Two-Sample T-Test

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    I have two data sets, which I wanted to perform a two-test upon with 95% confidence level. However, the P-value shows that they are not statistically equivalent (P=0.015). Is there any other ways I can test for equivalency? Or, is that anyway to justify that two datas set are equivalent? Thanks for your help.



    If you have strong confidence of those data should be equal, Let try to test @ 99%
    May be not good answer.


    Mike Carnell

    First make sure you ran through the correct sequence for the t test. Test for normality, test the vaiances then test the means. You have to know if the variances are equal to select the correct formula for the t test. You have to know normality for the correct test of equal variances.
    By any chance is the data matched up in sets? If it is a pairwise t test may be more appropriate.
    If you want to test means you can use a one way ANOVA.


    Bruce Gilbert

    If you have a very large sample size, the test will often show statistical significance when the practical significance is small. 
    I would be willing to look at the data set and give you further advice.  If you would like me to help further, send the data my email address.
    Bruce Gilbert


    Marc Richardson

    If you have a large sample size, say >30, you can use the Z test.
    Marc Richardson
    Sr. Quality Assurance Engineer


    Ranganadha Erra

    I agree with Mike.
    Firstly test normality of data. and then test for the variances and see if they are same. If the variances are same and the data is normay, then you may use either the t test or the anova.
    In cases of non normalily try and gather more data points so as to have a good comparision.


    Ali Askari

    Hi, Wei
    Sharing few fundamental ponits, hope these will be of some help.
    As a standard procedure, best to carry out a “Descriptive Statistics” on each data set.
    1. “Descriptive Statistics”
    (1a) Anderson-Darling Normality Test.
    (1b) P  value (higher then 0.05 is normal).
    (1c) mean, sd and many more data output post analysis.
    (1d) Boxplot
    (1e) 95% CI for Mu and 95% CI for median
    Via this approach – a snap shot of your each data set is obtained. Then this should allow you to plan next steps, what further tests are suitable. Mike, comments on Normality is cover with this approach and also comments made by othe contributors.
     2. Type of T-tests.
    (2a) Paired T-test: I have successful applied these when comparing old vs new equipment during the capital prog of puchase. For example, same sample two different equipment.
    (2b) Two Sample T-test: I have successfully applied these – raw material vs supplier’s. For example same raw material vs different supplier’s.
    3 “Test for Equal Variance”.
    This will give F-test (simple terms comparing sd) and Leavene’s test – these are for normal distribution and not normal distribution, respectively. P value is given.
    4. ANOVA – this also available. But, I usually go for ANOVA for data set more then 2.
    5. Have you considered the Gage and R&R, to enusre the data variability is understood – repeatability or reproducibility . What is part-to-part varition?
    Finally, if your data sets is comparison of two – then T-test and Test for Equal Variance will be valuable. However, without fully understanding the data type and n (no of data points) – hence a generic comments. 
    If you need further comments, contact via my email.

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