What is meant by a one-sided/two-sided hypothesis test? Is it just another term for a one-tailed/two-tailed hypothesis test?

And is a hypothesis test necessarily either one-tailed or two-tailed, or it could be neither?

  • $\begingroup$ What do you have in mind when you say non-tailed test? $\endgroup$ – RScrlli Mar 28 '19 at 8:39
  • $\begingroup$ I confess that I am not really sure. $\endgroup$ – Noppawee Apichonpongpan Mar 28 '19 at 8:57
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    $\begingroup$ Answer to your first question is 'yes', though the second terminology is somewhat more used I guess. $\endgroup$ – StubbornAtom Mar 28 '19 at 10:03
  • $\begingroup$ For instance in OLS framework sometimes you are interested is testing whether $b=0$ or not, in this case you use a two tailed test cause it could happen that $b<0$ or $b>0$. Instead if you wanna test for instance $b<0$ you will use a one tailed test. $\endgroup$ – RScrlli Mar 28 '19 at 10:46

For a one sided test you are only interested in results in one direction and conversely for two sided. For many tests this corresponds to using one or two tails of the reference distribution of the test statistic. However there are situations where the two sided test only uses one tail so people have come to use the term sided rather than tail. In practice confusion is unlikely

What you refer to as non sided is what happens in situation like the comparison of multiple groups, goodness of fit, and many others. In those cases it does not make sense to speak of a direction of difference. For instance if you compare three means all you can say is that they are different or not.

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