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Math Help - Hypothesis Test Problem

  1. #1
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    Hypothesis Test Problem

    Hello,

    I have a problem involving making a Hypothesis Test for a treatment being performed. The outcome is measured with a health rating FIM. There are 203 patients before treatment and 203 after treatment , each has a health measurement FIM. I found a sample mean of 41.8 before treatment with a variance of 58.5, and a sample mean of 61.5 after treatment with a variance of 99.7. I want to perform hypothesis testing on this. I made the null hypothesis that the average after the treatment was the same as the sample mean before the treatment (41.8). Was that wrong to do?




    When finding the z-score of the result I got approx. 28, which I do not think is correct because of how high it is. From what I understand I have too many samples for a two sample t-test correct? But nonetheless when I perform that I get a score of approx. 22. Which I think may also be incorrect.

    Any advice would help,

    Thanks,

    Jeff
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  2. #2
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    Re: Hypothesis Test Problem

    Hey jeff2222.

    You don't have too many samples for a t-test. Using the normal approximation is valid since you have a lot of samples.

    Can you show us how you calculated your test statistic? Are you using a paired t-test? (Are the relationships between each pair strong enough to consider a paired test?)
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  3. #3
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    Re: Hypothesis Test Problem

    Hey thanks for the response,

    (standard deviation of FIM at discharge)/sqrt(total number of patients) = 0.7006

    (mean of FIM at discharge - mean of FIM at admission) = 19.6108

    19.6018/0.7006 = 28

    For the t-test I used:
    t = (mean of FIM at admission - mean of FIM at discharge)/ sqrt((SD1^2/203 + SD2^2/203))

    (41.8 - 61.5)/ 0.883 = -22.2

    The patients at discharge are the same patients at admission, so there should be a strong relationship.
    I think I may understand what the problem is, I need to be calculating the mean differences between the tests. Is that correct?
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  4. #4
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    Re: Hypothesis Test Problem

    Are you using a paired t-test? You should probably switch to one if you are not already doing so.
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  5. #5
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    Re: Hypothesis Test Problem

    I wasn't. I now am. Thanks for your help.

    For anyone else reading this, the method for the paired t-test is explained well here:
    And the matlab function ttest has options to be used for a paired t-test.
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