# Why is it not standard to include minimum practical effect size in null hypothesis?

I am a new to statistics. I am confused by the common practice of having a null hypothesis of the form $$\theta = \theta_0$$ in hypothesis testing. It would seem to me that, in many cases, we are not interested in exact equality but instead $$|\theta - \theta_0|< \delta$$ for some threshold $$\delta$$ at which the difference between $$\theta$$ and $$\theta_0$$ would have practical significance.

Are there examples of researchers formulating their null hypotheses in this way? Why is this not more common?

• This is in fact very common; search for "non-inferiority" testing (and possible synonyms: inferiority testing, superiority testing, equivalence trials, etc...). The most common iterm s non-inferiority: proving that my statistic $\theta$ is less than $\delta$ lower from a "reference" $\theta_0$. CV has lots of posts on this, and Google will provide 100's of relevant sites. There is even a CV tag, found here stats.stackexchange.com/tags/non-inferiority/info. Commented Aug 1 at 18:15
– whuber
Commented Aug 1 at 18:28
• @whuber I would prefer not. Is it okay to have two accounts for different purposes? Commented Aug 1 at 18:35
• It is strongly frowned upon because it creates opportunities to game the system, such as voting for yourself.
– whuber
Commented Aug 1 at 18:58
• I understand. You can combine your accounts and de-identify the resulting single account.
– whuber
Commented Aug 1 at 23:26

• Significantly non-$$\theta_0$$ can be a more fair way to assess significance. Suppose we are interested in whether a potential confounder has a significant effect. Rejecting a value hypothesized under the null is easier than rejecting at least $$\delta$$ further away.
• It seems that in TOST the null hypothesis is $|\theta - \theta_0| > \delta$ and the alternative hypothesis is $|\theta - \theta_0| \leq \delta$. The rôle of $H_0$ and $H_1$ are reversed relative to my proposal. Cool stuff though, I had not heard of equivalence testing before. Commented Aug 1 at 18:41