I have also found your good self to be a perfectionist, so I am more than a little surprised
to see you advocating "Guestimation" and "hocus pocus" rather than the simple application
of a little bit of rigour to eliminate an effect documented in studies which you have
referenced before on this forum.
There is a simple matter of making X number of loadings of X test specimens:
I want to increase the information got from that, and believe that including two
knots per does that. By your insistence on that pristine-for-statistics 1-per-1
work you have X broken knots & data; by the current test plan we have that
AND add X more load-enduring knots, which hold some form that can be
analyzed. Statistics, as you point out, can point out that the latter sample
of 2X knots got data from the weaker of each pairing; well, then, we can
be happy that our results are more *solid* in finding minimum values (as
one tends to have a bigger complaint for things weaker than expected).
I'll surmise--w/o knowledge--that there is some statistical analysis that
can accommodate the unknown strengths of the surviving knots; and
that especially in a population where differences (stnDev) are small,
ultimate values are not going to change much: and, again, one could
use the X-values-only and proceed with a confidence of conservatism.
As this method can be applied I think for all knots (bends--2 in line--,
hitches), they all can be compared.
And you would prefer to have half the number of knots tested?
(And, yes, yet, I have not urged FOUR knots per test.)
AND, again, we are not seeking to make huge inferences or promotions
with these values vis-a-vis other tested values, about which a great
deal is unknown (in some cases, e.g., I wonder at transposition of
the digits!). And my Perfectionism relaxes there in realization that
such fine-tuned scrutinizing just cannot have much sway in anything
that matters (for one, conditions of material and loading in practical
cases will vary greatly).
I do urge the jettison of wanting photographer-studio conditions and
losing all capture of images in its absence--much is lost to us, now.
very highest standard of professionalism.
I've never thought that this was an issue, so I don't understand your words
on this point.
Their structure may well have been different in some significant aspect,
such as to bestow the additional strength on them.
But this has nothing to do with examination of a survivor, but everything to do
with photographing knots
during testing!
You also state that "hocus pocus" can be utilised to take the biased 'pair results'
back to full population results - fine, how about pointing us then to how this should be
done or to someone who can do it as I would not be able to advise Agent Smith how to do it.
I'll see if some statistically adept person has a definite answer,
beyond my remarks above about at least simply noting that the
data comes from a selectively weaker set than the survivor set.
"Guestimation" and "hocus pocus"?
I would suggest not, particularly when the solution is so easy to achieve.
You're making more of the words than is intended--I'm happy enough to use
them for statistics in general, after all. The "solution" of losing results doesn't
appeal; I will hope that statistics shows some way(s) to deal.
The hypothetical data set I used in the example was simply to demonstrate
the existence and mechanism of the effect for you. We cannot know the significance
of this effect unless we have access to unbiased data ...
Oh, but you can. You have unbiased weakest-knot data--i.e., the range of values
of randomly selected pairings. You also have Richards's results in some similar
cordage (i.p., 7mm accessory nylon kernmantle).
here:
www.caves.org/section/vertical/nh/50/knotrope.htmlThe largest stnDev in the 7mm (and about largest throughout, ignoring those
knots that required back-up knots to arrest slippage) is 3.2%. The smallest
value is 93% of the largest; in your set, it was 75%. Absent the exagerated
difference, there really is little to fuss about, other than the *purity* of the statistics
for statistics sake. Again, I'm happy to put a footnote "* NB: these values are
probably slightly understated." (or simply "understated"). We're not hiding
anything, anyway.
and we cannot begin to postulate reasons for strength variations ...
Oh?! I distinctly recall someone's red-painting a "GeeSpot" and vowing to get
water from rock on that! --even lacking some obvious aspects of the issue.
unless we have access to images of the knots from several perspectives under near terminal load.
It might well turn out that for some knots the strength-determining geometry
is set well shy of near-terminal load; but it will take some scrutiny of knots
preferably with sharable photos in order to understand this.
--dl*
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