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hypothesis testing

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  • May 10, 2002 at 12:06 am #29418

    Aguilar
    ★ 10 Years ★
    Member

    Hi!
    how dou you know best when to use a two tail test vs a one tail test when testing a hypothesis.

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    May 10, 2002 at 3:14 am #75359

    Sridhar
    ★ 10 Years ★
    Member

    Hi,
             That depends on your alternate hypothesis, if your alternate hypothesis is of not equal kind then you have to take two tail test, or if your alternative hypothesis is of type one is greather or lessers than the other then you consider one tailed hypothesis.
    thanks
    A.Sridhar
     

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    May 10, 2002 at 11:59 am #75362

    Joy Cowling
    ★ 20 Years ★
    Participant

    You use a two-tailed test when you are trying to compare two samples.  For example, you have two machines.  You made a change to one and not the other.  You would use a two sample test to compare samples taken from each to determine whether your change made a difference.  You can also do a before/after test.  Take a sample from your process before a change, then take another sample after the change.  Use two-sample t to determine if there is a difference in the samples.
    A one-sample test is used when you are comparing a sample to a target.  If you have a historic mean of your process and you want to know whether you have made a change from the target, one sample will get you there.  If you are trying to achieve a certain target performance, a one sample t can test a sample from the process against the target to see if you have achieved your goal.
    Hope this helps.
    Joy

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    May 10, 2002 at 5:13 pm #75371

    Erik L
    ★ 10 Years ★
    Participant

    Victor,
    Good question in regards to the one-tail vs two-tail test option.  The primary decision of option comes down to what you expect to see.  If you are looking at two options, the typical null hypothesis is that they are the same.  The alternate hypothesis then has a couple of different choices.  If we think that there is a chance that the alternate hypothesis is likely to be better or worse then the null hypothesis, we need to spread our alpha-risk to both tails.  If we state that I have two medicines that relieve pain, my typical null would be Mean pain A=Mean pain B.  If I’m going to switch from A to B only if there is parity or better relief of pain my alternate cannot be a two-tail test.  I would now go for the alternate to be one-tail with mean B l.t or equal mean A (if we assume down is better).  This has an added benefit that if I desire 95% confidence, I now have all 5% sitting in only one of the tails.  Therefore,  I’ll exceed the critical value, hence rejecting the null, quicker then if I had a two-tail alternate hypothesis. 
    Regards,
    Erik

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    May 10, 2002 at 9:31 pm #75380

    Joy E. Cowling
    ★ 20 Years ★
    Participant

    I guess I ought to read the question better next time.   You asked about tails, not samples.  Erik’s advice is good.  At least someone is paying attention!
    Joy

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    May 11, 2002 at 12:19 am #75383

    VIC
    ★ 20 Years ★
    Member

    Thankyou Joy for the answer that was very clear.

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    May 14, 2002 at 5:49 pm #75444

    RR Kunes
    ★ 20 Years ★
    Member

    The root of the one tailed test versus a two-tailed test is in the allocation of the alpha variable not the amount of samples you are testing, whomever gave that answer was misinformed.
    In a two tailed test the null hypothesis specifies only ONE value of the parameter under test i.e the means are equal. Whereas in a one-sided test the null hypothesis specifies a large number of values the mean is greater than or equal to X.
    As you can deduce from this definition to reach any conclusion in a one sided test would require a large number of tests to be performed. Generally, we perform a test only at the point of equality. When data tells you that all the variability resides in one tail or the other you then allocated all the alpha value to a single side of the distribution and perform a one sided test.
    The critical value of z then will be the value of z to the left of which lies the alpha value (typically 0.05) ofthe area under the standard normal curve.
    We know that in the standard normal distribution large values of “z” are located in the right tail and small values in the left tail. Half of the alpha value is assigned to each tail. “Two Sided test”
     

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