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Z-Test Vs T-Tests

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  • August 3, 2007 at 5:30 pm #47736

    DD
    ★ 10 Years ★
    Participant

    Dear Friends.
    I have a question…i’ll be obliges in the forum can provide me with some answers to these…
    When do we use 1 sample Z-test, especially when we say that a sample drawn may not follow a normal distribution and generally found to follow a t-distributions.
    Also like there are 2 sample t-tests and paired t-tests how come there is no 2 sample Z-test or paired Z-test. 

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    August 3, 2007 at 5:31 pm #159533

    Quality is life
    ★ 10 Years ★
    Participant

    Hi,
    z test is used when the sample size is more than 30 while t test is used for smaple size less than 30.

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    August 3, 2007 at 5:43 pm #159536

    DD
    ★ 10 Years ★
    Participant

    Hi,
    But in some situations even with samples more than 30 the data may be non-normal, in that case how can one use Z-test. I am sceptical of such thumb rules. One can not generalise all processe this way.
    If all we work with are samples(which are supposed to follow t-distributions) and never populations then wy this Z-Test at all???
    An what about 2 sample Z-test???
     

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    August 3, 2007 at 6:20 pm #159540

    BTDT
    ★ 10 Years ★
    Participant

    DD:The T-test was designed to handle sample sizes less than 30 (google Gosset). It is also very robust to deviations from normality. There are no circumstances where I would advise someone to use the Z-test over the T-test.Strictly speaking, the Z-test is a test for populations rather than samples. For example, if you look at the formulae you will see entries for sd(population) that are estimated by sd(hat).Cheers, BTDT

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    August 3, 2007 at 7:46 pm #159548

    Mikel
    ★ 10 Years ★
    Member

    Wrong

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    August 3, 2007 at 8:59 pm #159553

    Jim Shelor
    ★ 10 Years ★
    Participant

    DD,
     
    When using Variable Data, testing one sample mean against a standard:

    Variance known – One mean Z-test
    Variance unknown – One mean T-test.
     
    When using Variable Data, testing two sample means against each other:

    Variance known – Two mean Z-test
    Variance unknown:

    Variances assumed equal – Two sample pooled T-test.
    Variances assumed unequal – Two sample T-test.
    Paired Data – Paired T-test
     
    There is a two sample Z-test (see above).
     
    There is no paired data Z-test because there is no need for one.
     
    I hope this helps.
     
    Regards,
     
    Jim Shelor

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