It occurs with the probability (1-alpha). It is equal to the confidence coefficient (0.95, for example)– you can think of it as the probability that you fail to reject the null when the null is true. This should hint at the connectedness of confidence intervals and hypothesis tests.
Hope this helps.

 

[olajideanuoluwa001]

lol… It is simply called “Fail to reject Ho)

 

[tickersu]

olajideanuoluwa001 wrote:
lol… It is simply called “Fail to reject Ho)

Right, but his final question asked about the probability of FTR Ho given that Ho is true (this would be the confidence coefficient, 1-alpha and it is a correct decision).
He wasn’t very clear, though. The thread title asked only about the name for the given situation, but his final question asked about the probability.

 

[S2000magician]

kuromusha wrote:if we do not reject a true null, then is there a fancy terminology for this probability?

It’s called getting it right.
Some people call it a miracle.

 

[kuromusha]

tickersu wrote:
Right, but his final question asked about the probability of FTR Ho given that Ho is true (this would be the confidence coefficient, 1-alpha and it is a correct decision).
He wasn’t very clear, though. The thread title asked only about the name for the given situation, but his final question asked about the probability.

That given situation has a probability. So they are the same thing
Just like “post of a test” is a name given to probability of 1-Type II error.
Therefore the situation described in the title is even easier. It is 1 - alpha, since alpha is a probably, the situation in the title is therefore also a probability.

 

[kuromusha]

In confidence interval, this 1-alpha is called “degree of confidence”. Can that term be used to label 1-alpha in hypothesis testing?

 

[tickersu]

kuromusha wrote:
That given situation has a probability. So they are the same thing

Not particularly, although they are related. If alpha is the probability of rejecting the null when the null is true, and you make this error, you would say you’ve made a Type I error. You wouldn’t (if you know what you’re doing) say that “the probability of a Type I error has occurred.”

kuromusha wrote:Just like “post power of a test” is a name given to probability of 1-(beta or P[Type II error]) Type II error.

Right, it’s defining the probability of an event, not the event. If you reject a false null you don’t say “power has occurred” or something weird like that. Power refers to the probability that this (rejecting a false null) will occur. Type I and Type II errors are situations that represent the incongruence between reality and the decision from a statistical test.

kuromusha wrote:Therefore the situation described in the title is even easier. It is 1 - alpha, since alpha is a probably probability, the situation in the title is therefore also a probability.

Unfortunately for you, they aren’t the same thing. One is a probability, the other is an event.
Please let us know if you have further questions.

 

[tickersu]

kuromusha wrote:
In confidence interval, this 1-alpha is called “degree of confidence”. Can that term be used to label 1-alpha in hypothesis testing?

You need to understand the relationship between confidence intervals and hypothesis tests. A confidence interval can be interpreted as the range of null hypothesis values for which you would fail to reject the null, assuming the null is true.
Alpha is P(Rej Ho|Ho true), and the confidence coefficient represents P(FTR Ho|Ho true). You can see this with logic– for a given state of nature, say Ho True, there are only two outcomes from our test. We will either FTR Ho or we will Rej Ho. P(Rej Ho| Ho True)= alpha = P(Type I error). 1- alpha is the confidence coefficient.