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Hypothesis Testing

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This topic contains 2 replies, has 3 voices, and was last updated by  Robert Butler 2 weeks ago.

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  • #239624

    Vicbernie999
    Participant

    I know that in order to be able to do the Hypothesis Testing we must also be able to test for Normality and the “t-test”. I need help in Minitab or Excel to put the following data and calculate the p-value. I really don´t know to use Minitab. Somebody please help.

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    #239627

    Katie Barry
    Keymaster

    @vicbernie999 Have you tried Minitab’s support? It’s excellent!

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    #239629

    Robert Butler
    Participant

    I don’t know the basis for your statement “I know that in order to be able to do the Hypothesis Testing we must also be able to test for Normality and the “t-test”. but it is completely false. There is no prerequisite connection between the desire to test a random hypothesis and ANY specific statistical test. Rather, it is a case of formulating a hypothesis, gathering data you believe will address that hypothesis and then deciding which statistical test or perhaps group of tests you should use to address/test your initial question/hypothesis.

    If you have run afoul of the notion that data must be normally distributed before you can run a t-test – that notion too is wrong. The t-test is quite robust when it comes to non-normal data (see pages 52-58 The Design and Analysis of Industrial Experiments 2nd Edition – Davies). If the data gets to be “crazy” non-normal then the t-test may indicate a lack of significant difference in means when one does exist. In that case check the data using the Wilcoxon-Mann-Whitney test.

    As to what constitutes “crazy” non-normal – that is something you should take the time to investigate. The best way to do that would be to generate histograms of your data, and run both the t-test and the Wilcoxon tests side-by-side and see what you see. You can experiment by generating your own distributions. If you do this what you will see is that the data can get very non-normal and, if the means are different, both the t-test and the Wilcoxon will indicate they are significantly different (they won’t necessarily have the same p-value but in both cases the p-value will meet your criteria for significance).

    With regard to the data you have posted – one of the assumptions of a two sample t-test is that the data samples be independent. Your data strongly suggests you do not have independent samples. As posted, what you have are a group of 7 officials who have tried something using an old and a new method. The smallest unit of independence is the individual official. Therefore, if you want to use a t-test to check this data what you will have to do is use a paired t-test.

    The paired t-test takes the differences within each individual official between the old and the new method and asks the question: Is the mean of the DIFFERENCES significantly different from 0. What this will tell you is, within the group of officials you have tested, was the overall difference in their performances significantly changed – which is to say is the distribution of the DIFFERENCES really different from 0.

    If you want to ask the question – is method new really better than method old you will have to take measurements from a group of officials running the old method, get a second group of officials and have them run just the new method and then run a two sample t-test on the two distributions. If, as I suspect, these methods require training you will need to make sure the two independent groups of officials have the same level of training in both methods.

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