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Dr Biswas: Disease progression does not come into the picture. Whatever be the measurements and howsoever taken, the question is regarding asymptotic distribution of M-W test vis-a-vis Welch test.
Best.
~A. Indrayan
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Dr Abhaya Indrayan, MSc,MS,PhD(OhioState),FSMS,FAMS,FRSS,FASc
Personal website:Â http://indrayan.weebly.com
On Mon, Nov 1, 2021 at 11:22 AM Rakesh Biswas <rakesh...@gmail.com > wrote:
- Could this happen due to disease progression or recovery?
- On Mon, Nov 1, 2021, 10:17 AM Abhaya Indrayan <a.ind...@gmail.com> wrote:
- The theory suggests that the Welch test and Mann-Whitney (M-W) test are asymptotically (standard) normal irrespective of different n's. However, when I calculate these values for some inflammatory markers for differences between surviving and dead patients of COVID, for extremely large samples (n1>10000 and n2>1000), I find the values of Welch t and M-W z are very different. Both the distributions are highly skewed to the right and both are unimodal. The variances are very different. For example, for CRP, the values are as follows:
- n1 = 12226/mean1 = 29.86/SD1 = 49.97/ median = 8.61/
- n2 = 1038/mean2 = 74.98/SD2 = 86.39/median = 34.84/
- Welch t = 16.59 but M-W z = 22.29
- This is not an isolated case. I find similarly widely different values of Welch t and M-W z for all the inflammatory markers.
- What is it that I am missing?
- ~Abhaya
- --
- Dr Abhaya Indrayan,Â
- Personal website:Â http://indrayan.weebly.com
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I'm new to this group, so sorry if I'm missing the point somewhere, but there seem to be two issues.
First, just because two test statistics have the same (asymptotic) distribution, doesn't mean that they must always take the same value with a specific data set.
- Kind Regards, John
- Best.
- ~A. Indrayan
- --
- Dr Abhaya Indrayan, MSc,MS,PhD(OhioState),FSMS,FAMS,FRSS,FASc
- Personal website:Â http://indrayan.weebly.com
- On Mon, Nov 1, 2021 at 11:22 AM Rakesh Biswas <rakesh...@gmail.com > wrote:
- Could this happen due to disease progression or recovery?
- On Mon, Nov 1, 2021, 10:17 AM Abhaya Indrayan <a.ind...@gmail.com> wrote:
- The theory suggests that the Welch test and Mann-Whitney (M-W) test are asymptotically (standard) normal irrespective of different n's. However, when I calculate these values for some inflammatory markers for differences between surviving and dead patients of COVID, for extremely large samples (n1>10000 and n2>1000), I find the values of Welch t and M-W z are very different. Both the distributions are highly skewed to the right and both are unimodal. The variances are very different. For example, for CRP, the values are as follows:
- n1 = 12226/mean1 = 29.86/SD1 = 49.97/ median = 8.61/
- n2 = 1038/mean2 = 74.98/SD2 = 86.39/median = 34.84/
- Welch t = 16.59 but M-W z = 22.29
- This is not an isolated case. I find similarly widely different values of Welch t and M-W z for all the inflammatory markers.
- What is it that I am missing?
- ~Abhaya
- --
- Dr Abhaya Indrayan,Â
- Personal website:Â http://indrayan.weebly.com
- John
- ----------------------------------------------------------------
- Buckingham MK18 4EL, UK
- ----------------------------------------------------------------
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Both are asymptotically N(0, 1), but only under the null hypothesis. If the null hypothesis is false, the distribution would most certainly not be N(0, 1). A test statistics that was approximately N(0, 1) under the alternative hypothesis would have almost no power.
I'm guessing that the distributions would be non-central
something or other and that the non-centrality parameter would be
different for the two tests.
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Thanks for the responses. The major one is the difference in the null hypothesis for the two tests. I will examine how this affects the test-statistic values despite both being asymptotically N(0,1) under the null.
Nice to see this group active again.
~Abhaya
On Tue, Nov 2, 2021 at 4:07 AM Simon, Stephen D. <n...@pmean.com> wrote:
- Both are asymptotically N(0, 1), but only under the null hypothesis. If the null hypothesis is false, the distribution would most certainly not be N(0, 1). A test statistics that was approximately N(0, 1) under the alternative hypothesis would have almost no power.
- I'm guessing that the distributions would be non-central something or other and that the non-centrality parameter would be different for the two tests.
- On 10/31/2021 11:47 PM, Abhaya Indrayan wrote:
- The theory suggests that the Welch test and Mann-Whitney (M-W) test are asymptotically (standard) normal irrespective of different n's. However, when I calculate these values for some inflammatory markers for differences between surviving and dead patients of COVID, for extremely large samples (n1>10000 and n2>1000), I find the values of Welch t and M-W z are very different. Both the distributions are highly skewed to the right and both are unimodal. The variances are very different. For example, for CRP, the values are as follows:
- n1 = 12226/mean1 = 29.86/SD1 = 49.97/ median = 8.61/
- n2 = 1038/mean2 = 74.98/SD2 = 86.39/median = 34.84/Â
- Welch t = 16.59 but M-W z = 22.29
- This is not an isolated case. I find similarly widely different values of Welch t and M-W z for all the inflammatory markers.
- What is it that I am missing?Â
- ~Abhaya
- --
- Dr Abhaya Indrayan,Â
- Personal website:Â http://indrayan.weebly.com
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