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Re: statistics in Roberts' paper on Miller

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Tom Roberts:
> Anton Shepelev:
> > RichD:
> > > Tom Roberts:
> > >
> > > > Worse than lack of statistical errorbars is Miller's
> > > > lack of knowledge of digital signal
> > > > processing -- his analysis is essentially a comb
> > > > filter that concentrates his systematic error into
> > > > the DFT bin corresponding to a real signal -- that's
> > > > a disaster, and explains why his data reduction
> > > > yields data that look like a sinusoid with period
> > > > 1/2 turn.
> > >
> > > Can you elaborate on this filter?
> >
> > Mr. Roberts is referring to the procedure of "folding"
> > the data of each 16-azimuth turn into an 8-azimuth half-
> > turn by summing up the observations at azimuths 180
> > degrees apart.
>
> No. I am referring to Miller's averaging the 20 turns.

Sorry for the misunderstanding, them.  Yes, Miller averaged
his observrations over 20 or more (full) turns.

> As his final result for a single run is the plot at the
> bottom of my Fig. 1, with 8 points,

No, that plot is not the final result of his analysis, but a
digression made for the purposes of merely a "preliminary
study" -- quoth Miller:

   For the purpose of a preliminary study of the
   observations, it is convenient to obtain an
   approximate graphic representation of the effect by
   the following procedure. The second half of the line
   of sixteen average readings is placed under the first
   half and the mean of the two numbers in each column is
   obtained;

These half-period plots were /not/ used in the final analysis
(see below).

> my discussion is of the fact that he averaged 40 values to
> get each point of the plot.

Yes, he did average the 40 values for that plot, that is
averaged the 20 turns /and/ then folded the result in two.
But no, he did not employ the last (half-turn) averaging in
his actual data analysis:

   In the definitive study of the ether-drift effect,
   this set of sixteen average readings for the position
   of the interference fringes is plotted to a large
   scale and is subjected to mechanical harmonic analysis
   to evaluate precisely the second harmonic component,
   which represents the second-order, half-period ether-
   drift effect;
   [...]
   The twenty or more readings for each of the sixteen
   observed azimuths are averaged and the averages are
   compensated for the slow linear shift of the whole
   interference system during the period of observation,
   as explained previously in connection with Fig. 9. The
   average readings for each set are then plotted on
   coordinate paper, to a large scale, for the purpose of
   harmonic analysis.
   [...]
   These charted "curves" of the actual observa-tions
   contain not only the second-order, half- period ether-
   drift effect, but also a first-order, full-period
   effect, any possible effects of higher orders,
   together with all instrumental and accidental errors
   of observation.
   [...]
   In order to evaluate precisely the ether-drift effect,
   each curve of observations has been analyzed with the
   Henrici harmonic analyzer for the first five terms of
   the Fourier series.

The quotations above provide compelling evidence that Miller
did not combine the half-turn observations in his analysis.
Your second comb-filter, which raises the lowest DFT bin up
to the half-turn frequency, is absent from Miller's procedure,
whereas your first comb-filter, which raises the lowest DFT
bin up to the fundamental full-turn frequency, is no doubt
present.

> But this still holds for his averaging of all 16
> orientations -- it is still a comb filter, and with a
> rapidly-falling noise spectrum it pushes most of the noise
> into the lowest DFT bin.

Yes, no good, but in that case the lowest DFT bin is the
fundamental, full-perdoid, full-turn frequency, not the
half-turn one.

> Averaging raw data is a VERY BAD analysis technique. But
> back in 1933 this was not understood; we understand it
> today.

Absolutely correct, even as any transoformation that reduces
the amount information in the data before that information
can be availed of.

-- 
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/\  www.asciiribbon.org   -- against proprietary attachments

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statistics in Roberts. Was: RAW vs. raw image format Rich Ulrich <rich.ulrich@comcast.net> - 2023-02-27 16:00 -0500
  Re: statistics in Roberts. Was: RAW vs. raw image format davidd02@tpg.com.au (David Duffy) - 2023-02-28 07:47 +0000
    Re: statistics in Roberts. Was: RAW vs. raw image format davidd02@tpg.com.au (David Duffy) - 2023-02-28 09:12 +0000
      Re: statistics in Roberts. Was: RAW vs. raw image format davidd02@tpg.com.au (David Duffy) - 2023-03-13 01:23 +0000
        Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-13 10:32 +0300
        Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-13 10:58 +0300
          Re: statistics in Roberts. Was: RAW vs. raw image format davidd02@tpg.com.au (David Duffy) - 2023-03-14 04:13 +0000
  Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-02-28 12:42 +0000
    Re: statistics in Roberts. Was: RAW vs. raw image format nospam@de-ster.demon.nl (J. J. Lodder) - 2023-02-28 14:22 +0100
      Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-02-28 14:01 +0000
        Re: statistics in Roberts. Was: RAW vs. raw image format nospam@de-ster.demon.nl (J. J. Lodder) - 2023-02-28 15:12 +0100
          Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-02-28 14:57 +0000
            Re: statistics in Roberts. Was: RAW vs. raw image format nospam@de-ster.demon.nl (J. J. Lodder) - 2023-02-28 21:36 +0100
    Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@gmail.moc> - 2023-03-04 00:46 +0300
      Re: statistics in Roberts. Was: RAW vs. raw image format nospam@de-ster.demon.nl (J. J. Lodder) - 2023-03-03 23:40 +0100
    Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-03-09 17:07 +0000
    Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@gmail.moc> - 2023-03-19 00:41 +0300
      Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-03-19 00:08 +0000
        Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@gmail.moc> - 2023-03-20 01:08 +0300
          Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-03-19 23:14 +0000
            Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-03-19 23:48 +0000
            Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-20 11:58 +0300
              Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawkxx@nowherel.com> - 2023-03-20 17:23 +0000
                Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@gmail.moc> - 2023-03-24 00:11 +0300
                Re: statistics in Roberts. Was: RAW vs. raw image format "David Jones" <dajhawk18xx@@nowhere.com> - 2023-03-23 23:59 +0000
      Re: statistics in Roberts. Was: RAW vs. raw image format Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-19 14:22 -0500
        Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-20 14:07 +0300
          Re: statistics in Roberts. Was: RAW vs. raw image format nospam@de-ster.demon.nl (J. J. Lodder) - 2023-03-20 14:35 +0100
            Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-20 17:01 +0300
          Re: statistics in Roberts. Was: RAW vs. raw image format Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-20 16:20 -0500
        Re: statistics in Roberts. Was: RAW vs. raw image format nospam@de-ster.demon.nl (J. J. Lodder) - 2023-03-20 14:35 +0100
          Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-20 17:33 +0300
  Re: statistics in Roberts. Was: RAW vs. raw image format Anton Shepelev <anton.txt@gmail.moc> - 2023-03-03 23:33 +0300
  Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-05 12:48 -0600
    Re: statistics in Roberts' paper on Miller nospam@de-ster.demon.nl (J. J. Lodder) - 2023-03-05 21:47 +0100
      Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-08 21:26 -0600
    Re: statistics in Roberts' paper on Miller Rich Ulrich <rich.ulrich@comcast.net> - 2023-03-06 23:08 -0500
      Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-08 21:40 -0600
    Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-08 15:33 +0300
      Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-08 23:11 -0600
        Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-10 01:04 +0300
          Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-11 12:54 -0600
            Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-12 14:25 +0300
              Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-17 13:27 -0500
                Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-19 00:32 +0300
                Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-19 14:45 -0500
            Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-20 16:06 -0500
              Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-21 13:00 +0300
    Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-08 19:11 +0300
      Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-09 11:48 +0300
        Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-09 11:57 +0300
    Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-08 21:09 -0600
    Re: statistics in Roberts' paper on Miller "David Jones" <dajhawkxx@nowherel.com> - 2023-03-09 17:13 +0000
      Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-09 23:26 +0300
        Re: statistics in Roberts' paper on Miller "David Jones" <dajhawkxx@nowherel.com> - 2023-03-10 01:37 +0000
          Re: statistics in Roberts' paper on Miller nospam@de-ster.demon.nl (J. J. Lodder) - 2023-03-10 11:25 +0100
          Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-11 00:13 +0300
          Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-10 15:42 -0600
            Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-11 01:32 +0300
              Re: statistics in Roberts' paper on Miller - Data Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-11 12:18 -0600
                Re: statistics in Roberts' paper on Miller - Data Anton Shepelev <anton.txt@gmail.moc> - 2023-03-12 00:13 +0300
                Re: statistics in Roberts' paper on Miller - Data Anton Shepelev <anton.txt@gmail.moc> - 2023-03-20 00:38 +0300
        Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-10 15:25 -0600
          Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-12 00:01 +0300
      Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-10 15:10 -0600
    Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-11 01:14 +0300
      Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-11 13:08 -0600
        Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@gmail.moc> - 2023-03-12 01:51 +0300
    Re: statistics in Roberts' paper on Miller "David Jones" <dajhawkxx@nowherel.com> - 2023-03-15 17:10 +0000
      Re: statistics in Roberts' paper on Miller nospam@de-ster.demon.nl (J. J. Lodder) - 2023-03-15 22:36 +0100
        Re: statistics in Roberts' paper on Miller "David Jones" <dajhawk18xx@@nowhere.com> - 2023-03-15 22:18 +0000
          Re: statistics in Roberts' paper on Miller nospam@de-ster.demon.nl (J. J. Lodder) - 2023-03-15 23:28 +0100
      Re: statistics in Roberts' paper on Miller Tom Roberts <tjoberts137@sbcglobal.net> - 2023-03-19 13:46 -0500
        Re: statistics in Roberts' paper on Miller "David Jones" <dajhawkxx@nowherel.com> - 2023-03-19 22:57 +0000
          Re: statistics in Roberts' paper on Miller Anton Shepelev <anton.txt@g{oogle}mail.com> - 2023-03-20 12:05 +0300

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