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PRECISELY_ACCURATE
August 7, 2023
The canonical example is target shooting.
In the ideal case all your shots will group
together at the center, but in reality
they'll often be scattered widely, and the
center of the scatter might not even be at
the center of the target.
We often analyze these results by looking
at how well the average gets near the
bullseye, but also by looking at the size
of the grouping, e.g. by calculating the
"standard deviation".
In the usual jargon, we say that the shots
are "accurate" if the average is near the
center, but we say the shots are "precise"
if the grouping is tight.
This can be a useful way of analyzing the result:
You might, for example, find that all your shots
are actually grouped tightly together, but not
centered on the target-- which is to say you have
high precision and yet low accuracy.
That might indicate there's nothing wrong with
your aim, but there could be an issue with the
gun sight that needs to be fixed.
This distinction between "precision" and "accuracy"
is very conventional in this kind of statistical
analysis, and yet it's remarkably awkward-- it
doesn't map well to colloquial understanding of the
words, which seem like synonyms to anyone without
a technical background.
Myself, I've been familiar with it for many
years, but even so I need to stop and think
sometimes to make sure I haven't gotten the
terms backwards.
And further, I think that the distinction
between precision and accuracy is itself
an artificial imposition on the data:
this is a common statistical device for
analyzing results which *might* reveal
something about underlying phenomena, but
there's no reason it has to.
Treating accuracy and precision like
two knobs that can always be spun
independently of each other is often
going to be a mistake.
SCATTER_THE_NOISE
The reason I've indulged in
the above rather conventional
exposition is that something
similar is done in:
"Noise" (2021) by
Kahneman, Sibony and Sunstein See the introduction,
"Two Kinds of Error"
SCATTER_THE_NOISE
But I think the conventional exposition is
clearer, because it works with the individual
shooter case. Sunstein et al have got their
eye on cases like the predictions and
judgments made by multiple experts in an
organization, and so the authors keep trying
to talk about shooting teams, but that fuzzes
things up too much, e.g. it makes it harder to
bring in the issue of individual aim vs the The entire point of
quality of the gun sights. the distinction is
that it can point
you at an underlying
cause.
And rather than lean on the admittedly awkward
terms "precision" and "accuracy", the
authors introduce their own favored terms
"noise" and "bias".
Neither are without problems.
To my ear, the word The word "bias" has
"noise" suggests issues severe negative
with interference in connotations, technically
communications-- not it may just mean
scatter in judgment and systematic error, but
prediction. colloquially it suggests
things like racial bias.
Further "noise" also
strongly suggests
"randomness" which could "Noise" suggests something
be begging an important unintended, and "Bias"
question. suggests hidden agendas,
though neither, I think,
is something the authors
would want you to assume
at outset.
It's a continual irritation to me that
the word "noise" is abused in every
other sentence of this book-- if you want
to talk about noise, this one is in the This rhetorical
fingernails-on-blackboard class. "fingernails" still
feels like a useful
I think they were working too figure of speech to
hard at trying to sound edgey. me, though really
half of the people
NOISE alive now have never
even seen a
NOISE_ABOUNDS blackboard, let
alone heard one.
(But then, I'm capable of
intentional noise, myself.)
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