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t test

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  • #51407

    sherrie
    Member

    A t-value is actually a standard deviation score (this might give you a hint as to how it might be calculated) based on the t-distribution. The t-Test is useful if you have a small number of observations and only one or two groups of observations with which to conduct your hypothesis testing. When the number of observations (in each group) exceed 30, the t-distribution starts to look like the normal distribution, and the analysis of variance (ANOVA) becomes the preferred test.

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    #178129

    Pal
    Participant

    I’ll play: 
    The answer is “When do I use a t-test”? 
    I’ll take hypothesis testing for 200, Alex!

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    #178130

    Robert Butler
    Participant

       The t-test is used for a comparison of two samples.  This can be paired samples, independent samples from two populations or samples from a single population compared to a target. 
      The t-test is useful anytime you have the above conditions.  It was originally developed for comparisons where the sample sizes were small but sample size is not a driver as far as its use is concerned. A check of the appendix of any basic book on statistics will show t-tables with values up to infinity.
      “We have seen in Section 9.7 that two sample means can be compared with the two-sample t test.  The generalization of this problem to k means, k > 2, brings us to the body of techniques known as the analysis of variance.  – Statistical Theory and Methodology in Science and Engineering – Brownlee. pp. 309.
    Therefore
    t-test – two means
    ANOVA – more than two means.

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    #178131

    Bower Chiel
    Participant

    Hi RobertMay I pick a nit here? You can of course use ANOVA with just two means as you are no doubt aware. It’s quite interesting to do an example by both methods with people learning the ropes of hypothesis testing: -Row A B
    1 20.4 20.2
    2 24.2 16.9
    3 15.4 18.5
    4 21.4 17.3
    5 20.2 20.5
    6 18.5
    7 21.5T-Test of difference = 0 (vs not =): T-Value = 1.12 P-Value = 0.289 DF = 10
    Both use Pooled StDev = 2.3627
    One-Way ANOVA
    Source DF SS MS F P
    Factor 1 6.99 6.99 1.25 0.289
    Error 10 55.82 5.58
    Total 11 62.82The P-values are the same for both the t-test and the ANOVA and in fact the F statistic is the square of the t-statistic. Thus the t-test is equivalent to the ANOVA F-test in this case.Best Wishes
    Bower Chiel

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    #178141

    Craig
    Participant

    Let’s not forget the use of the t-test for regression coefficients!
     

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    #178143

    Bower Chiel
    Participant

    RobertApologies for my garbled post – what looked fine on screen appeared as a dog’s breakfast on-line!Sample A 20.4 24.2 15.4 21.4 20.2 18.5 21.5
    Sample B 20.2 16.9 18.5 17.3 20.5A t-test of mean for Population A equals mean for Population B, versus the alternative that they differ, gives t = 1.12 and P-value of 0.289 (equal population variances assumed).ANOVA for the same hypotheses gives F = 1.25 and P-value of 0.289.The P-values are identical and in fact the F value is the square of the t value – the two tests are exactly equivalent.It’s also interesting to consider the ANOVA alternative to the paired t-test.Best WishesBower Chiel

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    #178150

    Robert Butler
    Participant

    Bower, that was a good nit to pick.  You’re right,  I should have included a comment concerning the ANOVA case when k = 2.  Thanks for covering that situation as well as providing numbers so someone can run the test for themselves.

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