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I was reading about an article on One tailed test and Two tailed test. I know that using one tailed test we focus only in one direction and are not concerned about direction.

I came across the below example:

A one-tailed test tells you the effect of a change in one direction and not the
other. Think of it this way, if you are trying to decide if you should buy a 
brand name product or a generic product at your local drugstore, a one-tailed 
test of the effectiveness of the product would only tell you if the generic 
product worked better than the brand name. You would have no insight into whether 
the product was equivalent or worse.

Since the generic product is cheaper, you could see what looks like a minimal 
impact, but is in fact a negative impact (meaning it doesn’t work very well at 
all!), but you go ahead and purchase the generic product because it is cheaper.

What I am unable to get is if one tailed test tells me that the generic drug is better than branded drug, it implies that the products are not equivalent and not worse.

So how am I missing anything by using one tailed test. Where is the exact pitfall of one tailed test.

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That example is over-simplifying things.

If you do a one-tailed comparison and find that the generic is significantly better than the brand name then you do know that it is better. But remember that is only statistical significance, it does not tell you how much better or if it is enough to care about.

But if the test is not significant then you don't know whether the generic is "As Good" (equivalent) or if it is worse (and actually it could still be better, just not enough for your study to have detected).

In the one sample and two sample cases, the 2-tailed test is really just two 1-tailed tests looking in either direction. So the 2-tailed test can tell you if generic is better, generic is worse, or cannot determine (remember a non-significant result does not prove that they are the same or equivalent, just that you don't have enough power to detect the difference, equivalence testing requires more thought and planning).

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  • $\begingroup$ Agreed. But after using one tailed test if it comes out that generic is better than branded that implies it is not worse. So both scenarios are covered. We aren't missing anything by using one tailed test. $\endgroup$ Apr 3, 2020 at 5:52
  • $\begingroup$ @learnToCode, We are not missing anything by using a one-tailed test when the one-tailed test is significant. But what about when the one tailed test is not significant? A significant (in the other direction) two-tailed test will tell us that generic is worse, but a non-significant one-tailed test will not distinguish between generic worse and generic equivalent to the name brand. To me the example quoted is backwards, since the generic is cheaper I will want to buy the generic if they are equally effective or if generic is better, so one-tailed test if the generic is worse. $\endgroup$
    – Greg Snow
    Apr 3, 2020 at 15:12

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