In general, a Type 1 error makes you depart from the status quo and take some action that is wrong, while committing a Type 2 error means that you stick with the status quo when you should have acted.
Decision theory is always a trade-off.
In hypothesis testing, you make sure that the Type 1 error is the severe error, so you can control the probability of making it.
As a result, the Type 2 error may in fact have a larger probability of occurring (but it is the lesser of the 2 errors).
A pharmaceutical company is testing the safety of a new drug:
Type 1 error: concluding it is safe when it’s not (kill people)
Type 2 error: concluding it is not safe when it is (lose some money)
The criminal justice system:
Type 1 error: convicting an innocent person (terminology: the defendant is guilty)
Type 2 error: not convicting a guilty person (terminology: the defendant is not guilty. It’s important to note that you never say the defendant is innocent).
A scientific researcher
Type 1 error: publishing your research when it’s wrong (embarrassment)
Type 2 error: not publishing your research when it’s correct (usually this means continuing your research until you can show progress)
- There is sufficient evidence to reject the null hypothesis in favor of the alternative.
- The is insufficient evidence to reject the null hypothesis (NEVER ACCEPT THE NULL HYPOTHESIS – no one is ever declared innocent; they are declared not guilty)
I didn't make this stuff up. I credit a good friend, Dr. Pat Bond, a professor at Florida Tech, for these insights
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