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

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Cosine wrote:

> Hi:
> 
>   Sometimes we would like to demonstrate that the data has some
> particular type of trend, e.g., monotone increase or decrease. How do
> we demonstrate that this trend has statistical significance?
> 
>  Thank you,

As a first step, you need to think about the context of whatever data
you have. In particular, you need to consider whether there is temporal
correlation/dependence present in addtition to whatever trend you might
postulate. Also, you should think about whether a possible "trend"
should also include a possible change in variability instead-of or in
addition-to a change in location.

In the simplest case, you can just take a model-free approach whereby
you return to first-principles. Specifically: (a) find a numerical
measure of how much trend there is; (b) find the null distribution of
your numerical measure by evaluating the same numerical measure for
random permutations of the original data. It will be clear how the
assumptions needed for the validity of this relate to my first
paragraph.

In the more general case, you could resort to the usual thing of
building a full probabilistic model and testing via maximum likelihood.

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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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