Why aren't type II errors emphasized as much in statistical literature? I have seen many cases where type I errors are accounted for (denoted by an alpha value) in various research articles. I have found it rare that a researcher will take into consideration the power, or the type II error.
Type II errors can be a big deal right? We have accidentally rejected the alternative hypothesis when it was actually false. Why are alpha values emphasized so much instead of beta values?
When I took first year statistics, I never was taught beta—only alpha. I feel that these two errors should be treated equally. Yet, only alpha seems to be emphasized.
 A: This is a good question.  Let me begin with a couple of clarifications:  


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*It doesn't really mean anything for a "[t]ype II error [to] be significant" (or for a type I error to be).  Certainly, it might be very important that we missed a true effect, though.  

*Also, we do not generally "[accept] the null hypothesis".  (For more on that, it may help to read my answer here: Why do statisticians say a non-significant result means “you can't reject the null” as opposed to accepting the null hypothesis?)



I think you are (unfortunately) right that less attention is paid to power and type II errors.  While I think the situation is improving in biomedical research (e.g., funding agencies and IRBs often reqire power analyses now), I think there are a couple of reasons for this:  


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*I think power is harder for people to understand than simple significance. (This is in part because it depends on a lot of unknowns—notably the effect size, but there are others as well).  

*Most sciences (i.e., other than physics and chemistry) are not well mathematized.  As a result, it is very hard for researchers to know what the effect size 'should' be given their theory (other than just $\ne0$).  

*Scientists have traditionally assumed that type I errors are worse than type II errors.  

A: The reason is that we simply don't know the actual type II error rate and we never will. It depends on a parameter we usually don't know. In turn, if we would know this parameter, we would not need to do a statistical test.
However, we can plan an experiment such that a specific type II error rate is met given some alternative is true. This way, we would choose a sample size that does not waste resources: Either because the test doesn't reject in the end or because already a much smaller sample size would have been sufficient to reject the hypothesis.
