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Re: Q test of significance of the trend of the data

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Rich Ulrich wrote:

> On Sun, 8 Jan 2023 04:36:55 -0000 (UTC), "David Jones"
> <dajhawkxx@nowherel.com> wrote:
> 
> > Cosine wrote:
> > 
> >> Say we have five groups of subjects, and each receives different
> >> concentrations of medicine, from low to high.
> >> 
> >> At the endpoint, we measure the diameters of the lesion of each
> >> subject and calculate the mean diameter of each group.
> >> 
> >> We expect a monotone decrease trend of the mean diameters of the
> >> groups. But how do we demonstrate the significance?
> > 
> > As part of the first step in significance testing, you need to have
> > a null hypothesis as well as an alternative hypothesis. 
> 
> Or - you can have a situation where you want to provide a
> precise assessment, where basic "significance" is assumed, and
> readily established by any test. 
> 
> Having 5 concentrations, without a Zero comparison, implies
> that the questions (hypotheses) concern whether the lowest
> dose (concentration) has much effect, or if there is continued 
> gain from increasing dose by each step. 
> 
> A overall test: 
> Assuming that the doses here are judged (by the PI) to be 
> (in the relevant sense) equal intervals, a simple correlation
> will show that increasing dose matters.  This will be HIGHLY 
> significant, you hope. 
> 
> (Also, the outcome should probably take into account the size 
> of the original lesion. Log of the Pre/Post ratio might be natural, 
> if lesions don't decrease to 0.)
> 
> If I had data like these, I would want to plot the Pre vs. Post
> for the 5 doses, and figure out from the picture what there is
> to describe.  A strong linear trend of efficicay across dose (log 
> concentration) with tiny contributions from the nonlinear ANOVA
> components would be the outcome most convenient to describe. 
> 
> 
> >                     There are two
> > obvious but distinct possibilities for one aspect of what might be
> > going on: in one the null hypothesis has an unspecified but varying
> > pattern, to be compared to a monotone pattern, while in the other
> > the null hypothesis has constant value, to be compared with a
> > monotone pattern.

The OP has been very unclear, so there seems also to be at least one
other possibility, where the null hypothesis is that there is a
monotone pattern, with the alternative hypothesis (that which one is
looking evidence might be happening) is that there is a change in
direction of the pattern as the dosage increases (but possibly just one
turning point).

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Q test of significance of the trend of the data Cosine <asecant@gmail.com> - 2023-01-06 03:14 -0800
  Re: Q test of significance of the trend of the data "David Jones" <dajhawk18xx@@nowhere.com> - 2023-01-06 14:17 +0000
    Re: Q test of significance of the trend of the data Rich Ulrich <rich.ulrich@comcast.net> - 2023-01-06 17:11 -0500
      Re: Q test of significance of the trend of the data Cosine <asecant@gmail.com> - 2023-01-07 17:48 -0800
        Re: Q test of significance of the trend of the data "David Jones" <dajhawkxx@nowherel.com> - 2023-01-08 04:36 +0000
          Re: Q test of significance of the trend of the data Rich Ulrich <rich.ulrich@comcast.net> - 2023-01-08 01:36 -0500
            Re: Q test of significance of the trend of the data "David Jones" <dajhawkxx@nowherel.com> - 2023-01-08 10:48 +0000
              Re: Q test of significance of the trend of the data Rich Ulrich <rich.ulrich@comcast.net> - 2023-01-10 00:45 -0500

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