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Hypothesis Testing

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This topic contains 7 replies, has 7 voices, and was last updated by  Mike Carnell 3 months, 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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    #240022

    doe
    Participant

    Plot the data on a probability paper using median ranks on the y-axis, or use a box plot. If you need a data record; a ‘t-test’ where standard deviation is estimated from the data.

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    #240044

    Sergey Glukhov
    Participant

    The bad thing about statistical hypithesis testing is that it makes your decision look more unbiased when in reality you chose the criteria of the tipping point between false and true. If you were shown the real situation 95% chance that the pill is harmful and 5% that it heals. Would you chose to take one?

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    #240143

    Mike Carnell
    Participant

    @vicbernie999 The list of hypothesis tests you listed may have come from a flow chart Miguel Hernandez and I created when we were teaching hypothesis testing in Europe (there is an article on iSS somewhere about it). That flowchart was created to explain what we were teaching. There is no point where it says it is an excusive list of hypothesis tests.

    Robert Butler will always give you great advice. I am not saying other will not but I have read Robert’s posts over the years and they are rock solid. The part that seems to be missing is the importance of sample size. I can turn a hypothesis test result around simply by changing the sample size. You need to understand sample size before you do any of this.

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    #240196

    Darth
    Participant

    @vicbernie999 @mike-carnell You are correct in stating that the classical texts teach that the assumptions of the t-test are independence, normality and equal variance. Independence is important to determine. If not, the advice about using the paired t-test is good. Minitab gives you the option to choose equal variances or unequal variances so testing for them with the 2 variance test is easy enough to do. That leaves you with the issue of normality. The t distribution is a form of the normal in that the t distribution approaches normal as the sample size gets larger. Given that you only show a sample size of 8, I would be concerned that neither the t test or the paired t test would be really useful. Try doing a Power and Sample Size calculation and see what sample size you would need to have a valid outcome. As was stated, there is some robustness to the test with regards to normality. Non parametric tests can be used but they don’t approach the power of the parametric tests and one famous Minitab statistician once described nonparametric tests as “a big turd”. Of course, we always have members of the profession that would say you had to transform the data to establish normality and then see what happens. Easy enough to do. The initial question should be is the nonnormal data a result of the natural state of the process or is something weird going on. Since your data is Time it would naturally be non normal since there is no upper limit to time but certainly a lower one of zero. What does your professor say the correct answer is?

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    #240202

    Mike Carnell
    Participant

    @Darth Very happy to see you back even if it is for a little bit. Hope you are doing well.

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