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z and t test

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  • #38057

    Joseph Banerjee
    Participant

    Can some one explain whats the difference between one sample t and z test personally I dont find any in the Hypothesis testing except in z test you should know the standard deviation of the population ..Help please ..

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    #113389

    Da Agent
    Participant

    Joseph,
    Hopefully I can help shine some light on your question. (By no means am I an expert)…..The T-test is used when the standard deviation is unknown while the Z-test is used when the standard deviation is known.
    The T-test is a robust test where you can choose between a 1 sample test to compare 1 group against a fixed  target or known value and a 2 sample test to compare 2 groups to see if the means are the same.

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    #113396

    jimbo
    Participant

    A couple more points on the differences between the t and z statistic…
    The z statistic assumes that we know the standard deviation of the population.  In most cases we do not know the standard deviation of the entire population, but only of our population sample.   
    The z statistic has the same distribution for different sample sizes; the t statistic has a different distribution for different sample sizes.  For small sample sizes, the t distribution has more area under the curve at the outer regions (tails) and less area under the center of the distribution.  However, once you get up to about 30 samples the t distribution is very close to the z.
    Jimbo

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    #113404

    S
    Member

    Let me throw this out …
    I have often used Z distribution to compare a single data point relative to a population with a known standard deviation. 
    T-tests which are just comparing populations of means–e.g. why the distribution changes depending on the degrees of freedom, sample size.  It is true that the t-distribution effectively follows the z distribution for samples sizes of 30. 
    T-tests are conservative since the tails are longer so to get 95% confidence the required delta between test statistics and “estimated population means” is larger since the area under the tails is higher with t- curves.

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    #113406

    Lass
    Participant

    If you want to really simplify the answer, you could say the following:
     n = sample size
    n < 30, use T distribution (T-test)
    n > 30, use Z-distribution (Z-test)
    When comparing two samples, remember that your sample size is (n1 + n2)
    Lass

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    #113410

    S
    Member

    Lass,
    I haven’t done a manual t-test in quite a while but are you SURE? that the sample size of n1+n2 would determine which t curve you used?
    Don’t have my Box Hunter Hunter to check.

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    #113411

    e
    Participant

    mmmmm
     
    maybe n1+n2 – 2 is the df, assuming equal variances from what I can gather searching online….
     
    what is the answer?

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    #113412

    Lass
    Participant

    How did we jump from determining what type of distribution to use, to determining what type of t-curve to use?
    Allow me to backtrack….
    The orginal poster wanted to know the difference between Z and T tests.  From the tone of the post, I got the impression that the poster was a newbie and completely confused.  The resulting responses seemed a little complicated for someone who was “new”.  I was trying to simplify what criteria to use to decide between using the T- or Z- distributions.
    That being said…if your sample size was smaller than 30 (i.e. n1 + n2 < 30) you would use the T-distribution.  Your degrees of freedom (v) = n1 + n2 – 2, which would determine your t-curve.
    If I am mistaken in this, please let me know.
    Lass

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    #113433

    Joseph Banerjee
    Participant

    Thank you jimbo i think you are right when the sample size more than 30 choose z sample test
    thank you

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    #113441

    jimbo
    Participant

    From Box Hunter Hunter:
    “…when the size of the sample is infinite, there is no uncertainty in the estimate s2 [the sample size standard deviation] and the t distribution becomes the standard normal distribution of z.”
    “Except in the extreme tails of the distribution, the normal distribution provides a fair approximation of the t distribution when v [degrees of freedom] is greater than about 15.”

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    #135391

    Jose
    Participant

    I am new and have a few questions.  Your assistance would be greatful.  What would be two examples that I could use for each and how can I apply them?  Plese help.

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    #135395

    Jagadeesh
    Participant

    I am completely agree with Lass.
    T test is using for Small samples (N<30) and Z test is for large samples.
    When N is large, T distribution tends to Normal distribution.

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    #139277

    Kumpar
    Participant

    T tests are used when you have an unknow standard deviation.
    Assumptions:
    Sample size < 15:  Use t procedures if the data are close to normal.  If the data are clearly nonnormal or if outliers are present, do not use t.
    Sample size at least 15:  The t procedures ca be used except in the presence of outliers or strong skewness.
    Large Samples (> 40):  The t procedures can be used even for clearly skewed distributions.  This is because the t test is robust against skewness when you have a large sample.
    Z tests are used to test for a population mean.  Used when you want to test the hypothesis that a parameter has a specified value.

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    #139289

    Lorax
    Participant

    I’ll agree with Lass on this one, with one proviso:
    If you are comparing a sample to a single value to determine if the means are the same or different,
    and
    n>30
    Then use the One-sample-Z (which is pronounced “Zed” by the way).
    If
    If you are comparing a sample to a single value to determine if the means are the same or different,
    and
    n<30
    and
    The population is normally distributed
    Then
    Use one-sample-t
     
    Lorax
     

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    #165895

    vandehei
    Participant

    i was confused with what kind of test should i use if the the 2 samples are given and the first sample is >30 and the second sample is 30 and the second sample is 30 and the second sample is

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    #169173

    Siamack
    Member

    Hello Ann,
    with regard to your question, I think that t test is applicable with all sample sizes. In larger samples t becomes similar to z. so I think that you can use t test to compare two samples which are not equal in size.

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