next message in archive
no next message in thread
previous message in archive
previous message in thread
Index of Subjects
8</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px
Hi Dave and other weight watchers,
You're trying to discover the supposed 'law' behind the scale's readout
conversion but you're doing this inadequately, by testing it with a
small-sized, imperfect set of weights. These are the actual distribution of
Dave's mass on a limited number of days -- values unknown initially.
This doesn't sound promising, so the first thing is have a look at what the
sampled weight distribution looks like, graphically, to see what you can make
out. This might be normally distributed ('bell curve') or skewed, or might be
bi-variate (two peaks), e.g. if Dave periodically overeats then fasts to lose
weight.
Most likely with only 91 samples (not that many), it is going to look noisy.
I plotted this and the result is actually quite striking and rather
simple. The
counts at all the even-numbered sample points (178, 180 etc) give a
reasonable,
normal-looking distribution of values centered on Dave = 180 lb, a bit skewed
towards the low end. By contrast, the counts at all the odd-numbered samples
(181, 183...) are relatively small and most are actually zero. So it's
counting in twos (almost).
How do these things work? I don't know for bathroom scales, but it's
likely that
they follow a modern instrumentation balance with a digital readout.
These work
by either by measuring the resistance of a strain gauge or by measuring the
output of an electromagnetic detector, both analog outputs. So an analog
voltage output is converted to a digital output according to a built-in
internal conversion algorithm (an equation operating inside a chip) that
corrects for the undoubted non-linearity of the measuring system. This then
drives the meter you look at. Digital meters indicate to the most significant
digit*, so Dave's thing ought to be able indicate 180, 181, 182, etc and
wouldn't count in twos. All analog devices are noisy and also drift. If the
manufacturer allowed the measuring device to put out the raw output,
Dave would
see his weight flicker disconcertingly between neighboring values even though
he's keeping still. What's presumably going on is that the scale is averaging
over a few seconds to stabilize the reading, then the algorithm is rounding it
to a specified intervals. I can imagine how it could round to the nearest two
pounds, but that wouldn't explain how Dave had seven values at 179 (odd
number).
Maybe someone else can think what sort of algorithm could count, centred on
twos, but slop over at the edges occasionally into ones*. What if it counts in
intervals of, say 2.2 lb? Anyone else know the answer?
Seems implausible that the algorithm would record the conversion in kg then
convert this to lbs in such a clumsy way, such that rounding errors in
the last
conversion crept in.
Steve
*come to think, specifications are usually rated to the nearest significant
digit +1, so maybe that's something to do with what they are up to.
Quoting David & Alison Webster <dwebster@glinx.com>:
> Dear All, Dec 3, 2006
> There is, as usual, a lull in NatureNS traffic as we near winter
> and this lull provides an opportunity to comment on something that I
> found interesting; a digital readout with 'missing numbers'.
> I have weighed myself on digital bathroom scales, that have
> readout to the nearest pound, for about 255 sundays and readout spans
> 192 to 168 lb. It soon became clear that some weights were favoured
> relative to others. For example for the 91 weights on one page (May
> 4, 2003 to Jan 23, 2004), the readings cover a range of 172 to 185
> but some intermediate weights were not represented.
>
> The number of readings at each weight within this range were:
> 172; 7
> 173; 0
> 174; 6
> 175; 3
> 176; 9
> 177; 0
> 178; 15
> 179; 7
> 180; 20
> 181; 0
> 182; 15
> 183; 0
> 184; 8
> 185; 1
> indicating that some weights, such as 177, 181, and 183 are likely
> to be filtered out by some distortion in the instrument and appear as
> some different reading.
>
> Much of the world uses metric so I looked at the implications of
> a kilograms to pounds retrofit that was tacked onto scales that had
> been designed to read to the nearest kilogram. For one artificial
> case, with input being a series of weights difffering by 0.05 kg
> (76.50, 76.55...); assuming output rounded to nearest kilogram, then
> converted to lb by dividing by 0.45 and then rounded to the nearest
> pound, the frequency of weights is either zero or 20 within the
> range 171 to 187--
>
> Weights with a frequency of 20 were 171, 173, 176, 178, 180, 182, 184
> & 187 while
> weights with a frequency of zero were 172, 174, 175, 177, 179, 181,
> 183, 185 & 186.
>
> The gaps in the artificial readouts don't exactly match gaps in
> the actual readout (177, 181 and 183 do but not 179) but both
> examples show that a rock-solid digital readout to zero or more
> decimal places may not be as reliable as it appears.
>
> Yours truly, Dave Webster, Kentville
>
>
>
>
>
>
>
--
Stephen R. Shaw Ph.D.
Dept of Psychology & Neuroscience
Dalhousie University
1355 Oxford Street
Halifax, Nova Scotia, Canada B3H 4J1
e-mail: srshaw@dal.ca
phone: 1-902-494-2886
fax: 1-902-494-6585
next message in archive
no next message in thread
previous message in archive
previous message in thread
Index of Subjects