0

When I take a statistical inference course, the professor said that hypothesis testing emphasizes the rejection, and usually we would say that we cannot reject $H_0$ than accept $H_0$.

I'm confused about this statement and interpretation of hypothesis testing result.

Denote null hypothesis $H_0$ VS alternative hypothesis $H_a$, and test method has type 1 error $\alpha$ and type 2 error $\beta$.

Don't the two parameters mean:

  1. the probability of correctly accepting $H_0$ is $1-\alpha$
  2. the probability of correctly accepting $H_a$ is $1-\beta$

or equivalently

  1. the probability of correctly rejecting $H_a$ is $1-\alpha$
  2. the probability of correctly rejecting $H_0$ is $1-\beta$

Then why we don't just interpret that

  1. if we accept $H_0$, we have $100 \times (1-\alpha)$% confidence that accepting $H_0$ is the right choice.
  2. if we reject $H_0$, we have $100 \times (1-\beta)$% confidence that rejecting $H_0$ is the right choice.

So how can hypothesis testing emphasizes the rejection, and say that we cannot reject $H_0$ ?

HCR
  • 74
  • Usually $\beta$ , the probability to accept the hypothesis if it is false, is large. Moreover, in practice, we usually do not know the true distribution and often cannot even estimate $\beta$. – Peter May 02 '18 at 20:28
  • Its similar to legal outcomes. Not guilty doesn't mean innocent. Similarly, failure to reject the null doesn't mean there is no significant difference. You just don't have the evidence for it. Out of the two choices of doing this, failure to reject the null keeps options open for future rejection in case of a chance error. My 2 cents. – Phil H May 02 '18 at 20:41
  • Thank you for your explanations! – HCR Jun 05 '18 at 18:30

0 Answers0