one-tailed or two-tailed. which is right?

Discussion in 'SPSS' started by Mike, Oct 29, 2011.

  1. Mike

    Mike Guest

    Say, alpha=0.05 and I get p=0.08 when I compare two indepdent-sample
    If H1 mu1<>mu2, then I should not reject H0. This is two-tailed test.
    For one-tailed test, p is 0.08/2. right?
    If H1 mu1> or < mu2, then I should reject H0. This is one-tailed test.
    The result is mu1=mu2, but mu1> or < mu2.
    How to explain this? I am very confused.
    Thanks in advance.
    Mike, Oct 29, 2011
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  2. Mike

    Rich Ulrich Guest

    The null hypothesis must be chosen before the data are
    examined at all. If you are replicating something that is well
    known, you *might* be able to justify a one-tailed test.
    Or, some reviewers or editors who are suspicious of "convenient
    choices" might object to your one-tailed test, anyway.

    If the null hypothesis says that mu1 < mu2, then no matter
    *how* big the difference is for mu1 >> mu2 -- if that is how
    the result came out -- you would be forced to conclude
    "No Difference". Observing a huge effect in the wrong
    direction is only "suggestive" at best, just like seeing an
    effect with p-value of 0.12 or whatever is non-significant.

    But it doesn't have to be that way.

    The formal convention is to assign half of the "rejection region"
    to each side of the test. Technically, that is a convention,
    not a law. In practice, we sometimes tend to act as if we
    were observing a different convention, to the effect that we
    take something like "0.001" in the "wrong" direction, and the
    rest of the 0.05 is the "right" direction. Thus, we might be
    willing to act pretty much like an effect is "real" when it hits
    0.001 in the wrong direction, even though that was the
    wrong direction.
    Rich Ulrich, Oct 29, 2011
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  3. Mike

    Bruce Weaver Guest

    I think Rich meant *alternative* hypothesis on that line. In the most
    common application of hypothesis testing, it is the alternative
    hypothesis that is either directional or non-directional (i.e.,
    one-tailed or two-tailed).

    While I agree with you, Rich, I think that reviewers and editors might
    again become suspicious if one actually tried this.
    Bruce Weaver, Oct 30, 2011
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